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NAIRAS aircraft radiation model development, dose climatology, and initial validation

[1] The Nowcast of Atmospheric Ionizing Radiation for Aviation Safety (NAIRAS) is a real-time, global, physics-based model used to assess radiation exposure to commercial aircrews and passengers. The model is a free-running physics-based model in the sense that there are no adjustment factors applied to nudge the model into agreement with measurements. The model predicts dosimetric quantities in the atmosphere from both galactic cosmic rays (GCR) and solar energetic particles, including the response of the geomagnetic field to interplanetary dynamical processes and its subsequent influence on atmospheric dose. The focus of this paper is on atmospheric GCR exposure during geomagnetically quiet conditions, with three main objectives. First, provide detailed descriptions of the NAIRAS GCR transport and dosimetry methodologies. Second, present a climatology of effective dose and ambient dose equivalent rates at typical commercial airline altitudes representative of solar cycle maximum and solar cycle minimum conditions and spanning the full range of geomagnetic cutoff rigidities. Third, conduct an initial validation of the NAIRAS model by comparing predictions of ambient dose equivalent rates with tabulated reference measurement data and recent aircraft radiation measurements taken in 2008 during the minimum between solar cycle 23 and solar cycle 24. By applying the criterion of the International Commission on Radiation Units and Measurements (ICRU) on acceptable levels of aircraft radiation dose uncertainty for ambient dose equivalent greater than or equal to an annual dose of 1 mSv, the NAIRAS model is within 25% of the measured data, which fall within the ICRU acceptable uncertainty limit of 30%. The NAIRAS model predictions of ambient dose equivalent rate are generally within 50% of the measured data for any single-point comparison. The largest differences occur at low latitudes and high cutoffs, where the radiation dose level is low. Nevertheless, analysis suggests that these single-point differences will be within 30% when a new deterministic pion-initiated electromagnetic cascade code is integrated into NAIRAS, an effort which is currently underway.


Introduction
[2] The Earth's geospace environment is continuously bombarded by high-energy charged particles that penetrate deep within the atmosphere. Energetic particle radiation that reaches the upper troposphere and lower stratosphere adversely affects aircraft microelectronic systems and potentially the health of aircrew and passengers [IEC, 2006;Wilson, 2000]. This paper focuses on human exposure to this ionizing radiation field at commercial aircraft altitudes.
[3] The type of particle radiation with sufficient energy deposition characteristics to adversely affect human health is the so-called cosmic rays. There are two sources of cosmic rays: (1) galactic cosmic rays (GCR), which originate from outside the solar system and are always present, and (2) solar energetic particles (SEP) (or solar cosmic rays), which are transient events associated with eruptions on the Sun's surface lasting for several hours to days [Wilson et al., 1991;Gopalswamy et al., 2003]. Cosmic radiation is effective at directly breaking deoxyribonucleic acid (DNA) strands in tissue or producing chemically active radicals in biological tissue that alter cellular function. Both of these effects can lead to cancer or other adverse health outcomes [Wilson et al., 2003[Wilson et al., , 2005a. For example, adverse reproductive health disorders have been suggested by studies of female flight attendants [Aspholm et al., 1999;Lauria et al., 2006;Waters et al., 2000].
[4] Crews of commercial aircraft are classified as radiation workers by the International Commission on Radiological Protection (ICRP) [1991]. The United States (U.S.) National Council on Radiation Protection and Measurements (NCRP) reported that flight crews received the largest average effective dose in 2006 compared to other radiation workers monitored during the same study [NCRP, 2009]. A survey of radiation exposure of Air Canada pilots during solar cycle minimum showed that the majority of pilots received more than 1 mSv, which would require individual exposure assessment in some countries [Lindborg and Nikjoo, 2011], with the majority of the pilots receiving around 3 mSv and a few near 5 mSv [Bennett et al., 2013]. However, in most countries, aircrews are the only occupational group exposed to unquantified and undocumented levels of radiation over the duration of their career. Furthermore, the public and prenatal maximum exposure guidelines can be exceeded during a single SEP event for commercial passengers on intercontinental or polar routes, or even by frequent use ( 5-10 roundtrip flights per year) of these high-latitude routes during quiescent GCR exposure [AMS, 2007;Copeland et al., 2008;Dyer et al., 2009;Mertens et al., 2012].
[5] There is a recognized need to link scientific knowledge of the atmospheric ionizing radiation field to aviation decision making with respect to aircrew and passenger exposure to cosmic radiation [Fisher, 2009]. Kataoka et al. [2011] discussed the need for and conceptual requirements of atmospheric cosmic radiation forecast models, with particular focus on SEP events, while Stassinopoulos et al. [2003] emphasized the need for continuous global mapping of the atmospheric ionizing radiation field in order to improve aircraft radiation model performance. Cosmic radiation access to the neutral atmosphere is susceptible to spatial-temporal variability associated with complex magnetospheric and interplanetary processes, such as geomagnetic storms and the so-called Forbush decrease, which are not well represented in current models [Spurný et al., 2004;Getley, 2004;Getley et al., 2005].
[6] Significant advances in quantifying and documenting aircraft radiation exposure has been made via the models are driven by real-time measurement data in order to specify boundary conditions on the cosmic radiation at the interface between the distinct material media or to characterize the internal properties of the material media through which the cosmic radiation propagates. The realtime measurements provide observational constraints on the physics-based models that improve accuracy and reliability.
[9] This section contains a detailed description of the NAIRAS physics-based models and input measurement data used to describe the transport of GCR through the heliosphere, magnetosphere, and neutral atmosphere. The transport of GCR through the heliosphere is discussed in section 2.1. Transmission of GCR particles through the magnetosphere is described in section 2.2. The transport and transmutation of GCR through the neutral atmosphere are presented in section 2.3. The method of characterizing the internal properties of the atmosphere relevant to cosmic radiation transport is summarized in section 2.4. Finally, the dosimetric quantities and the method of quantifying human radiation exposure and biological risk are described in section 2.5.

Steady State Radially Symmetric Transport
[12] The specification of the GCR particle distribution at 1 AU in the H-BON10 model is based on steady state, radially symmetric transport through the heliosphere. Steady state is assumed to be achieved by a dynamical balance between inward diffusion, adiabatic energy loss, and outward convection by a constant solar wind speed. The equation that embodies this assumption is given by @ @r (r 2 U) -2r 3 @ @E (E (E)U) -@ @r ÄÂ Ä rr (r, E, t) V sw Ã r 2 @U @r = 0. (1) In the above equation, U is the differential number density of the GCR gas with respect to E, the kinetic energy per nucleon. The radial diffusion coefficient and constant solar wind speed are denoted Ä rr and V sw , respectively. The variable r is the radial distance from the Sun and the (E) factor is defined in (A11)-(A12).
[13] A detailed derivation of the GCR heliospheric transport equation and its reduction to a steady state, radial symmetric representation is presented in the Appendix. These details do not appear in previous publications on the Badhwar and O'Neill model [Badhwar and O'Neill, 1992, 1996O'Neill, 2006O'Neill, , 2010. Thus, the material in the Appendix will help elucidate the differences in the current GCR models used in space and atmospheric ionizing radiation applications [e.g., Mrigakshi et al., 2012;Matthiä et al., 2013;Zhao and Qin, 2013] and will also provide a reference description from which to facilitate future improvements in the physics of heliophysics GCR transport.
[14] In the Badhwar and O'Neill model, the steady state, radial transport equation in (1) is solved numerically given a specification of the key transport coefficient, which is defined as the ratio Ä rr /V sw , and given the boundary condition on the differential number density. The transport coefficient and boundary condition are discussed in the next section.

