We present a 3-D numerical model of atmospheric ionization due to precipitating particles with high spatial resolution. The Atmospheric Ionization Model Osnabrück (AIMOS) consists of two parts: a GEANT4-based Monte Carlo simulation and a sorting algorithm to assign observations from two polar-orbiting satellites to horizontal precipitation cells, depending on geomagnetic activity. The main results are as follows: (1) the sorting algorithm and thus the 3-D mapping of particle fluxes works reasonably well; (2) ionization rates are in good agreement with the ones from earlier models; (3) during quiet times, the major contribution to ionospheric ionization is from electrons both in the polar cap (solar electrons) as well as in the auroral oval (magnetospheric electrons) with the ionization in the auroral oval exceeding that in the polar cap; (4) during solar particle events the dominant effect in the polar cap in the stratosphere and mesosphere is from solar protons although solar electrons can contribute up to 30% to the ionization; (5) during strong shocks following a solar particle event, in the auroral oval magnetospheric electrons and protons lead to ionization rates of up to some 10% of the ones of solar particles; and (6) independent of particle source and precipitation site, in general, ionization by electrons is more important in the thermosphere.
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 One link in solar-terrestrial relationships are energetic particles: the precipitation of solar energetic particles into the atmosphere causes ionization, NOx and HOx production and eventually the depletion of ozone. An early observation of the role of solar energetic particles (SEPs) in ozone depletion was the large August 1972; its analysis established the role of NOx in stratospheric ozone chemistry [Crutzen et al., 1975; Heath et al., 1977].
 Early modeling attempts focused on stratospheric ozone. The relevant solar particles were protons with energies from a few MeV to a few hundred MeV; contributions from solar electrons and heavier particles were assumed to be negligible [McPeters and Jackman, 1985]. In addition, particle precipitation is assumed to occur uniformly over a nominal polar cap without considering the equatorward expansion of the cap and thus the particle precipitation area with increasing geomagnetic activity as observed, e.g., with SAMPEX [Kahler and Ling, 2001; Leske et al., 2001] or POES [Wissing et al., 2008]. This conventional approach still is used in modeling precipitating SEPs [see, e.g., Jackman et al., 2001, 2005; Randall et al., 2007; Rohen et al., 2005; Verronen et al., 2002]. In addition, the energy range under study (and thus the height range over which ionization occurs) is limited by the particle instrument considered in the study and thus only is a subset of the total precipitating solar proton inventory during the event. Only in rare cases instruments with different energy ranges are combined to yield a more comprehensive spectrum [Mewaldt et al., 2005] but to our knowledge these combined spectra did not enter into the calculation of atmospheric consequences.
 Electron precipitation into the atmosphere also has been analyzed; however, electrons are assumed to be magnetospheric electrons, at its low energetic end also called auroral particles. Here particle fluxes are derived from observations with a polar-orbiting satellite and assumed to be uniform over the auroral oval [e.g., Callis et al., 1996a, 1996b, 1998] or particle fluxes/ionization rates are determined from a parametrization relying on a geomagnetic index [e.g., Fang et al., 2008; Marsh et al., 2007; Roble and Ridley, 1987].
Wissing et al.  combined data from two POES spacecraft to analyze in more detail the spatial pattern of precipitating particles. As expected, the authors found a contribution of both electrons and protons in the polar cap (SEPs) as well as in the auroral oval where magnetospheric particles precipitate. Fluxes of these latter particles showed a strong dependence on local magnetic time: measurement of an auroral oval crossing from one satellite does not give a representative particle flux for the entire oval but, depending on local magnetic time, might overestimate or underestimate the average particle flux inside the oval by a factor of up to five.
