Source code for ocbpy.ocb_scaling

#!/usr/bin/env python# -*- coding: utf-8 -*-
# Copyright (C) 2017, AGB & GC
# Full license can be found in License.md
# ----------------------------------------------------------------------------
"""Scale data affected by magnetic field direction or electric field

Routines
--------
normal_evar(evar, unscaled_r, scaled_r)
    Normalise a variable proportaional to the electric field (such as velocity)
normal_curl_evar(curl_evar, unscaled_r, scaled_r)
    Normalise a variable proportional to the curl of the electric field (such
    as vorticity)

Classes
-------
VectorData(object)
    Holds vector data in AACGM N-E-Z coordinates along with location
    information.  Converts vector from AACGM to OCB coordinates.

Moduleauthor
------------
Angeline G. Burrell (AGB), 12 May 2017, University of Texas, Dallas

References
----------
Chisham, G. (2017), A new methodology for the development of high-latitude
ionospheric climatologies and empirical models, Journal of Geophysical
Research: Space Physics, 122, doi:10.1002/2016JA023235.

"""

from __future__ import absolute_import, unicode_literals
import numpy as np

import ocbpy


[docs]class VectorData(object): """ Object containing a vector data point Parameters ---------- dat_ind : (int or array-like) Data index (zero offset) ocb_ind : (int or array-like) OCBoundary record index matched to this data index (zero offset) aacgm_lat : (float or array-like) Vector AACGM latitude (degrees) aacgm_mlt : (float or array-like) Vector AACGM MLT (hours) ocb_lat : (float or array-like) Vector OCB latitude (degrees) (default=np.nan) ocb_mlt : (float or array-like) Vector OCB MLT (hours) (default=np.nan) aacgm_n : (float or array-like) AACGM North pointing vector (positive towards North) (default=0.0) aacgm_e : (float or array-like) AACGM East pointing vector (completes right-handed coordinate system (default = 0.0) aacgm_z : (float or array-like) AACGM Vertical pointing vector (positive down) (default=0.0) aacgm_mag : (float or array-like) Vector magnitude (default=np.nan) scale_func : (function) Function for scaling AACGM magnitude with arguements: [measurement value, mesurement AACGM latitude (degrees), mesurement OCB latitude (degrees)] (default=None) dat_name : (str) Data name (default=None) dat_units : (str) Data units (default=None) Attributes ---------- dat_name : (str or NoneType) Name of data dat_units : (str or NoneType) Units of data dat_ind : (int or array-like) Vector data index in external data array ocb_ind : (int or array-like) OCBoundary rec_ind value(s) that matches dat_ind or a single rec_ind value for all dat_ind unscaled_r : (float or array-like) Radius of polar cap in degrees scaled_r : (float or array-like) Radius of normalised OCB polar cap in degrees aacgm_n : (float or array-like) AACGM north component of data vector (default=0.0) aacgm_e : (float or array-like) AACGM east component of data vector (default=0.0) aacgm_z : (float or array-like) AACGM vertical component of data vector (default=0.0) aacgm_mag : (float or array-like) Magnitude of data vector in AACGM coordinates (default=np.nan) aacgm_lat : (float or array-like) AACGM latitude of data vector in degrees aacgm_mlt : (float or array-like) AACGM MLT of data vector in hours ocb_n : (float or array-like) OCB north component of data vector (default=np.nan) ocb_e : (float or array-like) OCB east component of data vector (default=np.nan) ocb_z : (float or array-like) OCB vertical component of data vector (default=np.nan) ocb_mag : (float or array-like) OCB magnitude of data vector (default=np.nan) ocb_lat : (float or array-like) OCB latitude of data vector in degrees (default=np.nan) ocb_mlt : (float or array-like) OCB MLT of data vector in hours (default=np.nan) ocb_quad : (int or array-like) AACGM quadrant of OCB pole (default=0) vec_quad : (int or array-like) AACGM quadrant of Vector (default=0) pole_angle : (float or array-like) Angle at vector location appended by AACGM and OCB poles in degrees (default=np.nan) aacgm_naz : (float or array-like) AACGM north azimuth of data vector in degrees (default=np.nan) ocb_aacgm_lat : (float or array-like) AACGM latitude of OCB pole in degrees (default=np.nan) ocb_aacgm_mlt : (float or array-like) AACGM MLT of OCB pole in hours (default=np.nan) scale_func : (function or NoneType) Funciton that scales the magnitude of the data vector from AACGM polar cap coverage to OCB polar cap coverage Methods ------- set_ocb(ocb, scale_func=None) Set the ocb coordinates and vector values Notes ----- May only handle one data type, so scale_func cannot be an array """ def __init__(self, dat_ind, ocb_ind, aacgm_lat, aacgm_mlt, ocb_lat=np.nan, ocb_mlt=np.nan, r_corr=np.nan, aacgm_n=0.0, aacgm_e=0.0, aacgm_z=0.0, aacgm_mag=np.nan, dat_name=None, dat_units=None, scale_func=None): """ Initialize VectorData object Parameters ---------- dat_ind : (int or array-like) Data index (zero