Transport Coefficient Parameterization and Boundary Condition
[15] The boundary condition on the steady state radial transport equation in (1) is given in terms of the differential local interstellar spectrum (LIS) at the outer extent of the heliosphere. The differential LIS of each GCR particle has been known to vary as a power law in total energy per nucleon (E + E 0 ) [O 'Neill, 2006]. Comparisons between the BON04 and BON10 models and NASA's Advanced Composition Explorer (ACE) GCR spectral flux measurements have demonstrated improvements in model accuracy if ǎ factor is also included in the differential LIS, whereˇis the ratio of the charged particle velocity (w) to the speed of light in vacuum (c). Thus, the differential LIS is assumed to have a functional form given by [O'Neill, 2006[O'Neill, , 2010 J LIS (E) = j 0ˇı (E + E 0 ) -. ( The free parameters ( , ı, and j 0 ) are determined by fitting the solutions of the steady state radial transport equation in (1) to ACE measurements, as described in more detail below. The differential LIS spectrum has units of spectral flux and is related to the differential number density in (1) by assuming a directionally isotropic distribution.
[16] The key transport coefficient in (1) is the ratio of the radial diffusion coefficient to the bulk solar wind speed. The diffusion coefficient can be expressed in terms of the scattering length such that Ä rr = (1/3)w , where (r, R, t) is a function of radial distance r, magnetic rigidity R, and time t [Axford, 1965;Gleeson and Axford, 1968]. Comparisons between solutions of the heliospheric GCR transport equation with GCR solar cycle modulation observed from surveys of neutron monitor data have shown that the spatial, rigidity, and temporal dependence of the scattering length can be factored into an analytical representation given by (r, R, t) = 0 (t)R(r/r 0 ) 2 for a heliospheric boundary defined to be r B = 50 AU [Quenby, 1967]. By combining these results, the functional form of the transport coefficient implemented in the BON04 and BON10 models is taken to be k(r, E, t) Á Ä rr (r, E, t)/V sw = (k 0 /V sw )ˇR(E) [1 + (r/r 0 ) 2 ] /ˆ(t). (4) In the above equation, the bulk solar wind speed V sw is set to 400 km/s for all time t; r is the distance from the sun in AU; t is time in years; k 0 and r 0 are constants given by 1.6 10 21 cm 2 /s and 4 AU, respectively; R is the particle's magnetic rigidity in MV (megavolts), which can be computed from the particle's kinetic energy per nucleon as shown in (14);ˆis the so-called solar modulation potential; anď has been previously defined. Thus, the time-dependent behavior of the heliospheric GCR particle distribution is completely embedded in the solar modulation potential. The solar modulation potential is physically related to the energy that interstellar GCR nuclei must have in order to overcome the heliospheric potential field, established by the large-scale structure of the interplanetary magnetic field carried by the solar wind, and propagate through the heliosphere to the radius r.
[17] It is important to note that the solar modulation potential is not a unique quantity and should not be directly compared between different models. For example, the solar modulation potential in the Burger-Usoskin model contains the time dependence in the solution of the steady state radial GCR transport equation as a result of the force field approximation [Usoskin et al., 2005;Burger et al., 2000]. In addition to the simplifications leading to the transport equation in (1), the force field approximation neglects the streaming of the cosmic ray gas [Gleeson and Axford, 1968]. Thus, the solar modulation potential is model-specific. Meaningful comparisons of different GCR models are made by directly comparing the charged particle spectra for the same date and time.
[18] The remainder of this section summarizes the method of deriving the solar modulation potential in the BON04 model, which forms the reference solar modulation potential for developing the real-time H-BON10 model implemented in NAIRAS.
[19] The solar modulation potential in (4) was determined by fitting the steady state solution of the radial transport equation in (1) for a specified GCR nucleus to corresponding spectral flux measurements throughout the solar cycle, given a heliospheric outer boundary of r B = 50AU and the functional form for the boundary condition on the differential number density and transport coefficient parameterization in (2)-(4) [O'Neill, 2006[O'Neill, , 2010. Specifically, by using a well-known, fixed parameterization of the differential LIS, the solar modulation potential was determined by fitting the solution of the steady state radial transport equation for oxygen nuclei to measurements of the corresponding spectral flux. For energies below roughly 1 GeV (i.e., 50-500 MeV/nucleon), the measurement data were obtained from the Cosmic Ray Isotope Spectrometer (CRIS) instrument on the NASA/ACE satellite [Stone et al., 1998]. For higher energies (1-35 GeV), the model was fit to data from the C2 instrument on the NASA High Energy Astrophysical Observatory (HEAO-3) satellite [Englemann et al. 1990].
[20] Once the solar modulation potential was derived based on the ACE/CRIS oxygen spectra, as described in the above paragraph, the free parameters ( , ı, and j 0 ) in the differential LIS for the remaining heavy-ion elements (i.e., lithium (Z = 3) through nickel (Z = 28)) were similarly determined by fitting the solutions of the steady state radial transport equation to the CRIS spectral flux measurements below 1 GeV and HEAO-3 spectral flux measurements above 1 GeV, as described above. The proton and alpha spectra in the BON04 model were fit to IMP-8 data; high-energy proton and alpha spectra were fit to the balloon-borne Isotope Matter-Antimatter Experiment (IMAX) measurements [Menn et al., 2000].
[21] The BON04 GCR model was extended beyond the time period of the ACE/CRIS measurements in the following way [O'Neill, 2006], since the ACE satellite has only been operational since 1997. First, the solar modulation potential was alternatively derived from the IMP-8 channel 7 (Z > 8, high energy) measurements over three solar cycles from 1973 through 2001 and was calibrated against the solar modulation potential derived from ACE/CRIS for the period of data overlap (1997.6 to 2001.8). GCR flux comparisons using both sets of solar modulation potential correlated to within 98.9%. Next, linear fit coefficients were derived between the IMP-8 solar modulation potential and Climax neutron monitor count rates from 1973 to 2001. The solar modulation potential computed using the Climax neutron count rates correlated with the solar modulation potential derived from IMP-8 data to within 97%. Three sets of linear fit coefficients were derived corresponding to the three polarity states of the solar polar magnetic field: (1) positive solar cycle (outward directed magnetic field), (2) negative solar cycle (inward directed magnetic field), and (3) transition state (intermediate between positive and negative polarities with a high degree of modulation). The solar modulation potential determined from Climax neutron count rates, using the derived linear fit coefficients, was computed from 1958-2005 and made available with the BON04 code distribution. This extended Climax-based solar modulation potential, i.e., computed over the period 1958-2005, provides the reference solar modulation potential which is used to derive a real-time GCR model suitable for integration into the NAIRAS model.

