Coordinate Transformations

Kameleon now allows users to work in their preferred coordinate system without requiring intimate knowledge of the underlying models. This document gives some examples illustrating the new capabilities, primarily using the kameleon python API.

Setup

Make sure the _CCMC module is compiled and placed in lib/ccmc/python/CCMC.

Detailed instructions may be found here (anaconda users) and here (main Kameleon site).

Load the ccmc python api into a python environment

Once compiled, replace the path variable with your /path/to/lib/ccmc/python/CCMC/

path = '/Users/apembrok/git/ccmc/ccmc-software/kameleon-plus/trunk/kameleon-plus-working/lib/ccmc/python/CCMC/'
import sys
sys.path.append(path)
import _CCMC as ccmc

Choose a kameleon-compatible file to work with

Kameleon-compatible model files may be obtained through our Runs-on-Request system, by searching the database or requesting a run. Requested model output will be automatically converted to a format the CCMC library understands.

filename = '/Users/apembrok/Work/New_Horizons/nh_mhd/3D_CDF/nh3d_mhd.enlil.0348.cdf' #sample enlil

Working with kameleon objects

Create a kameleon object that opens and interrogates the file

Kameleon objects allow access to model attributes without needing to know the particular structure of a given model. ### Global attributes

kameleon = ccmc.Kameleon()
kameleon.open(filename)

for i in range(kameleon.getNumberOfGlobalAttributes()):
    gname = kameleon.getGlobalAttributeName(i)
    gattr = kameleon.getGlobalAttribute(gname)
    if gname != 'README':
        print gname, gattr.toString()
model_type STRING: model_type: Heliosphere
grid_system_count STRING: grid_system_count: 1
model_name STRING: model_name: enlil
output_type STRING: output_type: Heliosphere
grid_system_1 STRING: grid_system_1: [r,theta,phi]
grid_1_type STRING: grid_1_type: HNM
run_type STRING: run_type: stationary_Solar_Wind
standard_grid_target STRING: standard_grid_target: HNM
original_output_file_name STRING: original_output_file_name: /tim.0348.nc
run_registration_number STRING: run_registration_number: nh3d_mhd
terms_of_usage STRING: terms_of_usage: ***For tracking purposes of our government sponsors, we ask that you notify the CCMC
whenever you use CCMC results in scientific publications or presentations: ccmc@ccmc.gsfc.nasa.gov
tim_type STRING: tim_type: TIM
tim_title STRING: tim_title: Values at the given time level
tim_program STRING: tim_program: enlil
tim_version STRING: tim_version: 2.8
tim_project STRING: tim_project: nh3d
tim_code STRING: tim_code: reg40low1.256-mcp1umn1cd-1
tim_model STRING: tim_model: mhd ethe splitted upwind llf minmod nototh difb
tim_geometry STRING: tim_geometry: spherical
tim_grid STRING: tim_grid: X1=0.1-40.1/uniform X2=50-130/uniform X3=0-360/uniform
tim_coordinates STRING: tim_coordinates: HEEQ+180
tim_rotation STRING: tim_rotation: sidereal
tim_case STRING: tim_case: reg40low1.dtb-a6b1r-donki500cme6-sa1.20150601
tim_cordata STRING: tim_cordata: wsadu
tim_observatory STRING: tim_observatory: gongb
tim_corona STRING: tim_corona: WSA_V2.2
tim_crpos STRING: tim_crpos: 2164_219
tim_shift_deg FLOAT: : 0
tim_boundary STRING: tim_boundary: LLVV=3./1./700./0. RRtilt=25./0./0. NTxcld=4./1./1. NTrcav=1./4./0.
tim_run STRING: tim_run: reg40low1.dtb-a6b1r-donki500cme6-sa1.256-mcp1umn1cd-1.g53q5.20150601
tim_parameters STRING: tim_parameters: g=1.6666667 q=0.05/1 xa=0.05 rot=sidereal cfl=0.4 difb=0.2/
tim_boundary_old STRING: tim_boundary_old: B=350./4./0./1 D=125./2. T=1.5/0 V=700./0./75./200. S=9. A=0.05
tim_obsdate_mjd FLOAT: : 0
tim_obsdate_cal STRING: tim_obsdate_cal: null
tim_crstart_mjd FLOAT: : 0
tim_crstart_cal STRING: tim_crstart_cal: 2015-05-21T09:13:14
tim_rundate_mjd FLOAT: : 0
tim_rundate_cal STRING: tim_rundate_cal: 2015-06-01
tim_rbnd FLOAT: : 0
tim_gamma STRING: :
tim_xalpha STRING: :
tim_mevo INT: tim_mevo: 71029
tim_mfld INT: tim_mfld: 0
tim_mslc INT: tim_mslc: 0
tim_mtim INT: tim_mtim: 349
tim_creation STRING: tim_creation: 2015-07-08T18:41:34
grid_system_1_dimension_1_size INT: grid_system_1_dimension_1_size: 6400
grid_system_1_dimension_2_size INT: grid_system_1_dimension_2_size: 20
grid_system_1_dimension_3_size INT: grid_system_1_dimension_3_size: 90
grid_system_1_number_of_dimensions INT: grid_system_1_number_of_dimensions: 3
time_physical_time FLOAT: time_physical_time: 3758578.5
time_physical_time_step FLOAT: time_physical_time_step: 274.08963
time_numerical_time_step INT: time_numerical_time_step: 71028
Conversion Time STRING: Conversion Time: 2015/07/09 16:37:34

