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Source code for spacepy.empiricals

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Module with some useful empirical models (plasmapause, magnetopause, Lmax)


Authors: Steve Morley, Josef Koller
Institution: Los Alamos National Laboratory
Contact: smorley@lanl.gov

Copyright 2010 Los Alamos National Security, LLC.
"""
import datetime
from functools import partial
import numpy as np

import scipy.integrate as integ
from spacepy import help
import spacepy.toolbox as tb
import spacepy.omni as om
import spacepy.time as spt

__contact__ = 'Steve Morley, smorley@lanl.gov'

[docs]def getLmax(ticks, model='JKemp'): """ calculate a simple empirical model for Lmax - last closed drift-shell Uses the parametrized Lmax from: Koller and Morley (2010) 'Magnetopause shadowing effects for radiation belt models during high-speed solar wind streams' American Geophysical Union, Fall Meeting 2010, abstract #SM13A-1787 Parameters ========== ticks : spacepy.time.Ticktock Ticktock object of desired times model : string, optional 'JKemp' (default - empirical model of J. Koller) Returns ======= out : np.ndarray Lmax - L* of last closed drift shell Examples ======== >>> from spacepy.empiricals import getLmax >>> import spacepy.time as st >>> import datetime >>> ticks = st.tickrange(datetime.datetime(2000, 1, 1), datetime.datetime(2000, 1, 3), deltadays=1) array([ 7.4928412, 8.3585632, 8.6463423]) See Also ======== spacepy.LANLstar.LANLmax """ omni = om.get_omni(ticks) Dst = omni['Dst'] Lmax = np.zeros(len(Dst)) if model is 'JKemp': for i, iDst in enumerate(Dst): Lmax[i] = 6.07e-5*iDst*iDst + 0.0436*iDst + 9.37 else: raise ValueError('Invalid model selection') return Lmax
[docs]def getPlasmaPause(ticks, model='M2002', LT='all', omnivals=None): """ Plasmapause location model(s) CA1992 -- Carpenter, D. L., and R. R. Anderson, An ISEE/whistler model of equatorial electron density in the magnetosphere, J. Geophys. Res., 97, 1097, 1992. M2002 -- Moldwin, M. B., L. Downward, H. K. Rassoul, R. Amin, and R. R. Anderson, A new model of the location of the plasmapause: CRRES results, J. Geophys. Res., 107(A11), 1339, doi:10.1029/2001JA009211, 2002. Parameters ========== ticks : spacepy.time.Ticktock TickTock object of desired times Lpp_model : string, optional 'CA1992' or 'M2002' (default) CA1992 returns the Carpenter and Anderson model, M2002 returns the Moldwin et al. model LT : int, float requested local time sector, 'all' is valid option omnivals : spacepy.datamodel.SpaceData, dict dict-like containing UTC (datetimes) and Kp keys Returns ======= out : float Plasmapause radius in Earth radii Examples ======== >>> import spacepy.time as spt >>> import spacepy.empiricals as emp >>> ticks = spt.tickrange('2002-01-01T12:00:00','2002-01-04T00:00:00',.25) >>> emp.getPlasmaPause(ticks) array([ 6.42140002, 6.42140002, 6.42140002, 6.42140002, 6.42140002, 6.42140002, 6.42140002, 6.26859998, 5.772 , 5.6574 , 5.6574 ]) """ def calcLpp(Kpmax, A, B): currLpp = A - B*Kpmax return currLpp model_list = ['CA1992', 'M2002'] if model == 'CA1992': if LT!='all': print('No LT dependence currently supported for this model') if model not in model_list: raise ValueError("Please specify a valid model:\n'M2002' or 'CA1992'") if LT=='all': parA = {'CA1992': 5.6, 'M2002': 5.39} parB = {'CA1992': 0.46, 'M2002': 0.382} priorvals = {'CA1992': datetime.timedelta(hours=24), 'M2002': datetime.timedelta(hours=12)} A, B = parA[model], parB[model] prior = priorvals[model] else: try: float(LT) except (ValueError, TypeError): raise ValueError("Please specify a valid LT:\n'all' or a numeric type") parA = {'CA1992': [5.6]*24, 'M2002': [5.7]*3+[6.05]*6+[5.2]*6+[4.45]*6+[5.7]*3} parB = {'CA1992': [0.46]*24, 'M2002': [0.42]*3+[0.573]*6+[0.425]*6+[0.167]*6+[0.42]*3} priorvals = {'CA1992': [datetime.timedelta(hours=24)]*24, 'M2002': [datetime.timedelta(hours=12)]*24} try: LThr = long(LT) except NameError: LThr = int(LT) prior = priorvals[model][LThr] A, B = parA[model][LThr], parB[model][LThr] #TODO: allow calling with ticks as dict of Kp (will also need UT for Kpmax) st, en = ticks.UTC[0]-prior, ticks.UTC[-1] if omnivals is None: omdat = om.get_omni(spt.tickrange(st, en, 1.0/24.0), dbase='QDhourly') else: #now test for sanity of input try: isinstance(omnivals, dict) except: raise TypeError('Not a valid input type for omnivals, expected spacepy.datamodel.SpaceData') try: assert 'UTC' in omnivals assert 'Kp' in omnivals except: raise KeyError('Required data not found in input dict-like (omnivals)') omdat = omnivals einds, oinds = tb.tOverlap([st, en], omdat['UTC']) utc = np.array(omdat['UTC'])[oinds] Kp = np.array(omdat['Kp'])[oinds] Lpp = np.zeros(len(ticks)) for i, t1 in enumerate(ticks.UTC): t0 = t1-prior iprevday, dum = tb.tOverlap(utc, [t0, t1]) if iprevday: Kpmax = max(Kp[iprevday]) Lpp[i] = calcLpp(Kpmax, A, B) else: Lpp[i] = np.nan return Lpp
[docs]def getMPstandoff(ticks): """Calculates the Shue et al. (1997) subsolar magnetopause radius Lets put the full reference here Parameters ========== ticks : spacepy.time.Ticktock TickTock object of desired times (will be interpolated from hourly OMNI data) OR dictionary of form {'P': [], 'Bz': []} Where P is SW ram pressure [nPa] and Bz is IMF Bz (GSM) [nT] Returns ======= out : float Magnetopause (sub-solar point) standoff distance [Re] Examples ======== >>> import spacepy.time as spt >>> import spacepy.empiricals as emp >>> ticks = spt.tickrange('2002-01-01T12:00:00','2002-01-04T00:00:00',.25) >>> emp.ShueMP(ticks) array([ 10.57319537, 10.91327764, 10.75086873, 10.77577207, 9.78180261, 11.0374474 , 11.4065 , 11.27555451, 11.47988573, 11.8202582 , 11.23834814]) >>> data = {'P': [2,4], 'Bz': [-2.4, -2.4]} >>> emp.ShueMP(data) array([ 9.96096838, 8.96790412]) """ if type(ticks) == spt.Ticktock: omni = om.get_omni(ticks) P, Bz = omni['Pdyn'], omni['BzIMF'] elif isinstance(ticks, dict): P, Bz = ticks['P'], ticks['Bz'] try: len(P) except TypeError: P = [P] try: len(Bz) except TypeError: Bz = [Bz] else: raise(TypeError('Invalid Input type')) try: # Initialize r0 and make P and Bz numpy arrays r0 = np.zeros((len(P)), dtype=float) Bz = np.array(Bz) P = np.array(P) # Find where Bz >= 0 and where it is < 0 iBzPos = np.where(Bz >= 0) iBzNeg = np.where(Bz < 0) # Calculate r0 r0[iBzPos] = (11.4 + 0.013*Bz[iBzPos])*P[iBzPos]**(-1/6.6) r0[iBzNeg] = (11.4 + 0.140*Bz[iBzNeg])*P[iBzNeg]**(-1/6.6) return r0 except TypeError: raise TypeError("Please check for valid input types")
[docs]def getDststar(ticks, model='OBrien'): """Calculate the pressure-corrected Dst index, Dst* We need to add in the references to the models here! Parameters ========== ticks : spacepy.time.Ticktock TickTock object of desired times (will be interpolated from hourly OMNI data) OR dictionary including 'Pdyn' and 'Dst' keys where data are lists or arrays and Dst is in [nT], and Pdyn is in [nPa] Returns ======= out : float Dst* - the pressure corrected Dst index from OMNI [nT] Examples ======== Coefficients are applied to the standard formulation e.g. Burton et al., 1975 of Dst* = Dst - b*sqrt(Pdyn) + c The default is the O'Brien and McPherron model (2002). Other options are Burton et al. (1975) and Borovsky and Denton (2010) >>> import spacepy.time as spt >>> import spacepy.omni as om >>> import spacepy.empiricals as emp >>> ticks = spt.tickrange('2000-10-16T00:00:00', '2000-10-31T12:00:00', 1/24.) >>> dststar = emp.getDststar(ticks) >>> dststar[0] -21.317220132108943 User-determined coefficients can also be supplied as a two-element list or tuple of the form (b,c), e.g. >>> dststar = emp.getDststar(ticks, model=(2,11)) #b is extreme driving from O'Brien We have chosen the OBrien model as the default here as this was rigorously determined from a very long data set and is pertinent to most conditions. It is, however, the most conservative correction. Additionally, Siscoe, McPherron and Jordanova (2005) argue that the pressure contribution to Dst diminishes during magnetic storms. To