offset) ocb_ind : (int or array-like) OCBoundary record index matched to this data index (zero offset) aacgm_lat : (float or array-like) Vector AACGM latitude (degrees) aacgm_mlt : (float or array-like) Vector AACGM MLT (hours) ocb_lat : (float or array-like) Vector OCB latitude (degrees) (default=np.nan) ocb_mlt : (float or array-like) Vector OCB MLT (hours) (default=np.nan) aacgm_n : (float or array-like) AACGM North pointing vector (positive towards North) (default=0.0) aacgm_e : (float or array-like) AACGM East pointing vector (completes right-handed coordinate system (default=0.0) aacgm_z : (float or array-like) AACGM Vertical pointing vector (positive down) (default=0.0) aacgm_mag : (float or array-like) Vector magnitude (default = np.nan) dat_name : (str) Data name (default=None) dat_units : (str) Data units (default=None) scale_func : (function) Function for scaling AACGM magnitude with arguements: [measurement value, mesurement AACGM latitude (degrees), mesurement OCB latitude (degrees)] Not necessary if no magnitude scaling is needed. (default=None) Raises ------ ValueError If the vector magnitude and AACGM components are inconsistent """ # Assign the vector data name and units self.dat_name = dat_name self.dat_units = dat_units # Assign the data and OCB indices self.dat_ind = np.asarray(dat_ind) self.ocb_ind = np.asarray(ocb_ind) # Assign the AACGM vector values and location self.aacgm_n = np.asarray(aacgm_n) self.aacgm_e = np.asarray(aacgm_e) self.aacgm_z = np.asarray(aacgm_z) self.aacgm_lat = np.asarray(aacgm_lat) self.aacgm_mlt = np.asarray(aacgm_mlt) # Test the initalization shape vshapes = [self.aacgm_lat.shape, self.aacgm_mlt.shape, self.dat_ind.shape, self.aacgm_n.shape, self.aacgm_e.shape, self.aacgm_z.shape] vshapes = np.unique(np.asarray(vshapes, dtype=object)) vshape = () if len(vshapes) == 0 else vshapes.max() if len(vshapes) > 2 or (len(vshapes) == 2 and min(vshapes) != ()): raise ValueError('mismatched VectorData input shapes') if len(vshapes) > 1 and min(vshapes) == (): if self.dat_ind.shape == (): raise ValueError('data index shape must match vector shape') # Vector input needs to be the same length if self.aacgm_n.shape == (): self.aacgm_n = np.full(shape=vshape, fill_value=self.aacgm_n) if self.aacgm_e.shape == (): self.aacgm_e = np.full(shape=vshape, fill_value=self.aacgm_e) if self.aacgm_z.shape == (): self.aacgm_z = np.full(shape=vshape, fill_value=self.aacgm_z) # Assign the vector magnitudes if np.all(np.isnan(aacgm_mag)): self.aacgm_mag = np.sqrt(np.asarray(aacgm_n)**2 + np.asarray(aacgm_e)**2 + np.asarray(aacgm_z)**2) else: aacgm_sqrt = np.sqrt(np.asarray(aacgm_n)**2 + np.asarray(aacgm_e)**2 + np.asarray(aacgm_z)**2) if np.any(np.greater(abs(aacgm_mag - aacgm_sqrt), 1.0e-3, where=~np.isnan(aacgm_mag))): ocbpy.logger.warning("".join(["inconsistent AACGM components ", "with a maximum difference of ", "{:} > 1.0e-3".format( abs(aacgm_mag - aacgm_sqrt).max())])) self.aacgm_mag = aacgm_mag # Assign the OCB vector default values self.ocb_lat = np.asarray(ocb_lat) self.ocb_mlt = np.asarray(ocb_mlt) self.r_corr = np.asarray(r_corr) if self.ocb_lat.shape == () and self.ocb_ind.shape != (): self.ocb_lat = np.full(shape=self.ocb_ind.shape, fill_value=ocb_lat) if self.ocb_mlt.shape == () and self.ocb_ind.shape != (): self.ocb_mlt = np.full(shape=self.ocb_ind.shape, fill_value=ocb_mlt) if self.r_corr.shape == () and self.ocb_ind.shape != (): self.r_corr = np.full(shape=self.ocb_ind.shape, fill_value=r_corr) # Test the OCB input shape oshapes = np.unique([self.ocb_lat.shape, self.ocb_mlt.shape, self.r_corr.shape]) oshape = () if len(oshapes) == 0 else oshapes.max() if(oshape != self.ocb_ind.shape or len(oshapes) > 2 or (len(oshapes) == 2 and min(oshapes) != ())): raise ValueError('OCB index and input shapes mismatched') if self.ocb_ind.shape == (): oshape = vshape elif self.dat_ind.shape == (): vshape = oshape if oshape != vshape: raise ValueError('Mismatched OCB and Vector input shapes') # Assign the OCB vector default values and location self.ocb_n = np.full(shape=vshape, fill_value=np.nan) self.ocb_e = np.full(shape=vshape, fill_value=np.nan) self.ocb_z = np.full(shape=vshape, fill_value=np.nan) self.ocb_mag = np.full(shape=vshape, fill_value=np.nan) # Assign the default pole locations, relative angles, and quadrants self.ocb_quad = np.zeros(shape=vshape) self.vec_quad = np.zeros(shape=vshape) self.pole_angle = np.full(shape=vshape, fill_value=np.nan) self.aacgm_naz = np.full(shape=vshape, fill_value=np.nan) self.ocb_aacgm_lat = np.full(shape=vshape, fill_value=np.nan) self.ocb_aacgm_mlt = np.full(shape=vshape, fill_value=np.nan) # Assign the vector scaling function self.scale_func = scale_func return def __repr__(self): """ Provide readable representation of the DataVector object """ out = "Vector data:" if self.dat_name is not None: out += " {:s}".format(self.dat_name) if self.dat_units is not None: out += " ({:s})".format(self.dat_units) out += "\nData Index {:}\tOCB Index {:}\n".format(self.dat_ind, self.ocb_ind) out += "-------------------------------------------\n" # Print AACGM vector location(s) if self.dat_ind.shape == () and self.ocb_ind.shape == (): out += "Locations: [Mag. Lat. (degrees), MLT (hours)]\n" out += " AACGM: [{:.3f}, {:.3f}]\n".format(self.aacgm_lat, self.aacgm_mlt) out += " OCB: [{:.3f}, {:.3f}]\n".format(self.ocb_lat, self.ocb_mlt) else: out += "Locations: [Mag. Lat. (degrees), MLT (hours), Index]\n" if self.dat_ind.shape == self.ocb_ind.shape: for i, dind in enumerate(self.dat_ind): out += " AACGM: [{:.3f}, {:.3f}, {:d}]\n".format( self.aacgm_lat[i], self.aacgm_mlt[i], dind) out += " OCB: [{:.3f}, {:.3f}, {:d}]\n".format( self.ocb_lat[i], self.ocb_mlt[i], self.ocb_ind[i]) elif self.ocb_ind.shape == (): for i, dind in enumerate(self.dat_ind): out += " AACGM: [{:.3f}, {:.3f}, {:d}]\n".format( self.aacgm_lat[i], self.aacgm_mlt[i], dind) if self.ocb_lat.shape == () and np.isnan(self.ocb_lat): out += " OCB: [nan, nan, {:d}]\n".format( self.ocb_ind) else: out += " OCB: [{:.3f}, {:.3f}, {:d}]\n".format( self.ocb_lat[i], self.ocb_mlt[i], self.ocb_ind) else: out += " AACGM: [{:.3f}, {:.3f}, {:d}]\n".format( self.aacgm_lat, self.aacgm_mlt, self.dat_ind) for i, oind in enumerate(self.ocb_ind): out += " OCB: [{:.3f}, {:.3f}, {:d}]\n".format( self.ocb_lat[i], self.ocb_mlt[i], oind) out += "\n-------------------------------------------\n" if self.aacgm_mag.shape == () and self.ocb_mag.shape == (): out += "Value: Magnitude [N, E, Z]\n" out += "AACGM: {:.3g} [{:.3g}".format(self.aacgm_mag, self.aacgm_n) out += ", {:.3g}, {:.3g}]\n".format(self.aacgm_e, self.aacgm_z) if not np.isnan(self.ocb_mag): out += " OCB: {:.3g} [{:.3g}".format(self.ocb_mag, self.ocb_n) out += ", {:.3g}, {:.3g}]\n".format(self.ocb_e, self.ocb_z) else: out += "Value: Magnitude [N, E, Z] Index\n" for i, mag in enumerate(self.ocb_mag): if self.aacgm_mag.shape == () and i == 0: out += "AACGM: {:.3g} [".format(self.aacgm_mag) out += "{:.3g}, {:.3g}, {:.3g}] {:d}\n".format( self.aacgm_n, self.aacgm_e, self.aacgm_z, self.dat_ind) elif self.aacgm_mag.shape != (): out += "AACGM: {:.3g} [".format(self.aacgm_mag[i]) out += "{:.3g}, {:.3g}, {:.3g}] ".format( self.aacgm_n[i], self.aacgm_e[i], self.aacgm_z[i]) out += "{:d}\n".format(self.dat_ind[i]) if not np.isnan(mag): out += " OCB: {:.3g} [{:.3g}, ".format(mag, self.ocb_n[i]) out += "{:.3g}, ".format(self.ocb_e[i]) out += "{:.3g}] {:d}\n".format( self.ocb_z[i], self.ocb_ind if self.ocb_ind.shape == () else self.ocb_ind[i]) out += "\n-------------------------------------------\n" if self.scale_func is None: out += "No magnitude scaling function provided\n" else: out += "Scaling function: {:s}\n".format(self.scale_func.__name__) return out def __str__(self): """ Provide readable representation of the DataVector object """ out = self.__repr__() return out
[docs] def set_ocb(self, ocb, scale_func=None): """ Set the OCBoundary values for this data point Parameters ---------- ocb : (OCBoundary) Open Closed Boundary class object scale_func : (function) Function for scaling AACGM magnitude with arguements: [measurement value, mesurement AACGM latitude (degrees), mesurement OCB latitude (degrees)] Not necessary if defined earlier or no scaling is needed. (default=None) Updates ------- self.unscaled_r : (float or array-like) Radius of polar cap in degrees self.scaled_r : (float) Radius of normalised OCB polar cap in degrees self.ocb_n : (float or array-like) Vector OCB North component self.ocb_e : (float or array-like) Vector OCB East component self.ocb_z : (float or array-like) Vector OCB vertical component (positive downward) self.ocb_mag : (float or array-like) Vector OCB magnitude self.ocb_lat : (float or array-like) Vector OCB latitude, if not updated already (degrees) self.ocb_mlt : (float or array-like) Vector OCB MLT, if not updated already (hours) self.r_corr : (float or array-like) OCB radius correction for vector location (degrees) self.ocb_quad : (int or array-like) OCB pole AACGM quadrant self.vec_quad : (int or array-like) Vector AACGM quadrant self.pole_angle : (float or array-like) Angle at the vector in the triangle formed by the poles and vector (degrees) self.aacgm_naz : (float or array-like) AACGM north azimuth angle (degrees) self.ocb_aacgm_lat : (float or array-like) AACGM latitude of the OCB pole (degrees) self.ocb_aacgm_mlt : (float or array-like) AACGM MLT of the OCB pole (hours) self.scale_func : (function) Function for scaling AACGM magnitude with arguements: [measurement value, unscaled polar cap radius (degrees), scaled polar cap radius (degrees)] Not necessary if defined earlier or if no scaling is needed. """ # Initialize the OCB index ocb.rec_ind = self.ocb_ind # If the OCB vector coordinates weren't included in the initial info, # update them here if(np.all(np.isnan(self.ocb_lat)) or np.all(np.isnan(self.ocb_mlt)) or