Viewing variable attributes

for i in range(kameleon.getNumberOfVariables()):
    varname  = kameleon.getVariableName(i)
    min_attr = kameleon.getVariableAttribute(varname, 'actual_min').getAttributeFloat()
    max_attr = kameleon.getVariableAttribute(varname, 'actual_max').getAttributeFloat()
    units = kameleon.getVisUnit(varname)
    units2 = kameleon.getNativeUnit(varname)
    print varname, '\t', min_attr,'\t', max_attr, units, units2
r   15427500032.0   5.99849225421e+12 m m
theta       0.907571196556  2.23402142525 radian radian
phi         0.0349065847695         6.24827861786 radian radian
rho         5.06677902223e-26       1.75479584072e-18 kg/m3 kg/m3
T   121.367195129   1424361.375 K
ur  250993.953125   717503.3125 km/s m/s
utheta      -29017.0996094  73542.9765625 km/s m/s
uphi        -68833.5078125  39320.1835938 km/s m/s
br  -1.32109281847e-10      3.1329065564e-07 nT T
btheta      -3.10669090453e-09      3.30375415913e-09 nT T
bphi        -5.49196386146e-08      1.08497091519e-11 nT T
dp  0.0     0.00549638364464 kg/m^3 kg/m^3
bp  -0.952782809734         0.954018414021 1000000000000.0 1000000000000.0
b1r         -3.1329065564e-07       1.32109281847e-10 nT nT
b1theta     -3.30375415913e-09      3.10669090453e-09 nT nT
b1phi       -1.08497091519e-11      5.49196386146e-08 nT nT

Loading variables

Usually you will need to load the variables you are interested in prior to interpolation. There are two ways to confirm if a variable exists:

  1. the doesVariableExist method
  2. return value of getVariableID
# Enlil only stores br,btheta,bphi
if kameleon.doesVariableExist('bx'):
    print 'bx exists!?!?'

br_id = kameleon.getVariableID('br')
if br_id != -1:
    print 'variable br exists, loading'
    kameleon.loadVariable('br')
variable br exists, loading

One can also load multiple components of vector variables in one call

kameleon.loadVectorVariable('b') #automatically loads br,btheta,bphi
kameleon.loadVariable('p')
kameleon.loadVariable('rho')

#Note: a bug causes loadVariable to always return true
if kameleon.loadVariable('non-existent_variable'):
    print 'non-existent_variable should not be loaded'
non-existent_variable should not be loaded

Interpolation

Native Interpolation

Native interpolation is performed by default, meaning that kameleon assumes the user knows what coordinate system the underlying model is in and will make no effort to convert query points. If you have used kameleon before, this behavior should match what you’re used to.