 The Atmospheric Ionization Module Osnabrück (AIMOS) model presented in this paper provides a tool to simulate the 3-D ionization effects of almost the total particle inventory on the entire atmosphere depending on geomagnetic activity. This allows (1) for a better comparison between observations and simulations and (2) for a comparison of the relative contributions of the different particle populations to atmospheric chemistry. This is important for long-term studies of atmospheric ionization that rely on proxies such as kp index for magnetospheric particles. In addition, the horizontal resolution also provides the necessary quality for local measurements such as the comparison of radar echoes at different locations in the polar cap and polar oval. With time, a long-term database of high-resolution 3-D ion pair production rates in the atmosphere will be made available to the public; a short version spanning the years 2002–2005 already can be found at http://aimos.physik.uos.de.
 The paper is structured as follows. In section 2 we discuss the flow chart of the model and the submodules for ionization and particle sorting. Section 3 describes the data from different satellites that enter into the model while section 4 is concerned with validation. In section 5 the relative contributions of the different particle species and populations to atmospheric ionization will be discussed. Model and results are summarized in section 6.
2. Model: AIMOS
 The intent of Atmospheric Ionization Module Osnabrück (AIMOS) is the consistent modeling of ion pair production due to precipitating particles for the entire particle inventory of energetic solar and magnetospheric particles. The model is designed to convert observations of energetic particles from satellites into a 3-D ionization pattern in the atmosphere.
Figure 1 shows the AIMOS scheme, consisting of two parts: (1) the retrieval of energetic particle spectra and the horizontal precipitation pattern from observations and (2) the simulation of particle interaction with the atmosphere using monoenergetic particle beams of different energies, angles of incidence and particle species. The latter data set is convoluted with the former to give the 3-D atmospheric ionization (or ion pair production) rates.
 A rather complex retrieval mechanism is required because energetic particle measurements are in situ measurements. Thus it is not possible to obtain some snapshot of particle distributions at the top of the atmosphere. Instead, a combination of data from at least two polar-orbiting spacecraft is required to determine such a precipitation map, as will be described in detail in section 2.2. These maps depend on particle energy, or more accurately rigidity, because the geomagnetic cutoff depends on rigidity. They also depend on geomagnetic activity: with increasing geomagnetic activity the polar cap and the auroral oval expand equatorward. The result is the square “Precipitating Particles sorted by Horizontal Cell” in the middle on the left side in Figure 1.
 The second part of the model describes the particle interaction with the atmosphere using a Monte Carlo simulation, as described in detail in section 2.1. This part requires an assumption concerning the atmosphere, namely its density and temperature profiles. The latter depends on season, latitude and solar activity. Therefore different runs have been performed for different states of the atmosphere. Thus a given input of precipitating particles yields different ionization profiles for different seasons and/or different levels of solar activity. The atmosphere most adequate for a given day is chosen by date (gives the season) and F10.7 index as a measure for solar activity.
 The models limitations are determined by the spatial resolution of the model atmosphere and by the energy spectrum covered by the particle instruments. The model atmosphere extends from ground up to 1.7 × 10−5 Pa, corresponding to an upper boundary between 250 to 600 km. The spatial grid is 3.6° × 3.6° in the horizontal with 67 logarithmically equidistant height layers. The energy range of precipitating particles is 150 eV to 500 MeV for protons, 4 MeV to 500 MeV for α particles and 150 eV to 5 MeV for electrons.
2.1. Monte Carlo Ionization Module
 The interaction between the precipitating particles and the atmosphere is evaluated using a Monte Carlo simulation. Generally speaking, Monte Carlo methods are a class of computational algorithms using repeated random sampling; they are particular useful in modeling systems with many degrees of freedom. The interaction of particles with matter is a process containing a lot of uncertainty: as in radioactive decay, only probabilities in the sense of average lifetime or cross sections are known. Thus when an incident particle approaches a target atom, they will interact with a certain likelihood. In the Monte Carlo Method this is reflected by using random numbers to choose from the different possible outcomes: interaction or not, kind of interaction with resulting energy loss, deflection from original path and secondary particle(s). This rolling of the dice is repeated along the particle track.
