The Martian surface radiation environment – a comparison of models and MSL / RAD measurements

Context: The Radiation Assessment Detector (RAD) on the Mars Science Laboratory (MSL) has been measuring the radiation environment on the surface of Mars since August 6th 2012. MSL-RAD is the first instrument to provide detailed information about charged and neutral particle spectra and dose rates on the Martian surface, and one of the primary objectives of the RAD investigation is to help improve and validate current radiation transport models. Aims: Applying different numerical transport models with boundary conditions derived from the MSL-RAD environment the goal of this work was to both provide predictions for the particle spectra and the radiation exposure on the Martian surface complementing the RAD sensitive range and, at the same time, validate the results with the experimental data, where applicable. Such validated models can be used to predict dose rates for future manned missions as well as for performing shield optimization studies. Methods: Several particle transport models (GEANT4, PHITS, HZETRN/OLTARIS) were used to predict the particle flux and the corresponding radiation environment caused by galactic cosmic radiation on Mars. From the calculated particle spectra the dose rates on the surface are estimated. Results: Calculations of particle spectra and dose rates induced by galactic cosmic radiation on the Martian surface are presented. Although good agreement is found in many cases for the different transport codes, GEANT4, PHITS, and HZETRN/OLTARIS, some models still show large, sometimes order of magnitude discrepancies in certain particle spectra. We have found that RAD data is helping to make better choices of input parameters and physical models. Elements of these validated models can be applied to more detailed studies on how the radiation environment is influenced by solar modulation, Martian atmosphere and soil, and changes due to the Martian seasonal pressure cycle. By extending the range of the calculated particle spectra with respect to the experimental data additional information about the radiation environment is gained, and the contribution of different particle species to the dose is estimated.


Introduction
The Mars Science Laboratory (Grotzinger et al. 2012) -Radiation Assessment Detector (MSL-RAD; Hassler et al. 2012) detector on board the Curiosity rover has been the first instrument to measure particle spectra and dose rates both during the cruise to Mars (Zeitlin et al. 2013;Guo et al. 2015;Köhler et al. 2015) and on the Martian surface (Ehresmann et al. 2014;Hassler et al. 2014;Köhler et al. 2014;Rafkin et al. 2014).Besides the continuous exposure to galactic cosmic radiation (GCR), the MSL-RAD instrument has measured several moderate solar energetic particle events during the cruise phase, from December 2011 to July 2012, and a few small solar particle events on the Martian surface since August 2012.During cruise, these events contributed approximately 5% to the total dose equivalents (Zeitlin et al. 2013), and since arriving at Mars, the contribution of the events to the observed total dose has been small (Hassler et al. 2014).In this paper, we therefore focus on the GCR spectra and their contribution to total radiation dose and dose equivalent.For the determination of the radiation exposure for different mission scenarios and the mitigation of the radiation risk of astronauts during such missions, numerical models are of great value as they allow, for instance, optimization of shielding conditions or selection of appropriate launching schedules (Cucinotta et al. 2010(Cucinotta et al. , 2011)).Additionally, models are not only helpful for prospective mission analysis but are also able to extend and complement the measurements that were performed and thereby broaden our understanding of the radiation field by, for instance, extending the energy range of the particle fluxes or providing estimates of particle fluxes and dose rates for arbitrary atmospheric, or human fabricated shielding scenarios as well as for different solar modulation.Comparing measured particle fluxes, especially neutrons, with model predictions may also provide information about the composition of the atmosphere and soil of Mars.
