Ice and attenuation models

Ice model implementation

Ice models are the object in NuRadioMC that holds all the information of the ice needed to calculate the trajectory, namely: the refractive index at all the relevant points in space, boundary conditions and other special features that determine the ice medium. It can be found in the utilities module under medium.py and medium_base.py.

The IceModel and IceModel_Simple class

medium_base.py holds the framework of which all the specific ice models depends. The most basic class of ice models is the IceModel from which all final models should inherit directly or via some daughter classes. It represents a planar medium with a top and bottom boundary and in between a refractive index. A reflective bottom layer may be added as well.

class IceModel():
    def __init__(self,z_airBoundary=0*units.meter,z_bottom=None):
        self.z_airBoundary = z_airBoundary
        self.z_bottom = z_bottom

    def add_reflective_bottom(self,refl_z,refl_coef,refl_phase_shift):
        self.reflection = refl_z
        self.reflection_coefficient = refl_coef
        self.reflection_phase_shift = refl_phase_shift

    def get_index_of_refraction(self,position):
        return index_of_refraction_at_position

    def get_average_index_of_refraction(self,position1,position2):
        return average_index_of_refraction_between_position1_and_position2

    def get_gradient_of_index_of_refraction(self, position):
        return gradient_index_of_refraction_at_position

Besides this basic class, medium_base also holds already a daughter class IceModel_Simple. This class can be use to build a so called simple ice model which is a model with a planar geometry and a refractive index with an exponential profile depending on the depth in the ice. Mathematically this translates in:

\[n(z) = n_{ice} - \Delta_n \exp(z/z_0)\]

where z is the depth and \(n_{ice}\), \(\Delta_n\), math:`z_0 are the parameters of the model. As an example of how to implement a specific simple ice model into medium.py is illustrated below with the help of the greenland_simple ice model.

class greenland_simple(IceModel_Simple):
    def __init__(self):
        # from C. Deaconu, fit to data from Hawley '08, Alley '88
        # rho(z) = 917 - 602 * exp (-z/37.25), using n = 1 + 0.78 rho(z)/rho_0
        super().__init__(
            z_bottom = -3000*units.meter,
            n_ice = 1.78,
            z_0 = 37.25*units.meter,
            delta_n = 0.51)

RadioPropaIceWrapper

The analytic ray tracer can only handle simple ice models. For other models you need the RadioPropa ray tracer. However, for this to work, the model needs a translation into proper RadioPropa object. To facilitate this, the RadioPropaIceWrapper class is defined in medium_base.py. This class hold the index of refraction as a RadioPropa scalar field and the boundary conditions and special features in the relevant RadioPropa modules.

class RadioPropaIceWrapper():
    def __init__(self, ice_model_nuradio, scalar_field):
        self.__ice_model_nuradio = ice_model_nuradio
        self.__scalar_field = scalar_field
        # these are predined modules that are inherent to the ice model like
        # discontinuities in the refractive index, reflective or transmissive
        # layers, observers to confine the model in a certain space ...
        self.__modules = {}

        """
        here stands some code handling the first modules like air boundary and bottom boundary etc.
        """

    def get_modules(self):
        return self.__modules

    def get_module(self,name):
        return self.__modules[name]

    def add_module(self,name,module):
        self.__modules[name]=module

    def remove_module(self,name):
        self.__modules.pop(name)

    def replace_module(self,name,new_module):
        self.__modules[name] = new_module

    def get_scalar_field(self):
        return self.__scalar_field

The most important point is that the index of refraction has to be translated in a RadioPropa scalar field. For simple ice models all this is is handled automatically but for other models one needs to implement specific scalar field of the ice models in RadioPropa (IceModel.h and IceModel.cpp). To access the RadioPropaIceWrapper object from the ice model, an extra function is implemented in the IceModel that is inherited by all the daughter classes but should be adapted to the specific implemented ice models. For the IceModel_Simpe class this is already implemented and this is handled automatically when defining a new simple ice model.

import radiopropa as RP

class IceModel_Simple():
    ...

    def get_ice_model_radiopropa(self):
        scalar_field = RP.IceModel_Simple(z_surface=self.z_airBoundary*RP.meter/units.meter,
                                         n_ice=self.n_ice, delta_n=self.delta_n,
                                         z_0=self.z_0*RP.meter/units.meter,
                                         z_shift=self.z_shift*RP.meter/units.meter)
        return RadioPropaIceWrapper(self,scalar_field)

An example of the implementation of a non-simple model if given by greenland_firn in medium.py. This model completely depends on an implementation through RadioPropa because it can only be used with RadioPropa.

Available models in NuRadioMC

Simple ice models

In the table below we can find the different parameters for the simple ice refractive index models available in NuRadioMC.

Simple Ice Models

Name	\(n_{ice}\)	\(Delta_n\)	\(z_0$ [m]\)
southpole_simple (RICE2014/SP)	1.78	0.425	71
southpole_2015 (SPICE2015/SP)	1.78	0.423	77
ARAsim_southpole (as implemented in AraSim)	1.78	0.43	75.75
mooresbay_simple (MB1)	1.78	0.46	34.5
mooresbay_simple_2 (MB2)	1.78	0.481	37
greenland_simple	1.78	0.51	37.25

The models mooresbay_simple and mooresbay_simple_2 also contain a reflective layer at -576 m with a reflection coefficient of 0.82, mimicking the bottom layer of Ross Ice Shelf, in Antarctica.