model_name = kameleon.getGlobalAttribute('model_name').getAttributeString()
coordinates = kameleon.getGlobalAttribute('grid_1_type').getAttributeString()

# HNM (radius[AU], longitude, latitude).
print model_name, 'uses', coordinates

#when intializing the interpolator with no arguments, we assume native interpolation
interpolator = kameleon.createNewInterpolator()

# The new horizons run extends past pluto.
point = 10.0,0,0
if br_id != -1:
    result = interpolator.interpolate(br_id, *point)
    print 'br',point,result,kameleon.getVisUnit('br')
enlil uses HNM
br (10.0, 0, 0) 0.0602672547102 nT

Preferred Coordinate Interpolation

To enable conversion between coordinate systems, create a coordinate interpolator object.

  • If initialized without argument, native interpolation is assumed.
  • If initialized with the name of a registered coordinate system, user query points will be converted from that coordinate system to that of the underlying model prior to interpolation.
  • If initialized with an unregistered coordinate system, an error message will print and native interpolation will be used.
coordinate_interpolator = kameleon.createCoordinateInterpolator() #no arguments assumes native

Model Epoch Time

The model epoch time will be used to convert between coordinate systems.

print model_name, 'epoch time:', coordinate_interpolator.getEphemTime(), 'seconds'
enlil epoch time: 489230172 seconds

one may also change the epoch time if it is not set properly in the file:

coordinate_interpolator.setEphemTime(200)
print model_name, 'epoch time:', coordinate_interpolator.getEphemTime(), 'seconds'
enlil epoch time: 200 seconds

Available transformations

Coordinate transformations may be performed from the following cartesian geocentric and heliocentric coordinate systems. Note that because of the length scales, it is helpful to think of geocenctric coordinates in R_E while Heliocentric are in km.

geo_coords = [  "J2000", #geocentric are in R_E
                "GEI",
                "GEO",
                "MAG",
                "GSE",
                "GSM",
                "SM",
                "RTN",
                "GSEQ",]

helio_coords = [ "HEE", #heliocentric are in km
                "HAE",
                "HEEQ"]

Example: Interpolating from SM coordinates:

coordinate_interpolator = kameleon.createCoordinateInterpolator("SM")
var = 'rho' #slightly slower, but interpolator may be called with string instead of variable ID
print var,  coordinate_interpolator.getPreferredCoordinates(), point,
print coordinate_interpolator.interpolate(var, point[0],point[1],point[2]),
print kameleon.getVisUnit(var)
rho SM (10.0, 0, 0) 1.83079636822e-17 kg/m3

note: this assumes that the variable is a scalar field! For example, if you ask for br, there will be no attempt to rotate the result into your preferred coordinate system - the result will be the radial component of Enlil’s field in Enlil’s coordinate system.

If you want to check the conversion to model coordinates, you can use the convertCoordinates method

coordinate_interpolator.setPreferredCoordinates("SM")
point = 10, 0, 0 # SM cartesian [Re]

query_point = ccmc.Position()
query_point.c0, query_point.c1, query_point.c2 = point

model_point = ccmc.Position()
coordinate_interpolator.convertCoordinates(query_point,model_point)
print coordinate_interpolator.get_model_coords(),
print model_point.c0, model_point.c1, model_point.c2 # HNM R[AU], latitude [deg], longitude [deg]
HNM 1.01669931412 -3.13182067871 360.0

Example: Interpolating between multiple coordinate frames

from pandas import DataFrame as df
import numpy as np
from collections import defaultdict