np.all(np.isnan(self.r_corr))): # Because the OCB and AACGM magnetic field are both time dependent, # can't call this function with multiple OCBs if self.ocb_ind.shape == (): (self.ocb_lat, self.ocb_mlt, self.r_corr) = ocb.normal_coord(self.aacgm_lat, self.aacgm_mlt) else: for i, ocb.rec_ind in enumerate(self.ocb_ind): if self.ocb_ind.shape == self.dat_ind.shape: (self.ocb_lat[i], self.ocb_mlt[i], self.r_corr[i]) = ocb.normal_coord(self.aacgm_lat[i], self.aacgm_mlt[i]) else: (self.ocb_lat[i], self.ocb_mlt[i], self.r_corr[i]) = ocb.normal_coord(self.aacgm_lat, self.aacgm_mlt) # Exit if the OCB coordinates can't be calculated at this location if(np.all(np.isnan(self.ocb_lat)) or np.all(np.isnan(self.ocb_mlt)) or np.all(np.isnan(self.r_corr))): return # Set the AACGM coordinates of the OCB pole self.unscaled_r = ocb.r[self.ocb_ind] + self.r_corr self.scaled_r = 90.0 - abs(ocb.boundary_lat) self.ocb_aacgm_mlt = ocbpy.ocb_time.deg2hr(ocb.phi_cent[self.ocb_ind]) self.ocb_aacgm_lat = 90.0 - ocb.r_cent[self.ocb_ind] # Get the angle at the data vector appended by the AACGM and OCB poles self.calc_vec_pole_angle() # Set the OCB and Vector quadrants if np.any(~np.isnan(self.pole_angle)): self.define_quadrants() # Set the scaling function if self.scale_func is None: if scale_func is None: # This is not necessarily a bad thing, if the value does # not need to be scaled. ocbpy.logger.info("no scaling function provided") else: self.scale_func = scale_func # Assign the OCB vector default values and location. Will also # update the AACGM north azimuth of the vector. self.scale_vector() return
[docs] def define_quadrants(self): """ Find the MLT quadrants (in AACGM coordinates) for the OCB pole and data vector Requires -------- self.ocb_aacgm_mlt : (float or array-like) OCB pole MLT in AACGM coordinates in hours self.aacgm_mlt : (float or array-like) Vector AACGM MLT in hours self.pole_angle : (float or array-like) vector angle in poles-vector triangle in degrees Updates ------- self.ocb_quad : (int or array-like) OCB pole quadrant self.vec_quad : (int or array-like) Vector quadrant Notes ----- North (N) and East (E) are defined by the AACGM directions centred on the data vector location, assuming vertical is positive downwards Quadrants: 1 [N, E]; 2 [N, W]; 3 [S, W]; 4 [S, E] Raises ------ ValueError If the required input is undefined """ # Cast the input as arrays self.ocb_aacgm_mlt = np.asarray(self.ocb_aacgm_mlt) self.aacgm_mlt = np.asarray(self.aacgm_mlt) self.pole_angle = np.asarray(self.pole_angle) # Test input if np.all(np.isnan(self.ocb_aacgm_mlt)): raise ValueError("OCB pole location required") if np.all(np.isnan(self.aacgm_mlt)): raise ValueError("Vector AACGM location required") if np.all(np.isnan(self.pole_angle)): raise ValueError("vector angle in poles-vector triangle required") # Determine where the OCB pole is relative to the data vector ocb_adj_mlt = self.ocb_aacgm_mlt - self.aacgm_mlt neg_mask = (np.less(ocb_adj_mlt, 0.0, where=~np.isnan(ocb_adj_mlt)) & ~np.isnan(ocb_adj_mlt)) while np.any(neg_mask): if ocb_adj_mlt.shape == (): ocb_adj_mlt += 24.0 neg_mask = [False] else: ocb_adj_mlt[neg_mask] += 24.0 neg_mask = (np.less(ocb_adj_mlt, 0.0, where=~np.isnan(ocb_adj_mlt)) & ~np.isnan(ocb_adj_mlt)) large_mask = (np.greater_equal(abs(ocb_adj_mlt), 24.0, where=~np.isnan(ocb_adj_mlt)) & ~np.isnan(ocb_adj_mlt)) if np.any(large_mask): if ocb_adj_mlt.shape == (): ocb_adj_mlt -= 24.0 * np.sign(ocb_adj_mlt) else: ocb_adj_mlt[large_mask] -= 24.0 * np.sign( ocb_adj_mlt[large_mask]) # Find the quadrant in which the OCB pole lies nan_mask = (~np.isnan(self.pole_angle) & ~np.isnan(ocb_adj_mlt)) quad1_mask = (np.less(self.pole_angle, 90.0, where=nan_mask) & np.less(ocb_adj_mlt, 12.0, where=nan_mask) & nan_mask) quad2_mask = (np.less(self.pole_angle, 90.0, where=nan_mask) & np.greater_equal(ocb_adj_mlt, 12.0, where=nan_mask) & nan_mask) quad3_mask = (np.greater_equal(self.pole_angle, 90.0, where=nan_mask) & np.greater_equal(ocb_adj_mlt, 12.0, where=nan_mask) & nan_mask) quad4_mask = (np.greater_equal(self.pole_angle, 90.0, where=nan_mask) & np.less(ocb_adj_mlt, 12.0, where=nan_mask) & nan_mask) if self.ocb_quad.shape == (): if np.all(quad1_mask): self.ocb_quad = np.asarray(1) elif np.all(quad2_mask): self.ocb_quad = np.asarray(2) elif np.all(quad3_mask): self.ocb_quad = np.asarray(3) elif np.all(quad4_mask): self.ocb_quad = np.asarray(4) else: self.ocb_quad[quad1_mask] = 1 self.ocb_quad[quad2_mask] = 2 self.ocb_quad[quad3_mask] = 3 self.ocb_quad[quad4_mask] = 4 # Now determine which quadrant the vector is pointed into nan_mask = (~np.isnan(self.aacgm_n) & ~np.isnan(self.aacgm_e)) quad1_mask = (np.greater_equal(self.aacgm_n, 0.0, where=nan_mask) & np.greater_equal(self.aacgm_e, 0.0, where=nan_mask) & nan_mask) quad2_mask = (np.greater_equal(self.aacgm_n, 0.0, where=nan_mask) & np.less(self.aacgm_e, 0.0, where=nan_mask) & nan_mask) quad3_mask = (np.less(self.aacgm_n, 0.0, where=nan_mask) & np.less(self.aacgm_e, 0.0, where=nan_mask) & nan_mask) quad4_mask = (np.less(self.aacgm_n, 0.0, where=nan_mask) & np.greater_equal(self.aacgm_e, 0.0, where=nan_mask) & nan_mask) if self.vec_quad.shape == (): if np.all(quad1_mask): self.vec_quad = np.asarray(1) elif np.all(quad2_mask): self.vec_quad = np.asarray(2) elif np.all(quad3_mask): self.vec_quad = np.asarray(3) elif np.all(quad4_mask): self.vec_quad = np.asarray(4) else: self.vec_quad[quad1_mask] = 1 self.vec_quad[quad2_mask] = 2 self.vec_quad[quad3_mask] = 3 self.vec_quad[quad4_mask] = 4 return