 The Monte Carlo simulation has an advantage over a continuous energy loss model: while protons and heavier particles basically follow a straight line, electrons experience multiple scattering. Thus the traveled path is much longer than the penetration depth and consequently results from a Bethe-Bloch or another continuous energy loss model cannot be converted correctly to penetration depth. In addition, the Monte Carlo simulation allows the identification and tracking of secondaries, both particles and electromagnetic radiation. Again, this is of particular importance for electrons since they produce Bremsstrahlung which can travel quite a long path before interacting with and ionizing the lower layers of the atmosphere. Bremsstrahlung even can cause ionization at lower heights than the one reached by the primary particle (see, e.g., example given by Schröter et al. ).
2.1.1. Processes Under Consideration
 The ionization module is an extended version of the one described in [Schröter et al., 2006]. It is based on the GEANT 4 simulation package [Agostinelli et al., 2003] as well, but differs from [Schröter et al., 2006] in three respects: (1) the extension and composition of the absorber (the atmosphere), (2) the energies of the precipitating particles cover a much broader range, and (3) a more complete range of interaction processes has to be considered to account for the broader energy range.
 The processes and cross sections considered in the model reflect the underlying physical processes. The most common process is continuous energy loss due to ionization. This process also can be described by Bethe-Bloch's equation for nuclei or Berger-Seltzer's equation for electrons. For electrons, one important process is multiple scattering: while during ionization nuclei follow more or less a straight line, electrons are deflected because the incident electron interacts with an electron from the atomic shell and both particles have the same mass. Thus electrons follow a zigzag path instead of a straight line. In particular in the low densities of the upper atmosphere, these deviations from a straight line can be quite pronounced; see for instance the example given by Schröter et al. . Electrons with sufficiently high energy (in the keV range and above) produce Bremsstrahlung. This is treated as a secondary generated during the interaction and leads to a shift of ionization into the lower atmosphere, as discussed above. To track the bremsstrahlung photon correctly and to calculate its final energy deposition, its interaction with the atmosphere must be tracked. The interaction processes are, with increasing photon energy, the photoelectric effect in which a photon ionizes a target atom transferring all its energy, the Compton effect (or Compton scattering) in which the photon ionizes a target atom and continues with a lower energy into a different direction, and finally pair production in which a photon of energy above 1.02 MeV decays into an electron and a positron. With the rather low energies of the incident electrons the latter process is rather unlikely. With increasing energy of the incident proton hadronic interaction might play a role: the incident particle interacts with the nucleus instead of the atomic shell, generating lighter nuclei and neutrons. Radiocarbon 14C is a result of such a hadronic interaction.
2.1.2. Model Particles
 A Monte Carlo simulation is time consuming. Thus simulations are not performed for particle spectra in a given event but for a large number of monoenergetic beams which then are convoluted with the observed particle spectrum. The energy range of precipitating particles considered in the model is 150 eV to 500 MeV for protons, 4 MeV to 500 MeV for α particles and 150 eV to 5 MeV for electrons. Note that the energy bands are not chosen for physical but for observational reasons: only within these bands a more or less continuous database can be established while observation at lower or higher energies are less frequent and/or not publicly available. Note that this is not exactly true for the electrons: here the observed spectrum only extends to 2.5 MeV but can be extrapolated up to 5 MeV. SOHO observations in the October 2003 events do not give any indication for a break in the electron spectrum in the MeV range [Klassen et al., 2005]. For the error estimate we have to keep in mind that charged particles loose the energy at the end of their track; Figure 2 gives the altitudes of maximum energy loss for electrons (red) and protons (black) depending on the energy of the incident particle. Extending the electron spectrum from 2.5 to 5 MeV therefore would mainly affect the lowest two altitude bins of the red curve. Thus in case of a pronounced steepening of the spectrum around 2.5 MeV, the ionization rates would not change in the thermosphere, would change by a few tenth of a percent in the lower mesosphere and at worst case might be strongly overestimated (up to a factor of 2) in the lower two altitude bins, that is around 50 km. Thus in the worst case the error is large in these two bins while owing to the spectrum of the electrons it is small (less than 10−4) if total ionization is considered.