def get_coordinate_table(kameleon, coordinate_list, variable_names, point):
    if type(variable_names) != list:
        variable_names = [variable_names]
    query_point = ccmc.Position()
    query_point.c0, query_point.c1, query_point.c2 = point
    coordinate_interpolator = kameleon.createCoordinateInterpolator()
    model_coordinates = coordinate_interpolator.get_model_coords()
    model_coordinates = str(point) + " ---> " + model_coordinates + '[AU, lat, lon]'
    missing_value = kameleon.getMissingValue()
    model_positions = []
    results = []
    table = defaultdict(list)
    for coord in coordinate_list:
        coordinate_interpolator.setPreferredCoordinates(coord)
        coordinate_interpolator.convertCoordinates(query_point,model_point)
        table[model_coordinates].append(np.array([model_point.c0, model_point.c1, model_point.c2]))
        for variable_name in variable_names:
            column_name = variable_name + '[' + kameleon.getVisUnit(variable_name) + ']'
            result = coordinate_interpolator.interpolate(variable_name, *point)
            if result == missing_value:
                table[column_name].append(np.NAN)
            else:
                table[column_name].append(result)
    table = df(table) #make a pretty pandas table
    table.index = coordinate_list
    return table

The above code makes a nice looking pandas data table from results of the interpolation in each of the available coordinate systems. Here are the results for geocentric coordinates.

geo_table = get_coordinate_table(kameleon,geo_coords,['br', 'rho', 'p'], (10, 0, 0))
geo_table
(10, 0, 0) ---> HNM[AU, lat, lon] br[nT] p[nPa] rho[kg/m3]
J2000 [1.01669943333, -3.13182067871, 3.67431243831e... 7.144619 896249.1250 1.830797e-17
GEI [1.01669943333, -3.13182067871, 3.67120128431e... 7.144619 896249.1250 1.830797e-17
GEO [1.01669943333, -3.13182830811, 360.0] 7.144630 896253.7500 1.830796e-17
MAG [1.01669943333, -3.13182067871, 9.96583594315e... 7.144619 896249.1250 1.830797e-17
GSE [1.01669931412, -3.13182067871, 360.0] 7.144633 896250.1250 1.830796e-17
GSM [1.01669931412, -3.13182067871, 360.0] 7.144633 896241.0625 1.830796e-17
SM [1.01669931412, -3.13182067871, 360.0] 7.144633 896250.7500 1.830796e-17
RTN [1.01669943333, -3.13182067871, 360.0] 7.144630 896250.1250 1.830796e-17
GSEQ [1.01669931412, -3.13182067871, 360.0] 7.144633 896250.8750 1.830796e-17

The results are not so senstive to the change in coordinates because ENLIL’s scale is much larger than the differences in geocentric coordinate systems. We see larger changes for heliocentric coordinate interpolations:

helio_table = get_coordinate_table(kameleon,helio_coords,['br', 'rho', 'p'], (1.5e8, 0, 0))
helio_table
(150000000.0, 0, 0) ---> HNM[AU, lat, lon] br[nT] p[nPa] rho[kg/m3]
HEE [1.00268721581, -3.13182067871, 360.0] 7.523039 1.208926e+24 1.831418e-17
HAE [1.00268721581, -7.03282165527, 78.6580734253] 2.221460 1.208926e+24 7.569455e-18
HEEQ [1.00268721581, 0.0, 0.0] 7.432927 1.208926e+24 1.883335e-17

Tolerance considerations

There is a significant loss of precision when converting between helio and geocentric coordinates, due to the vastly different length scales. As a result, if one attempts to convert a position from helio to geocentric and back, you will incur an error of order 1. The code below is meant to illustrate this.

from pandas import DataFrame as df
import numpy as np
from collections import defaultdict
def test_conversion(start_coord, start_point, to_coords, time_et):
    table = defaultdict(list)

    to = ccmc.Position()
    back = ccmc.Position()

    start = ccmc.Position()
    start.c0, start.c1, start.c2 = start_point

    start_point = np.array([start.c0,start.c1,start.c2])
    print "converting", start_point, "from", start_coord, "to new point and back to", start_coord
    for t in to_coords:
        kameleon._cxform(start_coord,t, time_et, start,to)
        to_vec = np.array([to.c0,to.c1,to.c2])
        table["new_point"].append(to_vec)

        kameleon._cxform(t,start_coord, time_et, to, back)
        back_vec = np.array([back.c0,back.c1,back.c2])
        table["return_point in " + start_coord].append(back_vec)
        table["error"].append(np.linalg.norm(start_point - back_vec))