[docs] def scale_vector(self): """ Normalise a variable proportional to the curl of the electric field. Requires -------- self.ocb_lat : (float or array-like) OCB latitude in degrees self.ocb_mlt : (float or array-like) OCB MLT in hours self.ocb_aacgm_mlt : (float or array-like) OCB pole MLT in AACGM coordinates in hours self.pole_angle : (float or array-like) vector angle in poles-vector triangle Updates ------- ocb_n : (float or array-like) OCB scaled north component ocb_e : (float or array-like) OCB scaled east component ocb_z : (float or array-like) OCB scaled vertical component ocb_mag : (float or array-like) OCB scaled magnitude Raises ------ ValueError If the required input is not defined """ # Ensure the input is array-like self.ocb_lat = np.asarray(self.ocb_lat) self.ocb_mlt = np.asarray(self.ocb_mlt) self.ocb_aacgm_mlt = np.asarray(self.ocb_aacgm_mlt) self.pole_angle = np.asarray(self.pole_angle) self.aacgm_n = np.asarray(self.aacgm_n) self.aacgm_e = np.asarray(self.aacgm_e) self.aacgm_z = np.asarray(self.aacgm_z) self.ocb_quad = np.asarray(self.ocb_quad) self.vec_quad = np.asarray(self.vec_quad) # Test input if np.all(np.isnan(self.ocb_lat)) or np.all(np.isnan(self.ocb_mlt)): raise ValueError("OCB coordinates required") if np.all(np.isnan(self.ocb_aacgm_mlt)): raise ValueError("OCB pole location required") if np.all(np.isnan(self.pole_angle)): raise ValueError("vector angle in poles-vector triangle required") # Determine the special case assignments zero_mask = ((self.aacgm_n == 0.0) & (self.aacgm_e == 0.0)) ns_mask = ((self.pole_angle == 0.0) | (self.pole_angle == 180.0)) norm_mask = ~(zero_mask + ns_mask) # There's no magnitude, so nothing to adjust if np.any(zero_mask): if self.aacgm_n.shape == (): self.ocb_n = np.zeros(shape=self.ocb_n.shape) self.ocb_e = np.zeros(shape=self.ocb_e.shape) self.ocb_z = np.zeros(shape=self.ocb_z.shape) else: self.ocb_n[zero_mask] = 0.0 self.ocb_e[zero_mask] = 0.0 self.ocb_z[zero_mask] = 0.0 # The measurement is aligned with the AACGM and OCB poles if np.any(ns_mask): if self.scale_func is None: if self.aacgm_n.shape == (): self.ocb_n = np.full(shape=self.ocb_n.shape, fill_value=self.aacgm_n) self.ocb_e = np.full(shape=self.ocb_e.shape, fill_value=self.aacgm_e) self.ocb_z = np.full(shape=self.ocb_z.shape, fill_value=self.aacgm_z) else: self.ocb_n[ns_mask] = self.aacgm_n[ns_mask] self.ocb_e[ns_mask] = self.aacgm_e[ns_mask] self.ocb_z[ns_mask] = self.aacgm_z[ns_mask] else: if self.aacgm_n.shape == (): self.ocb_n = np.full(shape=self.ocb_n.shape, fill_value=self.scale_func( self.aacgm_n, self.unscaled_r, self.scaled_r)) self.ocb_e = np.full(shape=self.ocb_e.shape, fill_value=self.scale_func( self.aacgm_e, self.unscaled_r, self.scaled_r)) self.ocb_z = np.full(shape=self.ocb_z.shape, fill_value=self.scale_func( self.aacgm_z, self.unscaled_r, self.scaled_r)) else: self.ocb_n[ns_mask] = self.scale_func( self.aacgm_n[ns_mask], self.unscaled_r[ns_mask], self.scaled_r) self.ocb_e[ns_mask] = self.scale_func( self.aacgm_e[ns_mask], self.unscaled_r[ns_mask], self.scaled_r) self.ocb_z[ns_mask] = self.scale_func( self.aacgm_z[ns_mask], self.unscaled_r[ns_mask], self.scaled_r) # Determine if the measurement is on or between the poles # This does not affect the vertical direction sign_mask = ((self.pole_angle == 0.0) & np.greater_equal(self.aacgm_lat, self.ocb_aacgm_lat, where=~np.isnan(self.aacgm_lat)) & ~np.isnan(self.aacgm_lat)) if np.any(sign_mask): if self.ocb_n.shape == (): self.ocb_n *= -1.0 self.ocb_e *= -1.0 else: self.ocb_n[sign_mask] *= -1.0 self.ocb_e[sign_mask] *= -1.0 # If there are still undefined vectors, assign them using the # typical case if np.any(norm_mask): # If not defined, get the OCB and vector quadrants if(np.any(self.ocb_quad[norm_mask] == 0) or np.any(self.vec_quad[norm_mask] == 0)): self.define_quadrants() # Get the unscaled 2D vector magnitude and # calculate the AACGM north azimuth in degrees if self.aacgm_n.shape == (): vmag = np.sqrt(self.aacgm_n**2 + self.aacgm_e**2) self.aacgm_naz = np.degrees(np.arccos(self.aacgm_n / vmag)) else: vmag = np.sqrt(self.aacgm_n[norm_mask]**2 + self.aacgm_e[norm_mask]**2) self.aacgm_naz[norm_mask] = np.degrees( np.arccos(self.aacgm_n[norm_mask] / vmag)) # Get the OCB north azimuth in radians ocb_angle = np.radians(self.calc_ocb_polar_angle()) # Get the sign of the North and East components