 40 logarithmically equidistant monoenergetic beams have been calculated for each order of magnitude in energy, giving a total of 264 monoenergetic beams, depending on particle species. To account for the angular distribution of the incident particles, 9 different equally spaced directions of incidence with respect to the vertical are considered. To assure statistical accuracy, each monoenergetic beam consists of 10000 particles for electrons and 100 particles for protons and αs. The higher number of electrons is required because Bremsstrahlung is considered.
 To account for the wide range of particle energies, the atmosphere must extend to heights of several hundred kilometers. For AIMOS we adopted the model atmosphere from HAMMONIA [Schmidt et al., 2006]: it extends from the ground up to 1.7 × 10−5 Pa. Depending on season, latitude and solar activity this corresponds to an upper boundary between 250 to 600 km. The spatial grid is 3.6° × 3.6° in the horizontal with 67 logarithmically equidistant geopotential height layers. The spatial resolution of AIMOS is the same as that of the model atmosphere. All monoenergetic beams have been calculated for four latitudes (80S, 60S, 60N, 80N), the four seasons and three levels of solar activity. For each time interval under study the most suitable atmosphere is selected in AIMOS; the selection criterion for the level of solar activity is not the date but the F10.7 index of solar activity.
2.2. Sorting Algorithm: Low Particle Energies
 The horizontal precipitation pattern depends on local magnetic time and geomagnetic activity. The combination of two polar-orbiting satellites with different equatorial crossing times allows an identification of polar cap and auroral oval as well as an approximation on the fluxes inside the polar cap and the auroral oval. Figure 3 shows fluxes of 30–80 keV protons observed simultaneously along the particle orbit for the POES satellites NOAA 15 and NOAA 16. The green line is the geomagnetic dipole axis, polar cap and auroral oval can be distinguished clearly in the northern hemisphere in both satellite orbits. On the southern hemisphere, the distinction is obvious in the NOAA 16 data while NOAA 15 only passes through the auroral oval. Owing to the satellite orbit such an image can be constructed every 2 h.
 To derive a map of the horizontal precipitation pattern as shown in Figure 4, the gaps between the orbits have to be filled. These maps depend on local magnetic time, geomagnetic activity, particle energy and the particle fluxes in the magnetosphere and in interplanetary space. To obtain them, the globe is split into 14 regions with similar precipitation patterns (for details, see Wissing et al. ). According to daytime-sector affiliation these regions have four subdivisions, depending on local time. The resulting map then gives the relative fluxes in all cells of the globe. The actual flux can be obtained by scaling the flux pattern along the orbit with the corresponding matrix. Scaling on the basis of individual cells is avoided to reduce statistical scatter. Thus the method basically also is an averaging procedure.
 Note that these maps must be derived separately for each particle species, each particle energy and different levels of geomagnetic activity. They are only valid for magnetospheric particles, the fluxes of the solar energetic particles inside the polar cap must be obtained separately from direct measurement: fluxes and spectra of solar energetic particles and magnetospheric particles are not (cor)related.
2.3. SEPs Inside the Polar Cap
 The reliable particle instruments/channels on the POES satellites extend to 2.5 MeV for the electrons (with our extrapolation to 5 MeV) and 6.7 MeV for protons. Consequently, the precipitation pattern only can be derived up to these energies. In SEPs significant fluxes of protons at higher energies up to some hundred MeV can be expected; with intensity increases of a few orders of magnitude above background even at 100 MeV. Although their contribution to total energy and therefore total ionization is in the range of a few percent at most, their contribution to the ionization height profiles is marked. Because energetic particles loose most of their energy at the end of their track, the consideration of the high energetic protons does not modify the ionization rates in the thermosphere but extend ionization to lower altitudes according to the height-energy relation in Figure 2.