    table = df(table)
    table = table[["new_point","return_point in " + start_coord,"error"]]
#     table = df([table["new_point"], table["return_point"], table["error"]], index = to_coords)
    table.index = to_coords
    return table
test_conversion("GSE", start_point = (10, 0, 0),
                to_coords = geo_coords + helio_coords,
                time_et = 0)
converting [ 10.   0.   0.] from GSE to new point and back to GSE
new_point return_point in GSE error
J2000 [1.80101644993, -9.02481365204, -3.91268110275] [10.0, 7.8837850026e-08, 3.2981541942e-09] 7.890681e-08
GEI [1.80101644993, -9.02481365204, -3.91268110275] [10.0, 7.8837850026e-08, 3.2981541942e-09] 7.890681e-08
GEO [9.20181369781, 0.132480040193, -3.91268110275] [10.0, 1.26621149121e-08, 1.06196843319e-07] 1.069490e-07
MAG [3.44704961777, 8.77182579041, -3.34259176254] [10.0, -9.95483517841e-08, 3.51740894189e-08] 1.055798e-07
GSE [10.0, 0.0, 0.0] [10.0, 0.0, 0.0] 0.000000e+00
GSM [10.0, 0.0, 0.0] [10.0, 0.0, 0.0] 0.000000e+00
SM [9.42481231689, 0.0, -3.34259176254] [10.0, -2.07942907338e-08, 1.94201689396e-07] 1.953118e-07
RTN [-10.0, 0.0, 0.0] [10.0, 0.0, 0.0] 0.000000e+00
GSEQ [10.0, 0.0, 0.0] [10.0, 0.0, 0.0] 0.000000e+00
HEE [147101264.0, -1.22464679965e-15, 0.0] [15.5077991486, -1.80147079476e-08, 0.0] 5.507799e+00
HAE [-26493180.0, 144695872.0, 0.0] [8.40400218964, 0.419026881456, 0.0] 1.650089e+00
HEEQ [146897904.0, 3.72529029846e-09, -7732361.0] [9.60768127441, 0.000253342703218, 0.002190539... 3.923249e-01
test_conversion("HEEQ", start_point = (1, 0, 0),
                to_coords = geo_coords + helio_coords,
                time_et = 0)
converting [ 1.  0.  0.] from HEEQ to new point and back to HEEQ
new_point return_point in HEEQ error
J2000 [26493182.0, -132756168.0, -57556040.0] [-0.404457479715, 0.185022413731, 1.50997173786] 2.070447e+00
GEI [26493182.0, -132756168.0, -57556040.0] [-0.404457479715, 0.185022413731, 1.50997173786] 2.070447e+00
GEO [135359856.0, 1948798.25, -57556040.0] [0.934973955154, 0.0493004247546, 0.860102057457] 8.639644e-01
MAG [50706540.0, 129034680.0, -49169952.0] [1.4498347044, 0.676015079021, 0.923388004303] 1.229631e+00
GSE [147101280.0, 0.00603915005922, 0.0522168129683] [-0.488757014275, -1.78320043176e-08, 0.078364... 1.490818e+00
GSM [147101280.0, 0.0115641998127, 0.0512770526111] [-0.488757014275, -1.77362000642e-08, 0.078364... 1.490818e+00
SM [138640192.0, 0.0115641998127, -49169952.0] [-1.86519682407, 0.499917596579, 2.37058091164] 3.752189e+00
RTN [-147101280.0, 7.31750478735e-05, 0.0518711544... [-0.488793492317, 9.47769137838e-07, 0.0776719... 1.490818e+00
GSEQ [147101280.0, 3.08773196593e-05, 0.0525648742914] [-0.488757014275, -1.78933579065e-08, 0.078364... 1.490818e+00
HEE [0.998617529869, -0.00603915005922, 0.05221681... [1.0, 6.34189090132e-11, -1.06054776072e-09] 1.062442e-09
HAE [-0.173912256956, 0.983375787735, 0.0522168129... [1.0, 1.08513087405e-09, -4.08465317125e-10] 1.159462e-09
HEEQ [1.0, 0.0, 0.0] [1.0, 0.0, 0.0] 0.000000e+00