In order to estimate the health risk of astronauts it is of great importance to have detailed information about the particle spectra.The dose concept commonly used in radiation protection on Earth might not describe adequately the biological effects of irradiation with heavy ions (National Research Council 1967) as encountered in space and on lightly shielded planetary surfaces.Even the quality factor, Q, used to describe the increased biological effectiveness of high charge and energy ions as compared to gamma rays, may not adequately describe carcinogenesis risk or impacts on the central nervous system and other degenerative tissue effects.It is therefore essential to know the energy spectra of each particle type as accurately as possible in order to apply suitable radiation risk concepts.
As stated above, during low solar activity (solar minimum) galactic cosmic radiation and secondary particles created by them are the main contributors to the radiation environment on the surface of Mars (Dartnell et al. 2007;Ehresmann 2012) and in the present work we focus on this aspect and do not discuss the influence of solar energetic particle events which will be covered in future work.Several numerical models exist that can calculate the transport of primary nuclei from the GCR through the Martian atmosphere and the backscattering from the soil.The following models are investigated in this work: HZETRN/OLTARIS (Wilson et al. 1991;Slaba et al. 2010aSlaba et al. , 2010bSlaba et al. , 2013;;Singleterry et al. 2011;Norman et al. 2013), GEANT4/PLANETOCOSMICS (Agostinelli et al. 2003;Allison et al. 2006), and PHITS (Niita et al. 2006;Sato et al. 2013).These transport models, which are discussed in more detail below, have to be combined with models of the primary GCR spectra taking into account the solar modulation.Following recent studies evaluating different GCR models concerning their applicability for the calculation of radiation exposure (Mrigakshi et al. 2012(Mrigakshi et al. , 2013b;;Slaba & Blattnig 2014)  The MSL-RAD instrument is, among other things, capable of measuring gamma and neutron spectra (Köhler et al. 2014) and several types of charged particles (Ehresmann et al. 2014).The published results of the first ~200 sols (1 solar day, sol, on Mars is about 24 h and 39 min long) on the Martian surface (between August 2012 and January 2013) are used in this work for a validation of the different numerical radiation transport models.While several publications exist in the literature in which different simulation models and tools have been used to estimate the radiation exposure in interplanetary space during a cruise to Mars (e.g.McKenna-Lawlor et al. 2012b), in the atmosphere and on the surface of Mars (e.g.Simonsen et al. 1990;Townsend et al. 2011;Kim et al. 2014;Gronoff et al. 2015), few data are available on predicted particle spectra.However, comparing such data with measurements gives deeper insight into the accuracy of the modeling of the underlying physical processes.Dose rate comparisons, on the other hand, may be misleading because the dose rate is obtained by integrating over different particle species and wide energy ranges.Thus, agreement in dose rate of model predictions and measurements for a certain scenario is less valuable for model validation in a given exposure scenario than is agreement in energy-dependent particle flux.In this work we make use of data provided by MSL-RAD to benchmark the transport models for the prediction accuracy of secondary particle fluxes as well as resulting dose rates.

