Empirical models
eppaurora.models.ssusiq2023
Empirical model for auroral ionization rates
Implements the empirical model for auroral ionization, derived from SSUSI UV observations [SB23].
Bender et al., in prep., 2023, preprint: https://doi.org/10.48550/arXiv.2312.11130
- eppaurora.models.ssusiq2023.ssusiq2023(gmlat, mlt, alt, sw_coeffs, coeff_ds=None, interpolate=False, method='linear', return_var=False)[source]
- Parameters:
gmlat (float) – Geomagnetic latitude in [degrees].
mlt (float) – Magnetic local time in [hours].
alt (float) – Altitude in [km]
sw_coeffs (array_like or xarray.DataArray) – The space weather index values to use (for the requested time(s)), should be of shape (N, M) with N = number of proxies, currently 4: [Kp, PC, Ap, log(f10.7_81ctr_obs)]. The xarray.DataArray should have a dimension named “proxy” with matching coordinates: [“Kp”, “PC”, “Ap”, “log_f107_81ctr_obs”] All the other dimensions will be broadcasted.
coeff_ds (xarray.Dataset, optional (default: None)) – Dataset with the model coefficients, None uses the packaged version.
interpolate (bool, optional (default: False)) – If True, uses bilinear interpolate in MLT and geomagnetic latitude, using periodic (24h) boundary conditions in MLT. Otherwise, the closest MLT/geomagnetic latitude bin will be selected.
method (str, optional (default: "linear")) – Interpolation method to use, see scipy.interpolate.interpn for options. Only used if interpolate is True.
return_var (bool, optional (default: False)) – If True, returns the predicted variance in addition to the values, otherwise only the mean prediction is returned.
- Returns:
q (xarray.DataArray) – log(q), where q is the ionization rate in [cm⁻³ s⁻¹] if return_var is False.
q, var(q) (tuple of xarray.DataArray`s) – log(q) and var(log(q)) where q is the ionization rate in [cm⁻³ s⁻¹] if `return_var is True.
- eppaurora.models.ssusiq2023.ssusiq2023_coeffs(file=None)[source]
SSUSI ionization rate model coefficients
Returns the fitted ionization rate model coefficents as read from the coefficient netcdf file.
- Parameters:
file (str, optional) – The coefficient file, defaults to the packaged coefficients.
- Returns:
coeffs – The default fitted model coefficients as read from the file.
- Return type:
xarray.Dataset
eppaurora.models.zhangpaxton2008
Empirical model for electron energy and flux
Implements the empirical Kp-driven model for auroral electrons, providing mean energy and energy flux as described in [ZP08].
Zhang and Paxton, JASTP, 70, 1231–1242, 2008, https://doi.org/10.1016/j.jastp.2008.03.008
- eppaurora.models.zhangpaxton2008.epstein_coeffs(angle, table)[source]
Epstein coefficients from table
Returns the Epstein coefficients as read from the table, ready for evaluation with
epstein_eval().- Parameters:
angle (float or array_like) – The magnetic local time hour angle: \(angle = \text{MLT} * 2\pi / 24\)
table (array_like) – Table of N harmonic (Fourier) coefficients. The 4 constant offsets are in the first row, then Nx4 cosine amplitudes followed by Nx4 sine amplitudes, each for the coefficients A, B, C, and D.
- Returns:
coeffs – The Epstein coefficients for the MLT angle.
- Return type:
array_like (4,)
See also
- eppaurora.models.zhangpaxton2008.epstein_eval(x, coeffs)[source]
Epstein function evaluated at x
The so-called Epstein function is defined by
\[E(x) = \frac{A\exp\{(x - B) / C\}}{(1 + \exp\{(x - B) / D\})^2}\]- Parameters:
x (float or array_like) – Argument of the Epstein function, e.g. the magnetic co-latitude \(x = 90 - |Mlat|\).
coeffs (array_like) – Epstein coefficients, e.g. from
epstein_coeffs().
- Returns:
y – The Epstein function with coefficients as given evaluated at x.
- Return type:
float or array_like
- eppaurora.models.zhangpaxton2008.hemispheric_power(Kp)[source]
Hemispheric Power in GW from Kp
Zhang and Paxton, 2008, Eqs. (1) and (2)
- eppaurora.models.zhangpaxton2008.read_zp2008_coeffs(file=None, nf=6, nKp=6)[source]
Read Epstein coefficient tables from file
- Parameters:
file (str, optional) – The text file containing the coefficient tables, with the same layout as in [ZP08]. Defaults to the packaged coefficient file.
nf (int, optional) – The number of harmonic (Fourier) terms, defaults to 6 as in [ZP08]
nKp (int, optional) – The number of Kp bins, defaults to 6 as in [ZP08]
- Returns:
Q0_table, Em_table – The tables for the total energy flux Q0 and the electron mean energy Em, the row names indicate the frequency and the columns the Epstein parameters A, B, C, D.
- Return type:
tuple of
numpy.recarray
References
[ZP08] (1,2,3)Zhang and Paxton, JASTP, 70, 1231–1242, 2008, https://doi.org/10.1016/j.jastp.2008.03.008
- eppaurora.models.zhangpaxton2008.zp2008(mlat, mlt, Kp, Q0table=None, Emtable=None)[source]
Electron total energy flux and mean energy model
Implements the model algorithm as given in Appendix A of [ZP08]. Defaults to using the packaged coefficients taken from that reference, but custom tables for the Q0 and Em Fourier coefficients can be provided.
- Parameters:
mlat (float) – (Geo)Magnetic latitude in [degrees].
mlt (float) – Magnetic local time in [hours].
Kp (float) – Geomagnetic Kp index value(s).
Q0table (np.recarray, optional) – Fourier coefficient table for the Epstein coefficients for the energy flux. E.g. as returned by read_zp2008_coeffs().
Emtable (np.recarray, optional) – Fourier coefficient table for the Epstein coefficients for the mean energy. E.g. as returned by read_zp2008_coeffs().
- Returns:
(Q0, Em) – Electron energy flux Q0 in [mW m⁻²] (= [erg s⁻¹ cm⁻²]), and electron mean energy in [keV].
- Return type:
References
[ZP08]Zhang and Paxton, JASTP, 70, 1231–1242, 2008, https://doi.org/10.1016/j.jastp.2008.03.008
Module contents
Empirical models for electron energy and flux and ionization rates
Implements the empirical proxy-driven models for auroral electrons, providing the proxy driven ionization rate model described in [1] and the empirical electron energy and flux model described in [2].
Bender et al., in prep., 2023, preprint: https://doi.org/10.48550/arXiv.2312.11130
Zhang and Paxton, JASTP, 70, 1231–1242, 2008, https://doi.org/10.1016/j.jastp.2008.03.008