Figure 1. (top) Daily-average neutron monitor count rates from the Izmiran, Lomnicky, Thule, and Oulu sites. (bottom) Daily-average H-BON10 solar modulation potential (ˆ(t))
determined from linear fits to the corresponding neutron monitor counts rates shown in the top. The BON04 reference solar modulation potentials determined from fits to the Climax neutron monitor data (ˆC LIMAX ) and NASA/ACE measurements (ˆA CE ) are also shown. . These high-latitude sites were chosen to maximize the solar cycle modulation information embedded in the GCR spectrum, which must also be reflected in the ground-level neutron count rates. The neutrons detected on the ground are secondary particles produced by nuclear fragmentation reactions between the incident GCR particles and the constituents of the neutral atmosphere [Wilson et al., 1991]. The geomagnetic shielding of the incident GCR particles is low at high latitudes. As a result, at high latitudes where R vc < 1 GV, the sensitivity of the ground-level neutron counts rates to the lower energy region of the GCR spectrum (< 10 GeV) is maximum. This is highly desirable since the lower energy range of the GCR spectrum is modulated the most by the interplanetary magnetic field carried by the solar wind, with the maximum in the GCR spectrum at 1 AU occurring around 500 MeV/n. Thus, solar modulation associated with solar cycle activity strongly influences the GCR spectrum with energies < 10 GeV [Mertens et al., 2012].

Real-Time GCR Model
[24] The H-BON10 solar modulation potential parameterization was developed by deriving linear fit coefficients between the Climax-based solar modulation potential (denotedˆC LIMAX ) and the count rates measured at the four high-latitude neutron monitor sites mentioned above. Figure 1 shows the daily-averaged count rates from the four high-latitude neutron monitor stations. Also shown are the BON04 reference Climax-based solar modulation potential (ˆC LIMAX ) and the BON04 solar modulation potential derived from NASA/ACE measurements (denotedˆA CE ). Linear fits were derived betweenˆC LIMAX and neutron counts rates obtained from each of the four high-latitude neutron monitor sites using all the data available from the beginning of operation of each site through 2005. For the Izmiran and Thule sites, this included more than four solar cycles of data. The Oulu data coverage was slightly less than this, while two solar cycles of data were available from Lomnicky. The derived fit coefficients are given in Table 1, and the solar modulation potential predicted by each neutron monitor site is shown in Figure 1.
[25] As discussed several times before, the heliospheric GCR diffusion coefficient depends on the large-scale structure of the interplanetary magnetic field carried by the solar wind [Parker, 1965]. As a result, the transport coefficient in (4) will depend on the polarity of the Sun's polar magnetic field [O'Neill, 2006]. Consequently, to improve the accuracy of the neutron count rate fits to the referenceˆC LIMAX , the neutron data were sorted according to the solar polar magnetic field polarity. Thus, three sets of fit coefficients were derived: (1) positive solar cycle (outward directed field), (2) negative solar cycle (inward directed magnetic field), and (3) transition state (intermediate between positive and negative polarities with a high degree of modulation), as described previously for theˆC LIMAX reference solar modulation potential. The parameterizations in Table 1 Figure 2 shows the WSO low-pass filtered solar polar magnetic field strength data for the northern solar hemisphere, the negative of the southern hemisphere solar polar magnetic field strength, and the average solar polar magnetic field strength. When all three of these field strength data are positive, the Sun's polar magnetic field polarity is taken to be positive. Likewise, when all three of these field strength data are negative, the Sun's polar magnetic field polarity is taken to be negative. If at least one of these three field strength quantities has a different sign compared to another, the polarity of the Sun's polar magnetic field is taken to be in the transitional state, as shown in Figure  [28] Once the polarity of the solar polar magnetic field is determined, the appropriate sets of linear fit coefficients in Table 1 are selected to compute, separately, solar modulation potentials for as many of the four high-latitude neutron monitor data as are available for the time period in question. These solar modulation potentials are averaged, and the average value is used to specify the transport coefficient in (4). Finally, given the transport coefficient, the GCR spectra at 1 AU for each nucleus from hydrogen (Z = 1) through nickel (Z = 28) is obtained by solving the steady state radial transport equation in (1). This comprises the key features of the H-BON10 GCR model.

Magnetospheric GCR Transport
[29] The H-BON10 model described in the previous section transports the cosmic ray gas through the heliosphere to 1 AU and specifies incident GCR spectral flux outside of the Earth's magnetosphere. The lower energy cosmic rays are essentially attenuated by the geomagnetic field, which includes an internal field component plus magnetospheric contributions, as these charged particles are transported through the magnetosphere and into the neutral atmosphere. The attenuation of charged particle transport by the geomagnetic field is a form of momentum shielding in the sense that the lower energy particles are deflected back out to space via the Lorentz force.
[30] GCR transport through the magnetosphere can be described in terms of a geomagnetic transmission function such that In the above equation,ˆi(r B , , E) is the spectral flux of GCR particle type i at the top of the neutral atmosphere (r B ) moving in direction with energy E; J i (E) is the isotropic spectral flux of GCR particle type i with energy E outside the magnetosphere (i.e., (2)), given by the H-BON10 model described in the previous section; and T i (r B ; , E; 0 , E 0 ) is the geomagnetic transmission function, which represents the probability that a charged particle type i with energy E 0 and moving in direction 0 outside the magnetosphere will be moving in direction with energy E at the top of the neutral atmosphere (r B ) after propagating through the magnetosphere.
[31] The geomagnetic transmission function is assumed to be factorable into a product of a spatial projection function and an energy transmission function, such that where H(x) is the Heavyside step function defined by H(x) = 1 if x > 0; otherwise, H(x) = 0. From the above representation of the energy transmission function, a charged particle i with energy greater than a cutoff energy E c,i is transported without energy loss through the magnetosphere to position r B in the neutral atmosphere with direction . On the other hand, particle i with energy less than or equal to E c,i does not arrive at location r B with direction . The geomagnetic cutoff rigidity R c in (6) is the canonical variable in quantifying the momentum shielding effect of the geomagnetic field. Once the cutoff rigidity is known, the cutoff energy E c,i for any charged particle i can be easily computed. The geomagnetic cutoff rigidity will be discussed in more detail below.
The angles Â and in the above equation are the polar and azimuthal angles, respectively, for a coordinate system with the z axis directed along the local vertical direction at location r B . By projecting along the local vertical direction r B , an effective 1-D transport procedure can be developed. In this case, By substituting (6)-(7) and (9) into (5), the specification of the incident GCR spectral flux at the top of the neutral atmosphere along the local vertical direction becomeŝ Since the GCR particles outside the magnetosphere have been projected along the local vertical axis, the cutoff energies and rigidity in (10) are given in terms of vertical cutoffs, as denoted by the subscript v.
[33] The relevance of the geomagnetic cutoff rigidity in quantifying charged particle transport through the magnetosphere is evident by considering the motion of a charged particle in a magnetic field. The trajectory of a Figure 3. Global grid of vertical geomagnetic cutoff rigidities (GV) calculated from charged particle trajectory simulations in the IGRF field for 2008.