The MSL-RAD measurements on the Martian surface
The Radiation Assessment Detector (RAD) has been conducting the first-ever radiation measurements on the Martian surface as part of NASA's Mars Science Laboratory (MSL) mission.RAD has been measuring almost continuously since the successful landing of the Curiosity rover in Gale crater on 6 August 2012, for large parts operating in a 100% duty cycle with a 16-or 32-minute operating cadence.
The time frame considered for this research spans from 18 August 2012 to 30 January 2013, or from sol 13 to 173 in MSL terminology.We compare the presented simulation results with particle spectra measured by RAD during this time period as published in Ehresmann et al. (2014) and Köhler et al. (2014).Measurements made by the Rover Environmental Monitoring Station (REMS; Gómez-Elvira et al. 2014) show that the average atmospheric column depth above the rover in this time frame was ~21-22 g/cm 2 (Haberle et al. 2014).In this work we used an atmospheric depth of 22 g/cm 2 for our simulation setup.

The RAD sensor head
The RAD sensor head (RSH, a schematic is shown in Fig. 1) contains a stack of detectors for charged and neutral particle measurements: three Si detectors (named A, B, and C), a CsI scintillator (D), and two plastic scintillators (E and F).A detailed description of the RSH can be found in Hassler et al. (2012).

Measurements of particle spectra, dose, and LET
Neutral particles are measured in D and E, with C and F acting as anticoincidence against charged particles (see Köhler et al. 2014 for details of the neutral particle measurements).Using an inversion technique, we are able to derive separate spectra for c-rays and neutrons, as both D and E have different sensitivities for those particle types.
For purposes of charged particle detection all detectors are used (a description of the charged particle measurement process is given by Ehresmann et al. 2014).Here, A and B act as a telescope defining the acceptance cone for incoming charged particles.RAD analysis distinguishes between two types of charged particles: particles penetrating the RSH and those that stop in either one of detectors B, C, D, or E. Stopping particles can be resolved as energy-and particle-typedependent spectra, while integral fluxes are derived for the different species of penetrating particles.The full opening angle for stopping particles is ~60°from the upper hemisphere, while particles penetrating the RSH have a full acceptance angle of 36°from both upper and lower hemisphere, although the fraction of penetrating particles coming from the lower half, the Martian soil, is estimated to be almost negligibly small (McKenna-Lawlor et al. 2012a).
RAD measures the absorbed radiation dose in two detectors: B (made of silicon) and E (tissue-equivalent plastic), both with a 4p acceptance angle.To derive the biologically-relevant dose equivalent from the absorbed dose, the typical approach is to use the average quality factor hQi of the incoming radiation for conversion.As described by Zeitlin et al. (2013), the quality factor is dependent on the linear energy transfer (LET) spectrum of the radiation, and thus the average hQi can be obtained by knowledge of this LET spectrum.RAD measures the LET in silicon in detector B in coincidence with detector A to limit the possible path length of the particles in the detector; the LET in silicon is then scaled to (approximate) LET in water for purposes of the quality factor calculation.

Galactic cosmic ray model
The main source of ionizing radiation in deep space is galactic cosmic radiation and, although MSL-RAD has measured several solar energetic particle events during its cruise phase and on the Martian surface, the present work is limited to investigations of the GCR induced radiation.Mrigakshi et al. (2012Mrigakshi et al. ( , 2013aMrigakshi et al. ( , 2013b) ) and Slaba et al. (2014) have investigated several models suitable as input for the calculation of radiation exposure in space and found that the most suitable models currently available are BO-10 model (O'Neill 2010) and the DLR model (Matthiä et al. 2013).GCR consists mainly of fully ionized atomic nuclei of which about 87% are hydrogen, 12% helium, and about 1% heavier nuclei (Simpson 1983).There is a slight dependence of the relative abundances on the solar cycle.Despite their comparably low intensity, heavy ions have a great impact on the radiation exposure in space due to their high biological relevance (Durante & Cucinotta 2008).In general, the contributions of primary nuclei up to atomic numbers of Z = 26 (Fe) are sufficient to estimate the radiation exposure to humans from GCR. Iron in particular is of great importance for the dose equivalent due to its high biological relevance in combination with its relatively high abundance (Simpson 1983).In this work, contributions of all nuclei from hydrogen up to iron were considered.
Figure 2 illustrates the primary GCR spectra of hydrogen (Z = 1), helium (Z = 2), carbon (Z = 6), and iron (Z = 26) as described by the two models used in this work: BO-10 and DLR.In order to benchmark the primary GCR models and the transport of particles through the Martian atmosphere the solar modulation for the time period of measurements (August 2012-January 2013) was considered in the GCR models.The modulation parameter / during this period was between 533 MV and 643 MV (cf.http://cosmicrays.oulu.fi/phi/Phi_mon.txt).Although Mrigakshi et al. (2013a) found differences of more than 20% in the estimated dose rates comparing the two GCR models during solar minimum periods, the primary spectra for the time of the MSL-RAD measurements considered here are very similar.Calculations of particle spectra and radiation exposure with PHITS and GEANT4 performed in this work showed that the differences arising from the application of the two GCR models for this period of solar modulation are small, yielding differences in the dose rates on the order of a few percent.The results shown below are limited to the results using the DLR model in case of PHITS and GEANT4, and to the BO-10 model in case of HZETRN/ OLTARIS.The Mars-GRAM 2001 atmospheric model consists of multiple layers with different mass densities.Each layer consists of 95.7 mass % CO 2 , 2.7 mass % N, and 1.6 mass % Ar.Starting at a total atmospheric height of 90 km, we set the soil and detector level at the surface to a depth of 22 g/cm 2 , corresponding to the mean atmospheric column density within the comparison time frame from DOY 232 2012 to DOY 48 2013 at the MSL rover.The mean pressure data is derived from the Mars Climate Database (MCD 5.0).For PHITS a pure CO 2 atmosphere with the same depth was used.Calculations performed with GEANT4 using the two atmospheric compositions did not result in a significant change in secondary particle intensities and dose rate.
The Martian soil composition is modeled based on the regolith definition in OLTARIS.It has a density of 1.7 g/cm 3 with molecular percentages given in Table 1.For all simulations the soil thickness was at least 20 m.

