Basis Functions

basis.eqvlat_fawa(ylat, vort, area, n_points, planet_radius=6378000.0, output_fawa=True) → Tuple[numpy.ndarray, Optional[numpy.ndarray]][source]

Compute equivalent latitude and finite amplitude wave activity with the full

Parameters

  • ylat (sequence or array_like) – 1-d numpy array of latitude (in degree) with equal spacing in ascending order; dimension = nlat.

  • vort (ndarray) – 2-d numpy array of vorticity values; dimension = (nlat, nlon).

  • area (ndarray) – 2-d numpy array specifying differential areal element of each grid point; dimension = (nlat, nlon).

  • n_points (int) – Analysis resolution to calculate equivalent latitude.

  • planet_radius (float) – Radius of spherical planet of interest consistent with input area. Default: earth’s radius 6.378e+6

  • output_fawa (bool) – Whether to output FAWA. If True, return tuple would consist of (qref, fawa). Else, this function will return (qref, None).

Returns

  • qref (ndarray) – 1-d numpy array of value Q(y) where latitude y is given by ylat; dimension = (nlat).

  • fawa (ndarray or None) – 1-d finite-amplitude local wave activity

basis.eqvlat_vgrad(ylat, vort, area, n_points, planet_radius=6378000.0, vgrad=None)[source]

Compute equivalent latitude, and optionally <…>_Q in Nakamura and Zhu (2010).

Parameters

  • ylat (sequence or array_like) – 1-d numpy array of latitude (in degree) with equal spacing in ascending order; dimension = nlat.

  • vort (ndarray) – 2-d numpy array of vorticity values; dimension = (nlat, nlon).

  • area (ndarray) – 2-d numpy array specifying differential areal element of each grid point; dimension = (nlat, nlon).

  • n_points (int) – Analysis resolution to calculate equivalent latitude.

  • planet_radius (float) – Radius of spherical planet of interest consistent with input area. Default: earth’s radius 6.378e+6

  • vgrad (ndarray, optional) – 2-d numpy array of laplacian (or higher-order laplacian) values; dimension = (nlat, nlon)

Returns

  • q_part (ndarray) – 1-d numpy array of value Q(y) where latitude y is given by ylat; dimension = (nlat).

  • brac (ndarray or None) – 1-d numpy array of averaged vgrad in the square bracket. If vgrad = None, brac = None.

basis.lwa(nlon, nlat, vort, q_part, dmu, ncforce=None)[source]

At each grid point of vorticity q(x,y) and reference state vorticity Q(y), this function calculate the difference between the line integral of [q(x,y+y’)-Q(y)] (and ncforce, if given) over the domain {y+y’>y,q(x,y+y’)<Q(y)} and {y+y’<y,q(x,y+y’)>Q(y)}. See fig. (1) and equation (13) of Huang and Nakamura (2016). dmu is a vector of length nlat: dmu = cos(phi) d(phi) such that phi is the latitude.

Parameters

  • nlon (int) – Longitudinal dimension of vort (i.e. vort.shape[1]).

  • nlat (int) – Latitudinal dimension of vort (i.e. vort.shape[0]).

  • vort (ndarray) – 2-d numpy array of vorticity values; dimension = (nlat,nlon).

  • Q_part (sequence or array_like) – 1-d numpy array of Q (vorticity reference state) as a function of latitude. Size = nlat.

  • dmu (sequence or array_like) – 1-d numpy array of latitudinal differential length element (e.g. dmu = planet_radius * cos(lat) d(lat)). Size = nlat.

  • ncforce (ndarray or None, optional) – 2-d numpy array of non-conservative force field (i.e. theta in NZ10(a) in equation (23a) and (23b))

Returns

  • lwact (ndarray) – 2-d numpy array of local wave activity calculated; dimension = (nlat,nlon).

  • bigsigma (ndarray or None) – 2-d numpy array of the nonconservative forces acting on local wave activity computed from ncforce. If ncforce = None, bigsigma = None.