charged particle in a magnetic field is determined by solving Newton's equation of motion with the external force supplied by the Lorentz force. For a positively charged particle, the equation of motion is
in cgs units. The quantity designates the vector cross product. The charged particle momentum and velocity are p and v, respectively, and B is the magnetic flux density. The magnitude of the charge of an electron is denoted e, and Z is the number of electron charge units. Equivalently, the equation of motion in (11) can be written as where the O symbol denotes units vectors, and is defined as the rigidity. The canonical aspect of the rigidity is now evident from the form of the equation of motion given in (12): Charged particles with the same rigidity follow identical trajectories for a given magnetic flux density (B).
[34] Based on the above discussion, the vertical geomagnetic cutoff rigidity R vc (r B ) in (10) is the minimum rigidity that a vertically arriving charged particle must have to reach the location r B . Consequently, charged particles with energies less than the cutoff energy (E vc,i ) will be deflected by the Lorentz force and not reach the location r B in the vertical direction. The cutoff energy for each charged particle type i with charge number Z i and mass number A i is calculated from the canonical cutoff rigidity using the relativistic energy equation, such that where E vc,i is the cutoff kinetic energy per nucleon (MeV/n) for particle type i, R vc is vertical geomagnetic cutoff rigidity (MV), c is the speed of light in vacuum, and amu = 931.5 MeV/c 2 (atomic mass unit). In effect, the geomagnetic field filters out lower energy charged particles as they are transported through the magnetosphere and into the neutral atmosphere.
[ [36] Figure 3 shows the global grid of vertical geomagnetic cutoff rigidities at 20 km in the internal IGRF magnetic field. The cutoffs are shown for 2008, the year of NAIRAS model comparisons with onboard aircraft radiation measurements presented in section 3.3. The vector cross product in the Lorentz force in (11) has the following effect: charged particle motions perpendicular to magnetic field lines will experience the maximum deflection; particle motions parallel to the magnetic field will experience no deflecting force whatsoever. Consequently, the maximum cutoff rigidity is at the magnetic equator Figure 4. Zonal-averaged vertical geomagnetic cutoff rigidity (GV) computed from charged particle trajectory simulations in the IGRF field. and the minimum cutoff rigidity is at the magnetic poles. The longitudinal variations in the cutoff rigidity arise from two sources: (1) geocentric offset and relative tilt of the magnetic dipole, with respect to the Earth's rotational axis, and (2) the nondipolar contributions to the internal geomagnetic field.
[37] Decadal and zonal-average vertical geomagnetic cutoff rigidities in the IGRF field are shown in Figure 4. From this figure it is evident that a vertically arriving proton at the equator must have a kinetic energy of 15 GeV in order to have access to the neutral atmosphere. In the polar regions, vertically arriving charged particles are parallel to the magnetic field lines. Therefore, the cutoff rigidity is zero; particles of all energies have access to the neutral atmosphere in this case. The slight temporal changes in the cutoffs are due to a combination of shifts in the location of the Earth's magnetic poles and a weakening of the magnetic dipole field. On geological timescales, these changes are quite rapid. In regards to the dose rate climatology presented in section 3.1, the changes are small. Thus, annual to decadal variations in GCR dose rates at fixed pressure levels are dominated by changes in the level of solar cycle activity rather than changes in geomagnetic cutoff.

Atmospheric GCR Transport
[38] The transport of cosmic rays through the neutral atmosphere is described by a coupled system of linear, steady state Boltzmann transport equations [Wilson et al., 1991]. The transport equation for the spectral flux j (x, , E) of particle type j is given by [Mertens et al., 2012] rˆj where j (E) and jk ( , 0 , E, E 0 ) are the projectile-target macroscopic interaction cross sections. The jk ( , 0 , E, E 0 ) are double-differential particle production cross sections that represent all processes by which type k particles moving in direction 0 with energy E 0 produce a particle of type j moving in direction with energy E, including radioactive decay processes. The total interaction cross section j (E) for each incident particle type j is where the first term refers to projectile collisions with atomic electrons of the target medium, the second term refers to elastic ion-nucleus scattering or elastic neutronnucleus scattering, and the third term contains all relevant nuclear reactions. The corresponding differential cross sections are similarly ordered.
[39] The principal mechanism for atomic interactions between the cosmic ray ions and the target medium of the atmospheric constituents is ionization and/or atomic excitation. This process is represented by the first term in (16). The result of this interaction is the transfer of energy [40] The range of an ion is the mean path length traveled in the target medium before coming to rest after losing its initial kinetic energy through ionization and/or atomic excitation energy loss. In the CSDA, the range is defined by where A j is the atomic mass number of ion particle type j. The above equation is referred to as the range-energy relation.
[41] Two approximations are made to the total ion-target interaction cross section in (16). First, elastic ion-nucleus scattering is neglected for cosmic ray transport through the atmosphere [Mertens et al., 2012]. Second, the CSDA is invoked in the representation of atomic ion-electron energy transfer collisions. As a consequence of these two approximations, the coupled Boltzmann transport equations in (15) can be expressed, alternatively, as The B[ˆj] in the above equations denote a differential operator acting on the spectral flux.
[42] The differential operator in (18) can be inverted using the method of characteristics in order to transform the integro-differential equation into a Volterra-type integral equation [Wilson, 1977]. As a result, the integral equation for cosmic ray transport through a material medium is given bŷ In the above equation, ,x is a position vector of a point on the boundary surface and E is given by The R -1 j operator in (21) is the inverse operation of obtaining the energy given the range using the range-energy relation in (17). The expression for the integral cosmic ray transport equation in (20) was made compact by introducing the total nuclear survival probability, which is defined by The first term in ( [44] The computation methods employed in HZETRN to solve the coupled cosmic ray integral transport equations in (20) are summarized below. The details are given in the references. The numerical procedures fall into two categories based on the fundamental physics of cosmic ray projectile-target nuclear interactions. The first category is heavy-ion transport. Ion beam experiments have shown that projectile fragments have a velocity and direction very near to that of the incident heavy-ion projectile [Wilson, 1977;Wilson et al., 1995a]. The observation of forward directed projectile fragments is the basis of the socalled straight-ahead approximation, where the integral over solid angle in (20) is neglected and the transport is reduced to one dimension along the direction of the incident heavy-ion beam. Moreover, the observation of equal velocity between the heavy-ion projectile and the projectile fragment suggests a delta function energy dependence in the projectile fragment production cross section, which effectively eliminates the integral over dE 00 on the righthand side of (20).
[45] In addition to the approximations discussed in the previous paragraph, the target fragments are produced at low energy and distributed nearly isotropically. At low energy, the target fragments do not travel far before coming to rest due to ionization energy loss. These observations justify a decoupling of the target and projectile fragments in the source term on the right-hand side of (20). The advantage of this decoupling is that the target fragments can be neglected in the heavy-ion transport procedure. The absence of the target fragments in the heavy-ion transport solution means that the summation over k type particles in (20) involves only projectiles with masses greater than the mass of the type j particle (i.e., P k>j ). These approximations enable a rapidly converging self-consistent solution of projectile fragment heavy-ion transport using backsubstitution and perturbation theory. The contribution of the target fragments to the dosimetric quantities is included using the approach described by Wilson et al. [1993]. Slaba et al. [2010aSlaba et al. [ , 2010b have recently made significant improvements in the accuracy and computational efficiency of HZETRN's heavy-ion numerical transport procedures.
[46] The numerical transport solution for light-particle trajectories does not permit the same approximations that were employed in solving (20) for heavy-ion transport. In HZETRN, light particles are defined as particles with charge number Z Ä 2 and mass number A Ä 4. There are six light particles: five charged particles (protons, deuterons, tritons, helium-3, and helium-4) and neutrons. One of the added complexities in the numerical solution of light-particle transport is that the equal velocity relationship between projectile and projectile fragments is no longer valid. Thus, the energy integral over dE 00 on the right-hand side of (20) must be explicitly evaluated. In addition, the light-particle numerical transport procedure must include both the projectile and target fragments. Finally, the straight-ahead approximation cannot be employed either, which means that the integral over solid angle in (20) must be evaluated. Directional effects are especially important for low-energy neutron transport. approach is to decompose the light-particle spectral flux into an isotropic component and a straight-ahead component. The transport solution for the straight-ahead component is described by Slaba et al. [2010aSlaba et al. [ , 2010b. The neutron spectral flux itself is decomposed into semi-isotropic forward and backward components. The numerical approach for this so-called directionally coupled forward-backward neutron transport scheme is described by Slaba et al. [2010cSlaba et al. [ , 2010d. These same references also describe the solution of the charged particle isotropic component: the key approximation is to assume that the source term originates from nuclear fragmentation reactions between the target medium and the low-energy semi-isotropic neutrons, which turns out to be a good approximation