GEANT4/PLANETOCOSMICS
GEANT4 (GEometry And Tracking) (Agostinelli et al. 2003;Allison et al. 2006) is a Monte-Carlo method based toolkit capable of calculating the transport of particles through matter.PLANETOCOSMICS (http://cosray.unibe.ch/laurent/planetocosmics/) is a GEANT4 application providing geometries and descriptions of planetary atmospheres, soils, and magnetospheres, for instance for Earth and Mars, and can be used to calculate the transport of arbitrary primary particles in and through these planetary environments and the creation of secondary particles.To obtain the results presented in this work GEANT4 version 10.p02 was used.GEANT4 provides a large number of so-called physics lists describing the interactions of particles with matter.One of the goals of this work is to investigate the applicability of different physics lists for the calculation of secondary particle spectra and dose rates on the Martian surface or on planetary surfaces in general.In the lower part of Table 2 an overview of the different selections of physics lists in GEANT4 is given.These lists were selected according to the recommendations given by the GEANT4 community for such an application.The different lists are mainly related to inelastic hadronic (nucleon or nuclear) interactions.For electromagnetic interactions the most precise standard list (emstandard_opt3) was selected.The application of an advanced list for electromagnetic interactions (emstan-dard_opt4) for one selected hadronic list did not affect the resulting dose rates or particle spectra.Comparison with these RAD data has resulted in improved selection of physics lists, and the differences arising from the selection of physics lists are discussed below.For the calculation with GEANT4 primary nuclei from hydrogen (Z = 1) to nickel were used (Z = 28).
For the calculations reported here, we used data from the Oulu neutron monitor (Usoskin et al. 2011) to determine a linear relation between neutron monitor count rates and u for 2012.This procedure is valid provided that the range of count rates is small, as it was in the period considered.The relationship was applied to Oulu neutron monitor count rate data from 2013 to determine monthly u values, so that we have a consistent set of values for the duration of the MSL mission from launch to present.Averaging over sols 13-173, we find an average u value of 577 MV.The results generated from HZETRN presented herein can also now be generated with the ''On-Line Tool for the Assessment of Radiation in Space'' (OLTARIS; Singleterry et al. 2011), and are labeled as HZETRN/OLTARIS in the following plots and tables.The only exceptions are the photon, pion, muon, electron, and positron results which are not yet available through the website.
In addition, we also show earlier results from the OLTARIS framework which were presented in Ehresmann et al. (2014) and obtained in 2013.These results are labeled as OLTARIS2013.
An important difference between the OLTARIS2013 and HZETRN/OLTARIS results presented herein is the geometry setup used in the OLTARIS2013 calculations.In those earlier calculations, the Martian geometry was represented by a 21 g/cm 2 sphere of CO 2 .Albedo particles were not included, and large off-vertical atmosphere thicknesses were not represented.The HZETRN/OLTARIS results, on the other hand, account for albedo neutrons and longer off-vertical atmospheric thicknesses in the ray-by-ray transport procedure, as described by Slaba et al. (2013).The comparison to the results from 2013 is performed in order to illustrate both the development of the code since the publication of the first charged particle spectra measured on the Martian surface (Ehresmann et al. 2014) and the limitations of the simplified geometry in the early calculations (21 g/cm 2 sphere of CO 2 ). ) was adopted in the simulation.The total nucleon-nucleus interaction cross-sections were calculated by a model specially adjusted for high-energy particle transport simulations (Sato et al. 2014).An updated version of the quantum molecular dynamics model, JQMD (Niita et al. 1995), was used for simulating nucleus-nucleus interactions.The charge and energy of primary particles were determined using the same model employed in the GEANT4 simulation.In the PHITS simulation, all primary and secondary particles were traced down to 1 MeV, except for neutrons, electrons, positrons, and photons, where the cut-off energy of neutrons was set to 0.1 meV and that for the others to 10 keV.

Calculation of dose rates
Particle spectra calculated with the different transport codes and primary input spectra were used to estimate the radiation exposure on Martian ground.The results were compared to the measurements of MSL-RAD.In order to convert the particle fluxes on ground to the dose rates, pre-calculated fluence-to-dose conversion factors were used.These conversion factors were the same for all transport codes which means that differences in the calculated dose rates originate in the transport models only.GEANT4 was used to calculate the conversion factors for different dose quantities: absorbed dose in silicon, absorbed dose in tissue, and dose equivalent in tissue.Figure 3a shows the conversion factors from fluence to dose in tissue and in silicon and to dose equivalent exemplarily for a-particles.The dose equivalent can be calculated by multiplying the dose in tissue with the quality factor Q (Fig. 3c) defined by the ICRP (ICRP 1991(ICRP , 2007)).Q is a function of the unrestricted LET in water (Fig. 3b).
The quality factor is used to weight the energy deposition with the biological impact which is LET dependent.