RadioPropa ice models

Besides the simple ice models above, there is also one other ice model implemented: greenland_firn

Attenuation model

NuRadioMC has also three attenuation models available. These models provide attenuation lengths that are depth- and frequency-dependent.

• GL1, for Greenland.

• MB1, for Moore’s Bay.

• SP1, for South Pole.

Using specific models

Both the ice model and the attenuation model can be specified in the config file. As an example, if we want to use the greenland_simple ice model together with the GL1 attenuation, we have to write on the yaml configuration file:

propagation:
    ice_model: greenland_simple
    attenuation_model: GL1

Example script

The following snippet shows how the ice properties can be retrieved from NuRadioMC for an independent analysis.

from NuRadioMC.utilities import medium, attenuation
from NuRadioReco.utilities import units

# Retrieving refractive index at a point
ref_index_model = 'greenland_simple'

ref_index_medium = medium.get_ice_model(ref_index_model)
z_coordinate = -100 * units.m
antenna_position = [0, 0, z_coordinate]
index_at_antenna = ref_index_medium.get_index_of_refraction(antenna_position)

# Getting the attenuation length
attenuation_model = 'GL1'
frequency = 200 * units.MHz
depth = -100 * units.m

attenuation_length = attenuation.get_attenuation_length(depth, frequency, attenuation_model)

Birefringence Ice Models

Birefringence is an optional propagation setting in NuRadioMC which allows to simulate radio pulses propagating in anisotropic ice. The details about how the calculations in the propagation work can be found here (Heyer & Glaser, 2023). When using birefringence several options exist about what birefringence-ice-model to propagate in and what propagation code should be used for the propagation.

There are several example scripts available demonstrating all available (NuRadioMC/SignalProp/examples/birefringence_examples) functions when dealing with birefringent ice. Check read_me.txt for a more detailed description of the examples and data used.

Warning

Using this code assumes that the ice flow points in the positive x-direction. Therefore, a rotation of the detector geometry into this coordinate system might be necessary. This rotation can be done by either changing the source/antenna positions or by using the ‘angle_to_iceflow’ parameter in the config file.

Available Birefringence Ice Models

The anisotropy of the ice at the South Pole was published here: (Jordan et al., 2020)

The anisotropy of the ice in Greenland was published here: (RNO-G, 2022)

To use these ice models in NuRadioMC the measurement data was interpolated using splines. As the measurements don’t extend from the ice surface to bedrock or to account for measurement uncertainties, there is some freedom in how to interpolate the data. Different interpolations are indexed via capital letters, A always denoting the most reasonable interpolation. The files NuRadioMC/utilities/birefringence_models/IceModel_interpolation_southpole.py and NuRadioMC/utilities/birefringence_models/IceModel_interpolation_greenland.py can be used to adjust the interpolation method and come up with new ice models.

South Pole Birefringence Ice Models

Name	description
southpole_A	assumes a constant index of refraction at shallow and deep depths
southpole_B	assumes a converging index of refraction at shallow depths
southpole_C	no birefringence as nx = ny = nz
southpole_D	assumes a constant average over all depths
southpole_E	assumes ny and nz to be the same value at the average of the two

Greenland Birefringence Ice Models

Name	description
greenland_A	the most reasonable interpolation
greenland_B	assumes ny and nx to be the same value at the average of the two
greenland_C	assumes ny and nx to diverge more than the data indicates

Ice-Flow Direction

As birefringence acts in a very specific coordinate system defined by the flow of the ice, one has to be careful when defining source and antenna locations. The standard code assumes an ice flow in the x-direction. In NuRadioMC this corresponds to the east-direction. When defining a detector geometry in terms of northing and easting the angle between the ice-flow direction and the easting direction can be passed by using the angle_to_iceflow parameter in the config file. The angle is passed in degrees.

For the South Pole this angle is measured to be -131 degrees with an uncertainty of 2 degrees (Jordan et al., 2020). For Greenland this angle is measured to be roughly 180 degrees (Hawley et al., 2020).

Available Birefringence Propagation Options

There is an option to use RadioPropa (birefringence branch) to speed up the pulse propagation. If both the ray tracing and the birefringence pulse propagation should be handled by the analytical ray tracer, use analytical in the config file. If the ray tracing should be handled by the analytical ray tracer but the birefringence pulse propagation by RadioPropa, use numerical in the config file. There is also the option to handle everything in RadioPropa.

Currently, the RadioPropa implementation of birefringence only supports the birefringence-ice-model southpole_A.

Using specific birefringence models

Birefringence is an optional setting in a NuRadioMC simulation. To use it in a simulation the following lines should be added to the config file:

propagation:
    birefringence: True
    birefringence_propagation: 'analytical'
    birefringence_model: 'southpole_A'
    angle_to_iceflow: -131