Meteorological Data
[49] This section briefly summarizes the important characteristics of the atmospheric state that are relevant to cosmic ray transport. Incident charged particles are shielded by the atmosphere itself, which is a function of the overhead mass at a given altitude. Subdaily global atmospheric depth is derived from the following: (1) pressure versus geopotential height data and (2) pressure versus temperature data. These data are obtained from the National Center for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) Reanalysis 1 project [Kalnay et al., 1996]. This project utilizes a state-of-theart analysis/forecast system to perform data assimilation [51] The relevant vertical coordinate in atmospheric ionizing radiation transport is atmospheric depth. Atmospheric depth (g/cm 2 ) at each horizontal grid point and altitude level is computed by integrating the mass density vertically from a given altitude to the top of the atmosphere. The mass density is computed from the ideal gas law using the temperature and pressure data at each altitude level. This step produces a 3-D gridded field of atmospheric depth.
[52] Representative atmospheric data are shown in

Dosimetric Quantities
[53] The energy deposited in a target medium by the radiation field of particle j is the dose, which is given by In the above equation, S j (E) is the target stopping power for particle j (Mev/g/cm 2 ), F j (x, E) is the spectral fluence for particle j (cm 2 MeV) -1 , and K is a unit conversion factor (1.602 10 -10 ) to convert dose to units of Gray (1 Gy = J/kg). Radiation health risk and the probability of biological damage depend not only on the absorbed dose but also on the particle type and energy of the radiation causing the dose. This is taken into account by weighting the tissue-averaged absorbed dose by a factor related to the quality of the radiation. The weighted tissue-averaged absorbed dose has been given the name equivalent dose by the ICRP [1991]. The unit of equivalent dose is the Sievert (Sv). Equivalent dose in tissue T from particle j, denoted H j,T , is defined in terms of the radiation weighting factor w j , such that  where D j,T denotes absorbed dose from particle j averaged over the tissue T. The radiation weighting factor is also a function of energy for neutrons [ICRP, 1991].
[54] The relationship between the probability of biological damage and equivalent dose depends also on the organ or tissue irradiated. The effective dose is an additional dosimetric quantity defined such that it includes the relative contributions of each organ or tissue to the total biological detriment caused by the radiation field. The effective dose, denoted E, is the sum of weighted equivalent dose in all the organs and tissues in the human body, such that The origan and/or tissue weighting factors are listed in the ICRP 60 report [ICRP, 1991].
[55] All ICRP recommended radiation exposure limits are expressed in terms of effective dose. The effective dose is not a measurable quantity, however. The ICRP/ICRU recommended operational quantity for radiation protection applications is ambient dose equivalent [ICRP, 2007; ICRU, 2010], which is denoted as H * (d) and defined as the dose equivalent that would be produced by the corresponding expanded and aligned field at a depth d in millimeters along the radius vector of a 300 mm diameter spherical tissue-equivalent phantom material opposing the direction of the aligned field. The ambient dose equivalent at a depth of 10 mm, H * (10), is recommended and widely used as a reasonable operational proxy for effective dose.
[56] The ambient dose equivalent is defined in terms of dose equivalent, which is not quite the same as the equivalent dose in (26). Equivalent dose is defined as the tissue-averaged absorbed dose weight by a discrete radi-

ation quality factor. Dose equivalent, on the other hand, is defined at a point x and is computed in terms of a continuous radiation quality factor. Specifically, the dose equivalent in tissue T from particle j (H j,T (x)) is defined in terms of the tissue LET-dependent quality factor Q, such that
where L is LET (linear energy transfer), which can be approximated by the stopping power in units of keV/m; D j (x, L) is the LET-spectral dose distribution absorbed in tissue T from particle j, and Q(L) is the tissue LETdependent quality factor [ICRP, 1991].
[57] It should be noted that ambient dose equivalent overestimates effective dose in most workplace radiation fields. However, ambient dose equivalent is not a conservative estimate for cosmic radiation exposure at aviation altitudes [Pelliccioni, 2000]. Nevertheless, it is still generally regarded as an acceptable approximation for effective dose at aircraft altitudes as well [Meier et al., 2009].
[58] Microdosimeters provide an "observation" of ambient dose equivalent by measuring the LET spectrum of absorbed dose in a tissue-equivalent material, followed by a conversion of the observed LET spectrum to H * (10) using the radiation quality factor in (26) and calibration coefficients from laboratory comparisons against a known dose equivalent source [ICRU, 2010].
[59] The dosimetric quantities computed by the NAIRAS model are effective dose rate, ambient dose equivalent rate, and absorbed dose rate in silicon. The effective dose rate is the primary quantity provided to the NAIRAS stakeholders for radiation risk assessment and radiation exposure mitigation. The ambient dose equivalent rate (dH * (10)/dt) is provided for [60] The NAIRAS model calculates the dosimetric quantities from the particle spectral fluence rates. The effective dose rate and ambient dose equivalent rate are calculated using precomputed fluence-to-effective dose and fluence-to-ambient dose equivalent conversion coefficients, respectively. The NAIRAS model uses neutron and proton conversion coefficients tabulated by Ferrari et al. [1997a, 1997b]. The contributions to these dosimetric quantities from the other GCR and SEP ions are obtained by scaling the proton conversion coefficients by Z 2 j,eff /A j , according to the stopping power dependence on charge and mass [Mertens et al., , 2012. The effective charge of particle j, i.e., Z j,eff , takes into account electron capture by heavy ions at low kinetic energies [Tai et al., 1997]. The absorbed dose rate in silicon is calculated at zero depth from (23) using the stopping power in silicon.