Neutral particle spectra
Figure 4 shows the calculated and measured neutron (4a) and photon fluxes (4b).The results of GEANT4 that are shown here were obtained with physics list setup [1] from  In Figure 4b the calculated photon spectra are compared to the MSL-RAD measurements.Again, GEANT4, HZETRN/ OLTARIS, and PHITS data are compatible.The photon results from HZETRN/OLTARIS appear to deviate from the Monte-Carlo results above 1 GeV by about one order of magnitude and below 10 MeV.The discrepancies at energies above 1 GeV are associated mainly with differing neutral pion production models, where the HZETRN/OLTARIS model needs improvement.The HZETRN/OLTARIS model also does not currently include photon production from nuclear collisions, explaining the underestimate below 10 MeV.

Charged particle spectra
Figures 5-10 show the calculated charged particle spectra and the values measured by the RAD instrument (Ehresmann et al. 2014).The particle fluxes in Figures 5-9 from PHITS, HZETRN/OLTARIS, and GEANT4 are averaged over the acceptance angle for the determination of the charged particle fluxes with RAD, i.e. zenith angles below 30°.OLTARIS2013 data is averaged over the upper hemisphere, i.e. zenith angles below 90°.Particle fluxes in Figure 10 are averaged over all incident angles.The averaged particle fluxes over all incident angles can be significantly different, especially at high energies where most or even all particles are incident at small zenith angles and there are very few or no albedo particles.
Figures 5 and 6 contain the spectra of: protons, deuterons, tritons, 3 He, and 4 He-particles.The energy range is limited to E < 110 MeV/n to facilitate a comparison to the RAD data.In Figure 7 the same data is illustrated for a much wider energy range up to 20 GeV/n.The GEANT4 results were obtained using the Intranuclear Cascade Model of Liège (INCL; Boudard et al. 2002;Leray et al. 2013;Mancusi et al. 2014) (setup [1] from Table 2) as it was found in this work that using other nuclear interaction models available in GEANT4 did not result in secondary hydrogen and helium isotope production comparable to the RAD measurements.In general, good agreement between GEANT4 predictions and RAD data is found for the lighter nuclei shown in Figures 5 and 6, with the exception of 3 He for which the measured flux seems to be underestimated by almost one order of magnitude by GEANT4 at energies above 20 MeV/n.PHITS reproduces the measured deuteron flux nicely but shows large discrepancies in case of the other nuclei.Especially for triton and 3 He the calculated values are more than one order of magnitude lower than the measurements.
Although all codes appear to overestimate the measured proton results, the results of HZETRN/OLTARIS are the largest of the model results.This is caused in part by differing nuclear models as well as by the lack of 3D effects in this version of HZETRN.Future work could use the 3DHZETRN code (Wilson et al. 2014(Wilson et al. , 2015) ) to gauge the impact of 3D corrections for these atmospheric/surface scenarios.The tendency of all models to overestimate the measured proton spectra, especially at these energies, might also be attributable to uncertainties in the primary GCR spectrum and atmospheric composition and thickness.
For deuterons, all codes appear to have better agreement with the measured results.However, the HZETRN/OLTARIS results are again larger than all other results, pointing to differing nuclear models and 3D effects not accounted for in this set of calculations.
The largest model errors (more than a factor of 10) occur for tritons and 3 He which are not present in the modeled primary GCR.Therefore, these model spectra are purely secondary reaction products.The HZETRN/OLTARIS results again provide the largest values; the overestimate is associated mainly with a cluster-knockout model (Cucinotta et al. 1996) that appears to need further study and improvement.On the other hand, PHITS results appear to underestimate the measurement by about the same amount as HZETRN/OLTARIS overestimates.Geant4 is also below the measured values.
Comparing the results for the light nuclei at high energies (Fig. 7) it is obvious that there is a good agreement between the different codes only for particles which are dominated by the primary components: protons and alpha particles.At high energies the flux of these particles is very similar to the flux of primaries on top of the Martian atmosphere.For deuterons, tritons, and 3 He, on the other hand, the differences between the models can reach almost an order of magnitude.As the RAD instrument cannot provide data at these energies it is not possible to decide which of the predictions is the more accurate.However, the contribution of these isotopes to the total dose is small and the effect of the differences in the particle flux on the total radiation exposure is negligible as will be shown below.
For the fluxes of heavier nuclei on the surface of Mars (Figs. 8 and 9) we observe a reasonable agreement between GEANT4, PHITS, OLTARIS, HZETRN/OLTARIS and the MSL-RAD data for nuclei up to aluminum (Z = 13) upper three panels in Figure 8.For the group of silicon to chromium (Z = 14-24) GEANT4 reveals good agreement with the measurement: OLTARIS2013 and HZETRN/OLTARIS seem to be compatible and PHITS overestimates the measured data.For nuclei with Z > 24 all codes seem to underestimate the experimental data.However, the low number of high-Z particles leads to a comparatively large statistical uncertainty in the measurement.At higher energies (Fig. 9) GEANT4 data is significantly higher than the results of the other models for the groups of (Li, Be, B), Z = 9-13 and Z > 24.
Figure 10 shows the calculated particle spectra for electrons/positrons (e À , e + ), muons (l À , l + ), and pions (p À , p + ).For these particles no measurement is currently available.The comparison of the models providing information about these particles (GEANT4, PHITS, and HZETRN/OLTARIS) shows good agreement for electrons and positrons over almost the whole energy range.For muons, however, agreement is only observed at energies above 1 GeV and for pions at energies above 3 GeV.At lower energies the calculated particle spectra differ by several orders of magnitude.