 The high energetic solar particles precipitate only inside the polar cap. Particle measurements thus can be taken from an interplanetary satellite, such as IMP or SOHO, or from one of the GOES satellites. The part of the particle spectra above the highest POES energies are determined from these measurement; thus the lowest GOES energy channels are omitted and only energies above 9 MeV are considered. The precipitation area is extrapolated from the polar cap size in the highest proton channel on POES: since the size of the polar cap increases with increasing particle energy, the SEPs with energies above 15 MeV are allowed to precipitate also into the next equatorward latitude bin. Nonetheless, this is not a completely correct consideration of the decrease in geomagnetic cutoff with rigidity and the total amount of precipitating high energetic protons thus is slightly underestimated; errors in total ionization in the relevant latitude bins depend on the particle spectrum but should not exceed 10% for spectra typically observed in solar energetic particle events. It should be noted that ionization inside the inner part of the polar cap as defined by the POES satellite is not subject to this error. Since the precipitation maps are determined for different values of kp separately, the increase of the size of the polar cap during strong geomagnetic storms is taken into account, too. In sum, spectral variation with geomagnetic cutoff is taken into account by allowing a wider polar cap for higher energies and polar cap variation with geomagnetic activity is taken into account by the dependence of the map on a geomagnetic index, in this case kp.
 The shift from POES to GOES does not affect the spatial resolution dramatically: while the precipitation pattern of the lower energies is highly variable (Figure 5, top) even the moderate energies in the higher POES channels show only a rather uniformly filled polar cap (Figure 5, bottom). Thus the continuation to higher energies only requires the identification of some polar cap extension but no further spatial resolution.
 The present data set in the AIMOS data server is limited to the time period 2002–2005 and is based on particle data from the EPS instruments on GOES 10 and GOES 11 and the SEM-2 instruments on board the POES satellites NOAA 15 and 16; the energy ranges and particle species are summarized in Figure 6. The two POES satellites are the important ones because they are used in the construction of the precipitation maps. As discussed above, the instruments measure electrons up to 2.5 MeV and protons up to 6.7 MeV but no alphas. Protons with higher energies (up to 500 MeV) are taken from the GOES satellite (as discussed in section 2.3).
 It should be noted that the ionization module and the sorting algorithm can be applied to any pair of polar-orbiting satellites with nonvanishing angular separation of the orbital planes; one example for application to a different satellite in a different orbit (NOAA 17) will be discussed in section 4.3. So far, the model therefore does not contain any specific assumption about the particle data to be processed with it.
3.1. Satellites and Instruments
 The POES satellites (POES: Polar Orbiting Environmental Satellite) are polar-orbiting satellites in a Sun-synchronous orbit with a height of 850 km and an inclination of 98°. Equatorial crossing in the southward direction nominally occurs at 7:30 UT for NOAA 15 and at 2:00 for NOAA 16. Particle measurements are performed with the Space Environment Monitor SEM-2 [Evans and Greer, 2005] which consists of the Total Energy Detector TED measuring low energetic particles and the Medium Energy Proton and Electron Detector MEPED. TED is a cylindrical electrostatic analyzer, MEPED consists of semiconductor detectors with passive shielding to define an aperture. Instruments are flown in pairs with the 0° instrument viewing upward along the radial and thus almost parallel to the magnetic field inside the polar cap, and the other instrument viewing backward along the satellite's trajectory (MEPED) or at a fixed angle with respect to the 0° detector. Since particle precipitation is strongest at high geomagnetic latitudes where the magnetic field is close to radial, AIMOS is limited to the analysis of the 0° detector.