Results and Discussion
[61] NAIRAS predictions of GCR aircraft radiation exposure rates are presented and analyzed. In section 3.1, a climatology of dosimetric quantities representative of solar cycle maximum and solar cycle minimum conditions is developed. Monthly-mean dose rates computed from the NAIRAS model are compared to reference measurement data in section 3.2 for the three solar polar magnetic field polarity states discussed previously. NAIRAS model dose rates are also compared to onboard aircraft radiation measurements taken during the recent solar cycle minimum, which is discussed in section 3.3. A summary and overall assessment of the NAIRAS model validation is given in section 3.4.

Atmospheric Dose Rate Climatology
[62] Five decades of annual-averaged GCR atmospheric dosimetric quantities were computed from 1960 to 2010. In this case, neutron count rates from Izmiran and Thule were used to compute the solar modulation potential, [66] The geomagnetic shielding effects on the solar modulation of the atmospheric dosimetric quantities described above can be understood as follows. Spectral filtering of the incident GCR spectrum by the geomagnetic field at the equator excludes all but the high-energy cosmic rays from gaining access to the neutral atmosphere. From Figure 4, for example, only protons with energies greater than 15 GeV can penetrate the geomagnetic field and gain access to the neutral atmosphere. The high-energy GCR particles are minimally modulated by the interplanetary medium, as evident from Figures 6 and 7. For example, there is less than a 20% difference in the dosimetric quantities between solar minimum and solar maximum conditions at the equator. However, the representative solar minimum and solar maximum dosimetric quantities differ by about a factor of 2 in the polar regions. In the polar regions there is virtually no momentum shielding by the geomagnetic field, which maximizes the variation in the atmospheric dosimetric quantities due to the modulation of the heliospheric GCR spectrum by the interplanetary medium. At 30 ı latitude (north or south), the dosimetric quantities for solar minimum are about 30% greater than the dosimetric quantities at solar maximum.
[67] The dose rate climatology is shown in Figures 8 and   9 as a function vertical geomagnetic cutoff rigidity. In this representation, the global grid of effective dose and ambient dose equivalent rates for solar maximum and solar minimum conditions were averaged in intervals of 1 GV in vertical geomagnetic cutoff rigidity. This representation of the dose rate climatology provides useful reference data for documenting the full range of NAIRAS GCR predictions at typical commercial aircraft altitudes, as well as provides a useful dataset for benchmarking NAIRAS results against other models and measurements.

Reference Aircraft Radiation Measurements
[68] Figure  within˙50% for the three flight levels, the full range of cutoff rigidities, and solar activity characteristics. NAIRAS underestimates the ICRU dose rates by about 60% for the highest cutoff rigidities at FL390. Despite a few exceptions, it is interesting to note that the NAIRAS/ICRU dose rate differences for cutoff rigidities between 0 and 4 GV are usually within˙25%. This range of cutoff rigidity corresponds to latitudes poleward of about 30 ı . In the equatorial region, the dose rates are quite low. Therefore, the dose rate differences are generally within˙25% except in the subtropical and equator regions where the radiation exposure is at its minimum. The relevance of this point will be revisited in section 3.4.
[71] The dose rate variation with altitude can be quantitatively compared using Tables 2-4. As an example, consider Table 2 the January 1998 solar cycle minimum case. The slope of ambient dose equivalent rate versus flight level at zero cutoff rigidity over the range FL310 to FL390 is 0.0412 Sv/(h 100 ft) for the ICRU reference data. The dose rate slope given by the NAIRAS model for the same conditions is 0.0238 Sv/(h 100 ft). Thus, the dose rates of the ICRU data in the polar region are increasing with altitude by a factor of 2 greater than the NAIRAS dose rates. The differences in altitude variation of dose between NAIRAS and ICRU data are even greater in the equatorial region where the geomagnetic cutoff rigidity is high. At 13 GV cutoff, for example, the ICRU slope of ambient dose equivalent rate versus flight level is 0.0112 Sv/(h 100 ft), while the corresponding slope from the NAIRAS model is 0.0013 Sv/(h 100 ft). It is noted that the dose rate variations with respect to altitude from the aircraft radiation measurements taken in 2006-2008 during solar cycle minimum are consistent with the ICRU reference data [Meier et al., 2009].
[72] Off-line numerical simulations suggest that the underprediction of NAIRAS dosimetric quantities at high cutoff rigidities is partly due to /EM electromagnetic cascade processes that are currently not included in the HZETRN 2010 version. The /EM processes can also partially explain the smaller variation in NAIRAS dose rates versus flight level relative to the ICRU reference data. This is discussed in more detail in the next section.
[73] Figures 11 and 12 show the NAIRAS profiles of effective dose and ambient dose equivalent rates for the vertical geomagnetic cutoff rigidities and solar activity characteristics corresponding to Figure 10. The horizontal lines indicate the three flight levels in Figure 10 on the U.S. Standard Atmosphere altitude grid. Although these three flight levels cover the range of cruising altitudes for typical commercial aircraft, it is clear from these figures that measurements over a broader altitude range are required to provide a comprehensive assessment of the model performance, since the particle composition and spectral flux of the ionizing radiation field varies as a function of atmospheric depth (see Figures 22  and 23).   [76] The Liulin-6G MDU was manufactured at the