Dose rate
Figure 11 and Table 2 summarize the results of the calculation of dose rates on the Martian surface and the comparison to the RAD measurements.In Figure 11, the contribution of different particle species to the total dose rates calculated with the different transport models is illustrated.The results from GEANT4 shown in Figure 11 were obtained with the physics list setup [1] for which the best agreement with the measured particle flux was found.For OLTARIS2013 for which only downward fluxes were available, it was assumed that these represent the full radiation field.
The values derived from the different transport models for the total dose equivalent rates (0.51-0.60 mSv/d) as well as the dose rate in tissue (0.16-0.20 mGy/d) and the dose rate in silicon (0.13-0.16 mGy/d) agree within 20%.The contributions of the different particle types to the total dose, however, are  J. Space Weather Space Clim., 6, A13 (2016) in some cases remarkably different.Particularly the contribution from heavy ions to the dose equivalent rate derived from the OLTARIS2013 results differs from the HZETRN/ OLTARIS, PHITS, and GEANT4 results by a factor of two to four which is a consequence of the simplified geometry used to generate the OLTARIS2013 results.On the other hand, the contribution of neutrons from OLTARIS2013 is only about 10%-15% of the HZETRN/OLTARIS, PHITS, and GEANT4 results.Both of these observations are a consequence of the simplified geometry used to generate the OLTARIS2013 results.The dose equivalent rates from HZETRN/OLTARIS, PHITS, and GEANT4 tend to agree better but also show some differences in the contribution of neutrons, which is about 20% (0.05 mSv/d) lower for GEANT4 and HZETRN/OLTARIS, and electrons, which is about 50% (0.02 mSv/d) lower for HZETRN/OLTARIS compared to PHITS and GEANT4.The quality factor for the whole radiation field derived from the different numerical models lies between Q = 2.7 (GEANT4) and Q = 3.2 (PHITS and HZETRN/OLTARIS).As the quality factor in the RAD measurement is derived from a limited acceptance angle we have also calculated the contribution to the dose rate and the dose equivalent rate from particles with an incident zenith angle below 30°.These values were calculated with all models and are given in Table 2 in brackets.The results of GEANT4 suggest that the quality factor for the limited sensitive solid angle is higher (Q = 3.0-3.5)than that for the whole radiation field (Q = 2.7-3.0).Dose rates calculated from PHITS (Q = 3.0 and Q = 3.4) and HZETRN/OLTARIS also show this feature, although for HZETRN/OLTARIS with lower significance: Q = 3.2 for the limited solid angle and Q = 3.0 for the whole field.A higher quality factor for the limited zenith angle range would imply that the RAD derived quality factor overestimates the quality factor of the whole radiation field by about 10-25%.If we consider the fact that the particles with the highest quality factor are heavy ions, which are primarily downward directed either as fragments of GCR projectiles or as fragments of atmospheric target nuclei, a lower quality factor for the whole field compared to the restricted solid angle is plausible.Neutrons which have a high quality factor as well, on the other hand, are almost isotropically distributed.Thus, if the contribution of neutrons to the total dose is higher in some models, the effect of the restricted sensitive angle on the calculated quality factor is lower.This is the case for the GEANT4 setup model and for which the contribution of neutrons to the total dose is much higher than for the other GEANT4 setups (0.27 mSv/d compared to ~0.18 mSv/d).Consequentially the difference in the quality factor from the limited zenith angle range (Q = 3.2) and the whole field is decreased (Q = 3.0).All numerical results for the quality factor are compatible with the experimental values within the uncertainty of the RAD measurements.Simonsen et al. (1990) have estimated the skin dose equivalent during solar minimum (GCR maximum) conditions on the Martian surface for a shielding of 22 g/cm 2 CO 2 to be 11.3 rem/year (0.31 mSv/d) which is significantly lower than the values measured by RAD and estimated in this work.Even more so if we consider the fact that the measurements and the calculations of this work have not been performed for solar minimum for which higher dose rates are expected.Townsend et al. (2011) estimated the skin dose rate on Mars during solar minimum for an atmospheric depth of 20 g/cm 2 to be 0.305 mGy/d and the effective dose rate to be 0.726 mSv/d.While skin dose rate estimated by Townsend et al. (2011) is about 50% greater than the values measured by RAD and calculated in this work, the effective dose rate is only about 15% greater than the measurement and about 40% greater than the calculations in this work.Parts of these discrepancies could be explained by differences in the solar modulation of the GCR.Also, Simonsen et al. (1990) and Townsend et al. (2011) have used different models for the primary GCR spectra, CREME (Adams et al. 1981) and Badhwar-O'Neil 2006(O'Neill 2006), and the transport, BRYNTRN (Wilson et al. 1989) and an older version of HZTREN (Nealy et al. 2007).Unfortunately, in retrospect it is impossible to disentangle the influences of the different factors from the results and what could have led to the observed discrepancies.In case of Townsend et al. (2011) a direct comparison to the results of this work is additionally complicated by the fact that they calculated the dose rate for vertically incident particles only and that the calculated organ dose values are affected by the selfshielding of the applied water phantom.Future work will show how the use of a numerical phantom or organ dose conversion factors influences the resulting dose rates for the Martian surface.