 The GOES satellites (GOES: Geostationary Operational Environmental Satellite) are in geostationary orbit located at W135 and W104. The Energetic Particle Sensor EPS (NOAA, GOES I-M DataBook, 1996; available at http://goes.gsfc.nasa.gov/text/databook/databook.pdf) is a telescope for the measurement of protons and α particles. The opening angle is rather wide (70°), in contrast to POES no estimate of particle anisotropies is possible. The dome detector measures the higher energetic end of all particle species, particle identification is made by pulse height analysis.
3.2. Particle Energy Spectra
 To perform the convolution with the Monte Carlo results we need a handy description of the incident particle spectrum. [Schröter et al., 2006] assumes for a smaller energy range a power law spectrum I(E) = I(E0) (E/E0)−γ fitted to the data with up to three different power law indices in different energy ranges. Mewaldt et al.  discuss different spectral shapes which also all go back to the power law spectrum. Therefore we adopt the approach of Schröter et al.  but allow for up to five separate segments to account for the wider energy range.
4. Test of the Model Components
 The most elementary test is energy conservation: does all energy deposited inside the atmosphere show up as energy loss and thus leads to ion pair production. This is the case for all particle species and all particle energies. Testing of the model is improved stepwise. We start with the ionization module and compare the Monte Carlo results to analytical solutions. We compare our fits of the energy spectra to other fits using data from different satellites in the same event and finally we test the sorting algorithm.
4.1. Ionization Module
 The validation of the ionization module is straightforward: here monoenergetic particle beams with fixed direction of incidence are used. The comparison between results from Bethe-Bloch and GEANT 4 for protons already have been discussed by Schröter et al. . Results from AIMOS differ neither from Bethe-Bloch nor from the results of Schröter et al.  for the height/energy range covered in both approaches. For low energetic protons, differences between GEANT and Bethe-Bloch can be observed with decreasing density of the absorber, that is with increasing height. Above about 150 km more energy is deposited within an atmospheric layer in the Bethe-Bloch code than in the Monte Carlo model. It should be noted that within one height layer the resulting difference in the ionization rate can be up to 20% although the “misplaced” amount of total energy and therefore also total ionization rate is of the order of 10−3 of the total energy/ionization rate.
 One physical reason might be energy transport into lower layers by secondaries. Another reason simply are the different corrections and assumptions in different interaction models. Although mathematically the difference exists, it should not be overrated because the main problems in comparisons between model results and observations will be (1) the assumption about atmospheric composition and density in the highly variable thermosphere and (2) the high variability of the ionization due to hard electromagnetic radiation. In addition, owing to the low density of the thermosphere, only a small amount of particle energy is deposited there: for protons with MeV energies less than 10−3 of the total energy is deposited in the thermosphere while for protons up to some tens of keV all energy is deposited in the upper thermosphere.
 For electrons, the Monte Carlo simulation has been compared to the results of Berger et al. : height of maximum ionization and energy deposition agree within a few percent; residual differences partly reflect the different methods and partly differences in the assumption about the model atmosphere. Compared to the results of Callis et al.  the ion pair production in the Monte Carlo model is lower by a factor of five in the ionization maximum around 100 km while it is comparable at lower altitudes. The reason could not be identified unambiguously; different assumptions about atmospheric density and the limitation of the atmosphere to lower altitudes of Callis et al.  might lead to a cumulated deposition of all energy deposited in the entire thermosphere in a limited height range around the ionization maximum. Since in our Monte Carlo simulation all incident energy (within the accuracy of the computer) is deposited, the latter point might be the appropriate explanation.
4.2. Combined Particle Spectrum and Ionization Module
 Spectra and resulting ion pair production rates from precipitating solar protons inside the polar cap were calculated with AIMOS. The particle spectra then were compared to the ones of Mewaldt et al.  derived for a different data set; the resulting ion pair production rates were compared to the ones of Jackman et al. .