vsigns = self.calc_ocb_vec_sign(north=True, east=True) # Scale the vector along the OCB north and account for # any changes associated with adjusting the size of the polar cap if self.scale_func is not None: if self.unscaled_r.shape == (): un_r = self.unscaled_r else: un_r = self.unscaled_r[norm_mask] if self.aacgm_z.shape == (): a_z = self.aacgm_z else: a_z = self.aacgm_z[norm_mask] vmag = self.scale_func(vmag, un_r, self.scaled_r) vz = self.scale_func(a_z, un_r, self.scaled_r) else: if self.aacgm_z.shape == (): vz = self.aacgm_z else: vz = self.aacgm_z[norm_mask] nan_mask = (np.isnan(vmag) | (np.isnan(ocb_angle) if ocb_angle.shape == () else np.isnan(ocb_angle[norm_mask]))) vz[nan_mask] = np.nan # Restrict the OCB angle to result in positive sines and cosines lmask = ocb_angle > np.pi / 2.0 if np.any(lmask): if ocb_angle.shape == (): ocb_angle = np.pi - ocb_angle else: ocb_angle[lmask] = np.pi - ocb_angle[lmask] # Calculate the vector components if vmag.shape == (): self.ocb_n = np.full(shape=self.ocb_n.shape, fill_value=(vsigns['north'] * vmag * np.cos(ocb_angle))) self.ocb_e = np.full(shape=self.ocb_e.shape, fill_value=(vsigns['east'] * vmag * np.sin(ocb_angle))) self.ocb_z = np.full(shape=self.ocb_z.shape, fill_value=vz) else: self.ocb_n[norm_mask] = (vsigns['north'][norm_mask] * vmag * np.cos(ocb_angle[norm_mask])) self.ocb_e[norm_mask] = (vsigns['east'][norm_mask] * vmag * np.sin(ocb_angle[norm_mask])) self.ocb_z[norm_mask] = vz # Calculate the scaled OCB vector magnitude self.ocb_mag = np.sqrt(self.ocb_n**2 + self.ocb_e**2 + self.ocb_z**2) return
[docs] def calc_ocb_polar_angle(self): """ Calculate the OCB north azimuth angle Requires -------- self.ocb_quad : (int or array-like) OCB quadrant self.vec_quad : (int or array-like) Vector quadrant self.aacgm_naz : (float or array-like) AACGM polar angle self.pole_angle : (float or array-like) Vector angle between AACGM pole, vector origin, and OCB pole Returns ------- ocb_naz : (float or array-like) Angle between measurement vector and OCB pole in degrees Raises ------ ValueError If the required input is undefined """ quad_range = np.arange(1, 5) # Test input if not np.any(np.isin(self.ocb_quad, quad_range)): raise ValueError("OCB quadrant undefined") if not np.any(np.isin(self.vec_quad, quad_range)): raise ValueError("Vector quadrant undefined") if np.all(np.isnan(self.aacgm_naz)): raise ValueError("AACGM polar angle undefined") if np.all(np.isnan(self.pole_angle)): raise ValueError("Vector angle undefined") # Initialise the output and set the quadrant dictionary nan_mask = (~np.isnan(self.aacgm_naz) & ~np.isnan(self.pole_angle)) ocb_naz = np.full(shape=(self.aacgm_naz + self.pole_angle).shape, fill_value=np.nan) quads = {oquad: {vquad: (self.ocb_quad == oquad) & (self.vec_quad == vquad) & nan_mask for vquad in quad_range} for oquad in quad_range} # Create masks for the different quadrant combinations abs_mask = (quads[1][1] | quads[2][2] | quads[3][3] | quads[4][4]) add_mask = (quads[1][2] | quads[1][3] | quads[2][1] | quads[2][4] | quads[3][1] | quads[4][2]) mpa_mask = (quads[1][4] | quads[2][3]) maa_mask = (quads[3][2] | quads[4][1]) cir_mask = (quads[3][4] | quads[4][3]) # Calculate OCB polar angle based on the quadrants and other angles if np.any(abs_mask): if ocb_naz.shape == (): ocb_naz = abs(self.aacgm_naz - self.pole_angle) else: ocb_naz[abs_mask] = abs(self.aacgm_naz - self.pole_angle)[abs_mask] if np.any(add_mask): if ocb_naz.shape == (): ocb_naz = self.pole_angle + self.aacgm_naz if ocb_naz > 180.0: ocb_naz = 360.0 - ocb_naz else: ocb_naz[add_mask] = (self.pole_angle + self.aacgm_naz)[add_mask] lmask = (ocb_naz > 180.0) & add_mask if np.any(lmask): ocb_naz[lmask] = 360.0 - ocb_naz[lmask] if np.any(mpa_mask): if ocb_naz.shape == (): ocb_naz = self.aacgm_naz - self.pole_angle else: ocb_naz[mpa_mask] = (self.aacgm_naz - self.pole_angle)[mpa_mask] if np.any(maa_mask): if ocb_naz.shape == (): ocb_naz = self.pole_angle - self.aacgm_naz else: ocb_naz[maa_mask] = (self.pole_angle - self.aacgm_naz)[maa_mask] if np.any(cir_mask): if ocb_naz.shape == (): ocb_naz = 360.0 - self.aacgm_naz - self.pole_angle else: ocb_naz[cir_mask] = (360.0 - self.aacgm_naz - self.pole_angle)[cir_mask] return ocb_naz