Summary
We present the first comprehensive comparison of results of different numerical radiation transport models, GEANT4, PHITS, OLTARIS2013, HZETRN/OLTARIS of particle spectra over a wide energy range and dose rates caused by galactic cosmic radiation on the surface of Mars with direct measurements on the surface of Mars from the MSL-RAD instrument.Although good agreement is found in many cases for GEANT4, PHITS, and HZETRN/OLTARIS, some models still show large, sometimes order of magnitude, discrepancies in certain particle spectra.We have also found that comparison with these RAD data is helping us make better choices of input parameters and physical models, and thus improving agreement of the simulation results with the data.The first-ever comparison between experimental data from the surface of Mars and model calculations is helping us to improve the reliability of numerical model predictions for particle spectra and radiation exposure on Mars as well as for other space travel scenarios.It was found that the selection of different physical model lists in GEANT4 in most cases does not affect the resulting radiation exposure severely: a maximum difference of 20% is calculated in the dose equivalent rate for the application of the Bertini cascade model; the dose rate in tissue agrees within approximately 5% for all GEANT4 model lists.In some cases, however, the model selection in GEANT4 affects the resulting prediction of secondary particle spectra on the surface: the application of the Intranuclear Cascade Model of Liège (INCL) results in a strongly improved agreement of hydrogen and helium isotope spectra with the RAD measurements; using the Bertini cascade model for inelastic interactions of neutrons and protons at energies below 10 GeV leads to strongly enhanced neutron fluxes on the surface and, as a result, to an increased quality factor.Based on the current results of RAD, however, it cannot be decided which of the models is most accurate concerning the prediction of neutron fluxes.
No significant difference in the prediction of particle spectra and dose rate was found for the two models of galactic cosmic radiation.However, from other published results it can be assumed that this is special for the solar modulation conditions for which the study was performed and it can be assumed that this could be different, e.g. for solar minimum conditions.Despite the agreement between calculated and measured dose it is necessary to further improve the numerical models and to continue the validation against experimental data.Measurements, especially for neutrons below 10 MeV and heavy ions in the range above several hundreds of MeV/n, would help to develop the models at these energies where in some cases large discrepancies were observed in this work.This energy range is also expected to become more important in case of heavier shielded environments, e.g.underground or in radiation shelters.Additionally, as stated above, the concept of dose and quality factor for the description of biological damage and radiation risk might not be fully adequate for space radiation applications.The contribution of particles and the importance of energy ranges might alter in different radiation risk models and experimental data would help to estimate the accuracy of the numerical models.