Mewaldt et al.  derived particles spectra for electrons, protons and αs from observations with instruments on the ACE, SAMPEX and GOES 11 satellites for different time periods during the event. For the same time periods, spectra were derived from AIMOS using observations of the TED and MEPED instruments on POES and GOES 10. Agreement of the spectra at the high energy end is not surprising since the instruments on the GOES satellites are similar. Although differing in details, the general spectral shape is the same for electrons and protons below a few MeV in both approaches, although entirely different instruments from satellites in different orbits have been combined. The total energy contained in the different spectra in the energy interval covered by both instruments agrees within a few percent and do not show indications for systematic differences between the two approaches. This agreement supports not only the methods but also suggests that the particle data are reliable.
Figure 7 shows ion pair production rates for the protons calculated with AIMOS from the spectra discussed above for the first four days of the event. The contours are at the same rates as in Figure 3 of [Jackman et al., 2005] to allow for an easy comparison. Spatial and temporal ion pair production rates agree quite well with one exception: ion pair production in AIMOS is observed at lower altitudes than by Jackman et al. . This is not a difference in the models but in the data used to calculate the incident particle spectrum: Jackman et al.  consider only protons with energies below 300 MeV while AIMOS considers protons up to 500 MeV. The differences between both models in the height range covered by both models mainly result from differences in timing, the differences in the spectrum calculation (the method is different than the one used in this paper and also that used by Mewaldt et al. ) and in the assumptions regarding the underlying model atmosphere.
4.3. Sorting Algorithm
 To test the precipitation map we used one of the maps derived from NOAA 15 and NOAA 16 to make predictions for particle fluxes. Figure 8 (top) shows predictions for the NOAA 16 satellite (red bars), averaged measurements (black bars) and the actual observations in high resolution (gray dots). The averages agree reasonably well, in particular the steep gradients at the fringes of the polar oval can be reproduced. Since NOAA 16 data were also used in map construction, this test does not support the spatial pattern but only the concept of scaling maps with fluxes.
Figure 8 (bottom) shows predictions for the same time period but for the NOAA 17 satellite. Data from NOAA 17 did not enter into the calculation of the precipitation maps and the orbital plane of NOAA 17 lies roughly in the middle between the ones of NOAA 15 and 16. Thus in this case, predictions are made for an entirely different orbit, which shows whether scaling with the interpolated precipitation map gives useful results or not. Again, the general features (radiation belt, polar cap, low latitudes) are predicted quite well; with the exception of one interval around 6:40 even the steep gradients at the fringes of the auroral oval are reproduced.
 We conclude from a large number of such comparisons that the sorting algorithm works well. Even when differences between prediction and observation occur, the error is smaller than in case of the simple assumptions of uniform fluxes across the entire polar oval and a nominal auroral oval.
5. Relative Contributions of Particle Species and Populations
5.1. Quiet Times
Figure 9 (top) shows typical background ionization rates inside the polar cap. All intervals are at geomagnetically quiet times and no increase in particle fluxes in interplanetary medium above background is observed, thus no solar energetic particles are present. The solid lines are for protons, the dashed ones for electrons. The sudden drop in ionization rate around 15 km for protons and around 50 km for electrons is an artifact: we do not have observations of particles with such high energies. Therefore we cannot make a reliable comparison between ionization rates of electrons and protons below 50 km. In the mesosphere ionization by electrons exceeds that by protons by at least an order of magnitude until both become comparable in the lower thermosphere. While ionization rates in the different time intervals are quite similar below the mesopause, in the thermosphere absolute ionization rates are highly variable as is the relative contribution of electrons and protons to ionization.
 The longitudinally averaged ionization rates for the same time periods are shown in Figure 9 (bottom). The maximum of ionization by precipitating particles is in the lower thermosphere; the ionization rates are more than one order of magnitude larger than the ones around the mesopause. Ionization by electrons exceeds that by protons by more than an order of magnitude. Ionization rates in the mesosphere and stratosphere are comparable to the ones in the quiet time polar while they are larger in the thermosphere, reflecting the steeper spectrum of the magnetospheric particles.