Solar-Terrestrial Influences Laboratory of the Bulgarian Academy of Sciences in Sofia. The Liulin MDU was orig-
inally developed for and successfully tested onboard aircraft [Dachev, 2009]. It is designed as a hand-held device and consists of a silicon diode (2.31 cm 2 , thickness 300 m), a charge-sensitive preamplifier (A225 by AMPTEK), a discriminator, a 12 bit analog-to-digital converter (ADC), two microcontrollers, a flash memory (2.0 MB), LCD display, and Li-ion cells (3.6 V, 1.8 Ah, LR1865PC type). Pulse height analysis technique is used to measure the energy deposition of charged particles in the detector. The amplitude of the pulses after the preamplifier processing is proportional to the energy loss. These amplitudes are digitized by the ADC and arranged in a 256-channel spectrum. The total energy loss in the detector is proportional to the channel-number-weighted sum of the number of counts in each channel. The absorbed dose rate is determined by dividing the total energy loss in the detector by the data collection time and multiplying this quantity by a constant that includes calibration and unit conversion factors [Stassinopoulos et al., 2002].
[77] The hourly-average and annual-average solar modulation potentials are shown in Figure 13   [79] The DUS-MRU 1 min TEPC measurements were averaged over roughly 1 h intervals and compared with NAIRAS hourly-average predictions. These results are shown in Figure 16. The NAIRAS ambient dose equivalent rates are systematically biased low relative to the TEPC data. Quantitative NAIRAS/TEPC comparisons are given in Table 5  [83] There are two features of the NAIRAS/TEPC and NAIRAS/Liulin differences that are discussed below. One, the measurement and model differences are largest at low latitudes and high geomagnetic cutoff rigidities. Two, NAIRAS/Liulin differences are significantly larger than the NAIRAS/TEPC differences, indicating that errors in charged particle transport dominate over neutron transport in the NAIRAS model. Off-line model simulations suggest that pion-initiated electromagnetic cascade processes, denoted by /EM, can partially explain these features. Pions in the atmosphere are produced by nuclear reactions between the primary cosmic ray particles and the constituents of the neutral atmosphere. The charged pions decay into muons, and the neutral pion decays into high-energy photons. The muons subsequently decay into electrons and positrons. The electrons, positrons, and photons interact with the atmospheric constituents producing more electrons, positrons, and photons, generating an electromagnetic cascade. The /EM processes will increase the charge particle component of the ionizing radiation field and will be comparatively more important at low latitudes and high geomagnetic cutoff rigidities where the primary GCR spectrum is dominated by highenergy ions with sufficient energy to create a copious number of pions.
[84] Figures 22 and 23 show the particle contributions to absorbed dose in silicon and tissue dose equivalent at 0 GV and 15 GV vertical geomagnetic cutoff rigidities, respectively. The particle contributions include the /EM generated particles using the deterministic code developed by Norman et al. [2012Norman et al. [ , 2013, and dose equivalent at zero depth in tissue is used as a proxy for ambient dose equivalent. Figure 22, representative of high latitudes, shows that /EM processes contribute less than 15% to tissue dose equivalent at commercial airline cruising altitudes but up to 50% of absorbed dose in silicon. Therefore, model errors in charged particle transport will have a larger influence on absorbed dose in a thin material, such as a silicon detector, compared to tissue dose equivalent. These features are enhanced at low latitudes and high cutoff rigidities. For the representative case shown in Figure 23, the /EM processes contribute up to 25% to tissue dose equivalent at typical cruising altitudes of commercial aircraft, while the contribution to absorbed dose in silicon can be as much as 70%.
[85] The particle contributions to tissue dose equivalent, shown in Figures 22 and 23 for two representative cutoff rigidities, were used to estimate the likely /EM contributions to the NAIRAS ambient dose equivalent   recently developed an empirical GCR model that is also suited for real-time applications. This model was shown to be more accurate than the BON10 when compared to heavy-ion flux measurements, even during the recent period of solar cycle minimum.
[90] One common element in the above discussion is that although the BON10 outperforms most models considered, it is still not fully capturing the increased GCR flux during the recent deep solar cycle minimum. However, the NAIRAS model dose rates are in good agreement with the DLR high-latitude aircraft radiation measurements presented in this section. It is important in assessing the overall NAIRAS model performance to know if the H-BON10 model, in addition to its use in real-time applications, provides an improvement in accuracy over the BON10 model or if there is cancelation of errors such that the accurate NAIRAS predictions at high latitudes is accidental. As a result, the subject of future work will include separate comparisons between H-BON10 and other widely available helisopheric GCR models. Furthermore, new radiation measurements on high-altitude balloon platforms will be taken during the These are some of the steps that will be taken to continue the assessment and advancement of the NAIRAS model.

Validation Assessment
[91] The ICRU has made recommendations on the acceptance levels for total uncertainty in radiation protection measurements and assessments of dose [ICRU, 1992[ICRU, , 2001]. These recommendations are broadly consistent with ICRP statements. For aircraft cosmic radiation exposure at flight altitudes, the combined relative standard uncertainty should not exceed 30% for an assessment of ambient dose equivalent equal to or greater than an annual dose of 1 mSv [ICRU, 2010].
[92] The above ICRU criterion on acceptable uncertainty in dose assessment was applied to the NAIRAS comparisons in the following way. The model/measurement differences in Tables 2-6 were averaged together for dose rates that would equate to or exceed an annual ambient dose equivalent of 1 mSv. The annual dose was estimated by multiplying the measurements of the ambient dose equivalent rates in Tables 2-6  . To be conservative, 800 block hours was assumed. This is a reasonable upper limit since 817 hours was the longest annual pilot flight time recorded in the recent survey of radiation exposure to Air Canada pilots [Bennett et al., 2013]. As a result, the model/measurement differences in Tables 2-6 were averaged together for all measurements of ambient dose equivalent rates that exceeded 1.25 Sv/h. Equivalently, the model/measurement differences in the tables were averaged together for geomagnetic cutoff rigidities less than or equal to 10 GV. By applying the ICRU criterion to the NAIRAS/measurement comparisons in Tables 2-6, as described above, the combined uncertainty in the NAIRAS prediction of ambient dose equivalent rate is within 25%.
[93] It is estimated, based on the discussion in the previous section, that the NAIRAS model uncertainty for GCR conditions will be roughly within 30% for any single-point comparison, irrespective of an annual dose greater than or equal to 1 mSv, after the /EM code is included in the HZETRN 2015 version and subsequently integrated into the NAIRAS model. This expectation will be quantitatively assessed in the near future.