Fig. 3 .
Fig. 3. Exemplary fluence-to-dose conversion factors for alpha particles versus particle energy (a).The quality factor Q (c) is calculated from the energy-dependent linear energy transfer (LET, b) following the ICRP definition of the Q(LET) dependence (ICRP 2007).

Fig. 5 .
Fig. 5. Hydrogen isotope spectra (from top to bottom: proton, deuteron, and triton) for zenith angles smaller than 30°on the Martian surface measured between 19 August 2012 and 17 February 2013 by MSL-RAD (black, Ehresmann et al. 2014) and calculated for the same period by different simulation tools: GEANT4 (red), PHITS (blue), OLTARIS2013 (green), ZETRN/OLTARIS (ocher).The data have been scaled by the factors given in parentheses.
Fig. 6. 4 He and 3 He (scaled by 0.1) spectra for zenith angles smaller than 30°on the Martian surface measured between 19 August 2012 and 17 February 2013 by MSL-RAD (black, Ehresmann et al. 2014) and calculated for the same period by different simulation tools: GEANT4 (red), PHITS (blue), OLTARIS2013 (green), HZETRN/OLTARIS (ocher).The data have been scaled by the factors given in parentheses.

Fig. 7 .
Fig. 7. Same data as Figures 5 and 6 but for an energy range from 10 MeV/n to 20 GeV/n.

Fig. 8 .
Fig. 8. Particle spectra for zenith angles smaller than 30°on the Martian surface measured between 19 August 2012 and 17 February 2013 by MSL-RAD (black, Ehresmann et al. 2014) and calculated for the same period by different simulation tools: GEANT4 (red), PHITS (blue), OLTARIS2013 (green), HZETRN/OLTARIS (ocher).Different nuclei are grouped together and scaled by the factors given in parentheses.

Fig. 9 .
Fig. 9. Same as Figure 8 but for an energy range from 10 MeV/n to 20 GeV/n.

Fig. 10 .
Fig. 10.Particle spectra on the Martian surface calculated for the time period between 19 August 2012 and 17 February 2013 by different simulation tools: GEANT4 (red), PHITS (blue), HZETRN/OLTARIS (ocher).Particle types are, from top to bottom: electron/positron, l À /l + , p À /p + .Positron, l + and p + are indicated by the dashed lines and scaled by 0.1 for separation.

Fig. 11 .
Fig. 11.Contribution of different particle types to the dose equivalent rate in tissue (a, in lSv/d), dose rates (in lGy/d) in tissue (b), and silicon (c) calculated with different transport models for the Martian surface (atmospheric shielding: 22 g/cm 2 ).MSL-RAD measured a dose rate in tissue of 0.21 ± 0.04 mGy/day and a dose equivalent rate of 0.64 ± 0.12 mSv/day Hassler et al. 2014).

Table 2 .
Dose rates measured by MSL-RAD on the surface of Mars and calculated values.Values in parentheses are the dose rates and the derived quality factor for a restricted zenith angle h < 30°.

Table 2 .
The selection of this physics list was guided by comparison with the RAD data.The measured data is taken from Köhler et al. (2014).The results of the PHITS, HZETRN/OLTARIS, and GEANT4 simulations agree reasonably well with each other over the whole energy range for both neutrons and photons.Apart from setup [2] from Table2the selection of the physics list in GEANT4 had no significant influence on the predicted neutron flux.Using the Bertini cascade model, as in setup [2], however, greatly enhances the calculated neutron