[docs] def calc_ocb_vec_sign(self, north=False, east=False, quads=dict()): """ Get the sign of the North and East components Parameters ---------- north : (boolean) Get the sign of the north component(s) (default=False) east : (boolean) Get the sign of the east component(s) (default=False) quads : (dictionary) Dictionary of boolean values or arrays of boolean values for OCB and Vector quadrants. (default=dict()) Requires -------- self.ocb_quad : (int or array-like) OCB pole quadrant self.vec_quad : (int or array-like) Vector quadrant self.aacgm_naz : (float or array-like) AACGM polar angle in degrees self.pole_angle : (float or array-like) Vector angle in degrees Returns ------- vsigns : (dict) Dictionary with keys 'north' and 'east' containing the desired signs Raises ------ ValueError If the required input is undefined """ quad_range = np.arange(1, 5) # Ensure the required input is array-like self.ocb_quad = np.asarray(self.ocb_quad) self.vec_quad = np.asarray(self.vec_quad) self.aacgm_naz = np.asarray(self.aacgm_naz) self.pole_angle = np.asarray(self.pole_angle) # Test input if not np.any([north, east]): raise ValueError("must set at least one direction") if not np.any(np.isin(self.ocb_quad, quad_range)): raise ValueError("OCB quadrant undefined") if not np.any(np.isin(self.vec_quad, quad_range)): raise ValueError("Vector quadrant undefined") if np.all(np.isnan(self.aacgm_naz)): raise ValueError("AACGM polar angle undefined") if np.all(np.isnan(self.pole_angle)): raise ValueError("Vector angle undefined") # If necessary, initialise quadrant dictionary nan_mask = (~np.isnan(self.aacgm_naz) & ~np.isnan(self.pole_angle)) if not np.all([kk in quads.keys() for kk in quad_range]): quads = {o: {v: (self.ocb_quad == o) & (self.vec_quad == v) & nan_mask for v in quad_range} for o in quad_range} # Initialise output vsigns = {"north": np.zeros(shape=quads[1][1].shape), "east": np.zeros(shape=quads[1][1].shape)} # Determine the desired vector signs if north: pole_minus = self.pole_angle - 90.0 minus_pole = 90.0 - self.pole_angle pole_plus = self.pole_angle + 90.0 pmask = (quads[1][1] | quads[2][2] | quads[3][3] | quads[4][4] | ((quads[1][4] | quads[2][3]) & np.less_equal(self.aacgm_naz, pole_plus, where=nan_mask)) | ((quads[1][2] | quads[2][1]) & np.less_equal(self.aacgm_naz, minus_pole, where=nan_mask)) | ((quads[3][4] | quads[4][3]) & np.greater_equal(self.aacgm_naz, 180.0 - pole_minus, where=nan_mask)) | ((quads[3][2] | quads[4][1]) & np.greater_equal(self.aacgm_naz, pole_minus, where=nan_mask))) if np.any(pmask): if vsigns["north"].shape == (): vsigns["north"] = 1 else: vsigns["north"][pmask] = 1 if np.any(~pmask): if vsigns["north"].shape == (): vsigns["north"] = -1 else: vsigns["north"][~pmask] = -1 if east: minus_pole = 180.0 - self.pole_angle pmask = (quads[1][4] | quads[2][1] | quads[3][2] | quads[4][3] | ((quads[1][1] | quads[4][4]) & np.greater_equal(self.aacgm_naz, self.pole_angle, where=nan_mask)) | ((quads[3][1] | quads[2][4]) & np.less_equal(self.aacgm_naz, minus_pole, where=nan_mask)) | ((quads[4][2] | quads[1][3]) & np.greater_equal(self.aacgm_naz, minus_pole, where=nan_mask)) | ((quads[2][2] | quads[3][3]) & np.less_equal(self.aacgm_naz, self.pole_angle, where=nan_mask))) if np.any(pmask): if vsigns["east"].shape == (): vsigns["east"] = 1 else: vsigns["east"][pmask] = 1 if np.any(~pmask): if vsigns["east"].shape == (): vsigns["east"] = -1 else: vsigns["east"][~pmask] = -1 return vsigns
[docs] def calc_vec_pole_angle(self): """Calculate the angle between the AACGM pole, a measurement, and the OCB pole using spherical triginometry Requires -------- self.aacgm_mlt : (float or array-like) AACGM MLT of vector origin in hours self.aacgm_lat : (float or array-like) AACGM latitude of vector origin in degrees self.ocb_aacgm_mlt : (float or array-like) AACGM MLT of the OCB pole in hours self.ocb_aacgm_lat : (float or array-like) AACGM latitude of the OCB pole in degrees Updates ------- self.pole_angle : (float or array-like) Angle in degrees between AACGM north, a measurement, and OCB north Raises ------ ValueError If the input is undefined or inappropriately sized arrays """ # Cast inputs as arrays self.aacgm_mlt = np.asarray(self.aacgm_mlt) self.aacgm_lat = np.asarray(self.aacgm_lat) self.ocb_aacgm_mlt = np.asarray(self.ocb_aacgm_mlt) self.ocb_aacgm_lat = np.asarray(self.ocb_aacgm_lat) # Test input if np.all(np.isnan(self.aacgm_mlt)): raise ValueError("AACGM MLT of Vector(s) undefinded") if np.all(np.isnan(self.aacgm_lat)): raise ValueError("AACGM latitude of Vector(s) undefined") if np.all(np.isnan(self.ocb_aacgm_mlt)): raise ValueError("AACGM MLT of OCB pole(s) undefined") if np.all(np.isnan(self.ocb_aacgm_lat)): raise ValueError("AACGM latitude of OCB pole(s) undefined") # Convert the AACGM MLT of the observation and OCB pole to radians, # then calculate the difference between them. del_long = ocbpy.ocb_time.hr2rad(self.ocb_aacgm_mlt-self.aacgm_mlt) if del_long.shape == (): if del_long < -np.pi: del_long += 2.0 * np.pi else: del_long[del_long < -np.pi] += 2.0 * np.pi # Initalize the output self.pole_angle = np.full(shape=del_long.shape, fill_value=np.nan) # Assign the extreme values if del_long.shape == (): if del_long in [-np.pi, 0.0, np.pi]: if abs(self.aacgm_lat) > abs(self.ocb_aacgm_lat): self.pole_angle = 180.0 else: self.pole_angle = 0.0 return else: zero_mask = (((del_long == 0) | (abs(del_long) == np.pi)) & np.greater(abs(self.aacgm_lat), abs(self.ocb_aacgm_lat), where=~np.isnan(del_long))) flat_mask = (((del_long == 0) | (abs(del_long) == np.pi)) & np.less_equal(abs(self.aacgm_lat), abs(self.ocb_aacgm_lat), where=~np.isnan(del_long))) self.pole_angle[flat_mask] = 