Conceptual model

This protocol is extracted from research article:

Phase coherence between precipitation in South America and Rossby waves

**
Sci Adv**,
Dec 19, 2018;
DOI:
10.1126/sciadv.aau3191

Phase coherence between precipitation in South America and Rossby waves

Procedure

A key hypothesis we intend to test in this study is that the variability mode corresponding to the South American precipitation dipole could be explained by northward propagating waves triggered by the southern hemisphere Rossby wave train. For this purpose, we first introduced the following conceptual model: Denoting the dimensionless GPH along an arbitrary direction *x* as *h* and the precipitation along the direction as *p*, we chose to model *h* with a wave equation*p* as its spatial derivative*p*(*x*, *t*). By embedding this traveling wave in the same grid as the data and adding Gaussian damping along and perpendicular to the propagation direction, we generated the model data *P*_{M}(λ, ϕ, *t*). Its parameters are the mean values of the Gaussian damping λ_{0}, ϕ_{0}, their SDs σ_{λ}, σ_{ϕ}, the wavelength *L*, and the direction θ of the wave (see the Supplementary Materials for the full equations). The model data *P*_{M}(λ, ϕ, *t*) could be used to calculate the first two EOFs of the conceptual model. These EOFs were then fitted, by optimizing the model parameters via least squares, to the EOFs of the precipitation data (see Fig. 2). While the parameters referring to the Gaussian damping and the direction θ roughly account for the location and orography, the wavelength or wave number is an important parameter of the modeled wave.

The CEOF analysis extends the standard EOF analysis by applying the PCA to the complexified time series, i.e., the analytical signal [e.g., (*21*)]. The analytical signal *20*). We followed here the notation of Barnett (*20*): The eigenvectors *B*_{n}(**x**) of the covariance matrix of the spatiotemporal complexified data

1) Spatial phase function

2) Spatial amplitude function

3) Temporal phase function

More details on CEOF analysis are given in (*20*).

Note: The content above has been extracted from a research article, so it may not display correctly.

Q&A

Your question will be posted on the Bio-101 website. We will send your questions to the authors of this protocol and Bio-protocol community members who are experienced with this method. you will be informed using the email address associated with your Bio-protocol account.