show the relative differences, run the following example: >>> import matplotlib.pyplot as plt >>> params = [('Burton','k-'), ('OBrien','r-'), ('Borovsky','b-')] >>> for model, col in params: dststar = getDststar(ticks, model=model) plt.plot(ticks.UTC, dststar, col) """ model_params = {'Burton': (15.8, 20), 'OBrien': (7.26, 11), 'Borovsky': (20.7,27.7)} if isinstance(model, str): try: b, c = model_params[model] except KeyError: raise ValueError('Invalid pressure correction model selected') else: try: b, c = model[0], model[1] except (KeyError, IndexError): raise ValueError('Invalid coefficients set: must be of form (b,c)') if isinstance(ticks, spt.Ticktock): omni = om.get_omni(ticks) P, Dst = omni['Pdyn'], omni['Dst'] elif isinstance(ticks, dict): P, Dst = ticks['Pdyn'], ticks['Dst'] if isinstance(P, list): P, Dst = np.array(P), np.array(Dst) #get Dst* Dststar = Dst - b*P**0.5 + c return Dststar
[docs]def vampolaPA(omniflux, **kwargs): '''Pitch angle model of sin^n form Parameters ========== omniflux : arraylike or float omnidirectional number flux data order : integer or float (optional) order of sin^n functional form for distribution (default=2) alphas : arraylike (optional) pitch angles at which to evaluate the differential number flux (default is 5 to 90 degrees in 36 steps) Returns ======= dnflux : array differential number flux corresponding to pitch angles alphas alphas : array pitch angles at which the differential number flux was evaluated Examples ======== Omnidirectional number flux of [3000, 6000] >>> from spacepy.empiricals import vampolaPA >>> vampolaPA(3000, alpha=[45, 90]) (array([ 75.99088773, 151.98177546]), [45, 90]) >>> data, pas = vampolaPA([3000, 6000], alpha=[45, 90]) >>> pas [45, 90] >>> data array([[ 75.99088773, 151.98177546], [ 151.98177546, 303.96355093]]) Notes ===== Directional number flux integrated over pitch angle from 0 to 90 degrees is a factor of 4*pi lower than omnidirectional number flux. ''' defaults = {'order': 2, 'alpha': tb.linspace(5,90,18)} if hasattr(omniflux, '__iter__'): omniflux = np.asanyarray(omniflux) else: omniflux = np.asanyarray([omniflux]) #substitute defaults for key in defaults: if key not in kwargs: kwargs[key] = defaults[key] if hasattr(kwargs['order'], '__iter__'): try: assert len(kwargs['order'])==len(omniflux) except AssertionError: raise ValueError('order must be either single-valued or the same length as omniflux') else: kwargs['order'] = np.asanyarray([kwargs['order']]*len(omniflux)) normfac = np.empty(len(kwargs['order']), dtype=float) def sinfunc(x, order=kwargs['order']): #define distribution function dum = np.sin(x) return dum**order for idx, tmporder in enumerate(kwargs['order']): #def partial function so that order is fixed sinfunc_o = partial(sinfunc, order=tmporder) normfac[idx] = 4*np.pi*integ.quad(sinfunc_o, 0, np.pi)[0] #quad returns (val, accuracy) #now make the differential number flux dnflux = np.zeros((len(kwargs['alpha']), len(omniflux))).squeeze() for i, a_val in enumerate(np.deg2rad(kwargs['alpha'])): dnflux[i] = omniflux * sinfunc(a_val) / normfac return dnflux, kwargs['alpha']
[docs]def getVampolaOrder(L): '''Empirical lookup of power for sin^n pitch angle model from Vampola (1996) Vampola, A.L. Outer zone energetic electron environment update, Final Report of ESA/ESTEC/WMA/P.O. 151351, ESA-ESTEC, Noordwijk, The Netherlands, 1996. Parameters ========== L : arraylike or float Returns ======= order : array coefficient for sin^n model corresponding to McIlwain L (computed for OP77?) ''' lmc = np.arange(3,8.00001,0.25) vamp_n = [5.38, 5.078, 4.669, 3.916, 3.095, 2.494, 2.151, 1.998, 1.899, 1.942, 1.974, 1.939, 1.970, 2.136, 1.775, 1.438, 1.254, 1.194, 1.046, 0.989, 0.852] if not hasattr(L, '__iter__'): L = [L] L = np.asanyarray(L) #if outside valid range, use end value L[L<=3] = 3 L[L>=8] = 8 #interpolate to get order for the given L order = np.interp(L, lmc, vamp_n) return order
ShueMP = getMPstandoff get_plasma_pause = getPlasmaPause get_Lmax = getLmax