180.0 self.pole_angle[zero_mask] = 0.0 update_mask = (~zero_mask & ~flat_mask) if not np.any(update_mask): return # Find the distance in radians between the two poles hemisphere = np.sign(self.ocb_aacgm_lat) rad_pole = hemisphere * np.pi * 0.5 del_pole = hemisphere * (rad_pole - np.radians(self.ocb_aacgm_lat)) # Get the distance in radians between the AACGM pole and the data point del_vect = hemisphere * (rad_pole - np.radians(self.aacgm_lat)) # Use the Vincenty formula for a sphere del_ocb = np.arctan2(np.sqrt((np.cos(np.radians(self.ocb_aacgm_lat)) * np.sin(del_long))**2 + (np.cos(np.radians(self.aacgm_lat)) * np.sin( np.radians(self.ocb_aacgm_lat)) - np.sin(np.radians(self.aacgm_lat)) * np.cos( np.radians(self.ocb_aacgm_lat)) * np.cos(del_long))**2), np.sin(np.radians(self.aacgm_lat)) * np.sin(np.radians(self.ocb_aacgm_lat)) + np.cos(np.radians(self.aacgm_lat)) * np.cos(np.radians(self.ocb_aacgm_lat)) * np.cos(del_long)) # Use the half-angle formula to get the pole angle sum_sides = 0.5 * (del_vect + del_ocb + del_pole) half_angle = np.sqrt(np.sin(sum_sides) * np.sin(sum_sides - del_pole) / (np.sin(del_vect) * np.sin(del_ocb))) if self.pole_angle.shape == (): self.pole_angle = np.degrees(2.0 * np.arccos(half_angle)) else: self.pole_angle[update_mask] = np.degrees( 2.0 * np.arccos(half_angle[update_mask])) return
[docs]def normal_evar(evar, unscaled_r, scaled_r): """ Normalise a variable proportional to the electric field Parameters ---------- evar : (float or array) Variable related to electric field (e.g. velocity) unscaled_r : (float or array) Radius of polar cap in degrees scaled_r : (float or array) Radius of normalised OCB polar cap in degrees Returns ------- nvar : (float or array) Normalised variable Notes ----- Assumes that the cross polar cap potential is fixed across the polar cap regardless of the radius of the Open Closed field line Boundary. This is commonly assumed when looking at statistical patterns that control the IMF (which accounts for dayside reconnection) and assume that the nightside reconnection influence is averaged out over the averaged period. References ---------- Chisham, G. (2017), A new methodology for the development of high‐latitude ionospheric climatologies and empirical models, Journal of Geophysical Research: Space Physics, doi:10.1002/2016JA023235. """ nvar = evar * unscaled_r / scaled_r return nvar
[docs]def normal_curl_evar(curl_evar, unscaled_r, scaled_r): """ Normalise a variable proportional to the curl of the electric field Parameters ---------- curl_evar : (float or array) Variable related to electric field (e.g. vorticity) unscaled_r : (float or array) Radius of polar cap in degrees scaled_r : (float or array) Radius of normalised OCB polar cap in degrees Returns ------- nvar : (float or array) Normalised variable Notes ----- Assumes that the cross polar cap potential is fixed across the polar cap regardless of the radius of the Open Closed field line Boundary. This is commonly assumed when looking at statistical patterns that control the IMF (which accounts for dayside reconnection) and assume that the nightside reconnection influence is averaged out over the averaged period. References ---------- Chisham, G. (2017), A new methodology for the development of high‐latitude ionospheric climatologies and empirical models, Journal of Geophysical Research: Space Physics, doi:10.1002/2016JA023235. """ nvar = curl_evar * (unscaled_r / scaled_r)**2 return nvar
[docs]def hav(alpha): """ Formula for haversine Parameters ---------- alpha : (float or array-like) Angle in radians Returns ------- hav_alpha : (float or array-like) Haversine of alpha, equal to the square of the sine of half-alpha """ alpha = np.asarray(alpha) hav_alpha = np.sin(alpha * 0.5)**2 return hav_alpha
[docs]def archav(hav): """ Formula for the inverse haversine Parameters ---------- hav : (float or array-like) Haversine of an angle Returns ------- alpha : (float or array-like) Angle in radians Notes ----- The input must be positive. However, any number with a magnitude below 10-16 will be rounded to zero. More negative numbers will return NaN. """ # Cast the output as array-like hav = np.asarray(hav) # Initialize the output to NaN, so that values of NaN or negative # numbers will return NaN alpha = np.full(shape=hav.shape, fill_value=np.nan) # If the number is positive, calculate the angle norm_mask = (np.greater_equal(hav, 1.0e-16, where=~np.isnan(hav)) & ~np.isnan(hav)) if np.any(norm_mask): if hav.shape == (): alpha = 2.0 * np.arcsin(np.sqrt(hav)) else: alpha[norm_mask] = 2.0 * np.arcsin(np.sqrt(hav[norm_mask])) # The number is small enough that machine precision may have changed # the sign, but it's a single-precission zero small_mask = (np.less(abs(hav), 1.0e-16, where=~np.isnan(hav)) & ~np.isnan(hav)) if np.any(small_mask): if hav.shape == (): alpha = 0.0 else: alpha[small_mask] = 0.0 return alpha