Summary and Conclusions
[94] A detailed description of the NAIRAS model was given, focusing on GCR transport and dosimetry under quiet geomagnetic conditions. Transport through the heliosphere is based on the H-BON10 model, which was developed for real-time applications by parameterizing the solar modulation potential in the BON10 model in terms of high-latitude neutron monitor data. The transport and interactions between the primary GCR particles and the constituents of the neutral atmosphere are modeled using the HZETRN version 2010 code. The NAIRAS model computes the fundamental spectral flux for neutrons and 58 other fully ionized nuclear isotopes ranging from hydrogen through nickel. The particle flux spectra, in turn, are used to compute the primary dosimetric quantities that are important for radiation protection applications and model verification and validation-namely, effective dose rate, ambient dose equivalent rate, and absorbed dose rate in silicon. NAIRAS is a free-running physics-based model in the sense that no adjustment factors are applied to nudge the model into agreement with measurement data.
[95] Five decades of global, annual-average dose rates, computed by the NAIRAS model, were used to construct a climatology of effective dose and ambient dose equivalent rates representative of solar maximum and solar minimum conditions. Both the effective dose and ambient dose equivalent rates are on the order of 1 Sv/h at the equator for typical commercial airline cruising altitudes, with a roughly 20% variation between solar maximum and solar minimum. The dose rates in the polar region differ by about a factor of 2 between solar maximum and solar minimum at airline flight levels. For solar maximum, the effective dose and ambient dose equivalent rates at aircraft altitudes in the polar region are in the range of 4-5 Sv/h and 3-4 Sv/h, respectively. The effective dose and ambient dose equivalent rates at airline altitudes are in the range 9-10 Sv/h and 7-8 Sv/h, respectively, for solar minimum conditions in the polar region.
[96] The NAIRAS model predictions of GCR atmospheric radiation dose rates were compared with ICRU tabulated reference measurement data [ICRU, 2010] and compared to onboard aircraft radiation measurements taken in 2008. The ICRU reference measurements covered the typical range of commercial aircraft cruising altitudes and the full range of geomagnetic cutoff rigidities and solar cycle activity characteristics. The NAIRAS/ICRU comparisons of ambient dose equivalent rate were generally within˙50% for any single-point comparison and generally within 25% at cutoff rigidities less than 4 GV (or latitudes poleward of 30 ı ). Radiation measurements taken by DLR in 2008 on a high-latitude and a low-latitude flight during the minimum between solar cycle 23 and solar cycle 24 were also analyzed. The two DLR flight measurements covered the range of geomagnetic cutoff rigidities at commercial aircraft flight levels. The NAIRAS/DLR-TEPC comparisons of ambient dose equivalent rates were generally within 10% for the high-latitude flight and roughly within 50% for the low-latitude flight.
[97] The ICRU criterion on acceptable uncertainty in dose assessment of aircraft ionizing radiation exposure at commercial flight levels is that the combined relative standard uncertainty should not exceed 30% for an assessment of ambient dose equivalent equal to or greater than an annual dose of 1 mSv. When this criterion is applied to the combined NAIRAS/ICRU and NAIRAS/DLR comparisons, the model/measurement differences are within 25%. Therefore, based on the ICRU/ICRP criterion, the NAIRAS model can be reliably used in commercial aircraft radiation risk assessment and radiation mitigation decisions for GCR exposure.
[98] Due to limited availability and accessibility to aircraft radiation measurements during solar-geomagnetic storms, NAIRAS model predictions of SEP atmospheric radiation exposure have not yet been validated. Continuous aircraft radiation measurements on select highlatitude flights would quickly close the measurement data gap that is prohibiting the development and validation of accurate and reliable aircraft radiation model predictions during radiation and geomagnetic storms.
[99] The largest differences between the NAIRAS model GCR atmospheric dose predictions and the aircraft radiation measurements presented in this paper consistently occurred at low latitudes where the geomagnetic cutoff rigidity is high. The NAIRAS/Liulin comparisons of absorbed dose rate in silicon, combined with off-line model simulations, revealed that /EM processes missing in the HZETRN 2010 version can partially explain the underprediction of the NAIRAS model at high cutoff rigidities. Model simulations also estimate that including the /EM processes can increase NAIRAS model calculations of ambient dose equivalent by 20% or more for high cutoff rigidities, suggesting that NAIRAS model/measurement differences may be within 30% for any single-point comparison. This expectation will be explicitly evaluated when the HZETRN version 2015, which will include the electromagnetic cascade particles via the deterministic /EM code, is integrated into the NAIRAS model. Part of the HZETRN-/EM validation of atmospheric dosimetric quantities calculated by the NAIRAS model will include comparisons with dosimetric quantities computed using the PARMA analytic functions.
[100] In the meantime, there are a number of upcoming opportunities to continue NAIRAS model validation activities. The Automated Radiation Measurements for Aviation Safety (ARMAS) project, funded by the NASA Small Business Innovation Research (SBIR) Program and led by Space Environment Technologies, will conduct 50 or more hours of radiation dosimetry measurements on a NASA DC-8 aircraft. The dosimetry measurements will be taken by a Hawk version 2.0 TEPC and a total ionizing dose detector (TID) developed by The Aerospace Corporation and manufactured by Teledyne microelectronic technologies [Mazur et al., 2011]. The NASA Minority University Research and Education (MUREP) program has funded a project to conduct microdosimetry measurements in microgravity. The dosimetry measurements collected by the ARMAS project and the MUREP program will be compared to NAIRAS model predictions for a range of altitudes not included in the ICRU and DLR measurement data. Furthermore, H-BON10, developed specifically for the NAIRAS model, will be compared to other widely available heliospheric GCR models, in order to isolate NAIRAS model uncertainty in specifying the GCR spectral flux outside the geospace environment. This effort will be complemented by the dosimetry measurements taken from a high-altitude balloon platform during the NASA Radiation Dosimetry Experiment (RaD-X) flight mission, currently scheduled for 2015. These model comparisons and measurement campaigns will broaden the assessment of the NAIRAS model performance, which will inevitably lead to further improvements in accuracy and reliability.
condition for negligible radial current density is met (i.e., Á 1), the cosmic radiation differential number density is approximated by   U(r, E; t) U(r B , E)M(r, r B , E; t)=U(r B , E) where M is the solar modulation function of Balasubrahmanyan et al. [1967].
[110] However, the Gleeson and Axford [1968] condition is not met at charged particle kinetic energies on the order of 400 MeV/n or less for protons, which is near the peak in the modulated GCR spectrum at 1 AU. This is based on R 1 AU, which seems to be supported by analysis of neutron monitor data [Gleeson and Axford, 1968]. The characteristic radial variation in the Badhwar and O'Neill diffusion coefficient, on the other hand, is roughly 8-9 AU (see section 2.1.2), which is due to r 0 = 4 AU in (4). The value of r 0 in the Badhwar and O'Neill model was not derived based on physical arguments but was simply determined from best fit comparisons to measurement data [O'Neill, 2006]. Nevertheless, the main point is that at low enough energy, radial streaming of the cosmic ray gas is no longer negligible. In the Badhwar and O'Neill model, the radial current density is not assumed to be negligible and adiabatic energy loss is included in the solution of the radial transport equation, which is represented by the second term in the equation below.
[111] In addition to the assumption of radial symmetry, the steady state heliospheric GCR transport equation in the Badhwar and O'Neill model also assumes a constant solar wind speed. In this case, equation (A14) reduces to @ @r (r 2 U) -2r 3 @ @E (E (E)U) -@ @r ÄÂ Ä rr (r, E, t) V sw Ã r 2 @U @r = 0. (A18) The above equation is solved numerically given a specification of the key transport coefficient, which is defined as the ratio Ä rr /V sw , and given the boundary condition on the differential number density, as described in sections 2.1.2 and 2.1.3.