5.2. Solar Energetic Particles
Figure 10 shows the relative contribution of ionization by solar energetic electrons to the total ionization by solar energetic particles during the first four days in the October/November event; the ionization rates by solar protons have been shown in Figure 7. Figures 7 and 10 both represent the ionization at the geomagnetic north pole. A value of 0.5 indicates an equal contribution of electrons and protons, electron domination to the ionization rates is shown in red, proton domination in blues. Again, below about 50 km the contribution of electrons is underestimated because of the limited information about the energy spectrum. The ratios below 15 km also result from limited information and must be discarded: the highest proton energy considered is 500 MeV, corresponding to a stopping height of about 15 km. Thus no proton ionization is calculated below that line while small amounts of ionization due to electron Bremsstrahlung still occurs.
 Again, in the lower thermosphere during most of the time ionization by electrons dominates. In the mesosphere, ionization by electrons only is dominant at times of rather low intensities, e.g., before event onset and in the late phase. Early in the event, protons dominate while during the event electrons can contribute more than 30% to the ionization of the mesosphere.
 These numbers are not large enough to nullify earlier studies or to change our understanding of the relation between precipitating particles and atmospheric chemistry. However, the numbers are large enough to be considered when model results are compared to observations.
5.3. Solar and Magnetospheric Particles
Figure 11 shows ionization rates during the October/November 2003 event for protons (solid lines) and electrons (dashed lines) for four different time intervals: early in the event, in the rising phase, at event maximum and in the late phase of the second event. Again, the top shows observations inside the polar cap, and the bottom shows the longitudinally averaged rates inside the auroral oval. The most prominent feature is the persistent ionization maximum due to precipitating electrons in the lower thermosphere. Note that the rates are of the same order of magnitude as during the quiet times shown in Figure 9.
 Much stronger variations in ionization rates by both particle species can be found inside the polar cap, reflecting the development of the particle spectrum during the event. Let us start with the protons: at first only particles with high energies arrive at Earth, leading to an increase in ionization compared to background conditions by more than one order of magnitude in the stratosphere. In the next 2-h time interval, particle intensities at high energies continue to rise while particles with lower energies start to arrive: consequently, the ionization rate continues to increase in the stratosphere and also starts to increase in the mesosphere. Owing to the shape of the spectrum, the height of the ionization maximum increases. During maximum times, the ionization rate inside the polar cap is increased at all altitudes with its maximum in the mesosphere. Late in the event intensities in highest energies already have decreased while intensities in the MeV range and below still are high because these low energetic particles still are accelerated at the interplanetary shock. Thus ionization rates already are low in the stratosphere and have a maximum in the lower thermosphere.
 The temporal development of the ionization-height profile for the electrons follows the same pattern, except that we cannot draw any reliable conclusions about ionization in stratosphere. The details of the profiles and the increases in ionization rate of course are different, as has already been discussed in connection with Figure 10.
 The first three profiles are obtained during geomagnetically quiet conditions, thus the flux of magnetospheric particles is not as high as during a violent geomagnetic storm but it is markedly increased compared to quiet time conditions. Note that certain similarities between the proton ionization profiles of solar and magnetospheric protons are an artifact of the longitudinal averaging in Figure 11.
 In sum, it appears that during solar particle events the dominant effect in the polar cap in the stratosphere and mesosphere is from solar protons although solar electrons can contribute up to 30% to the ionization. In addition, during strong shocks following a solar particle event, in the auroral oval magnetospheric electrons and protons lead to ionization rates of up to some ten percent of the ones of solar particles. Independent of particle source and precipitation site, in general ionization by electrons is more important in the thermosphere.
 To our knowledge, AIMOS is the first model to give reliable three dimensional ion pair production rates for precipitating solar and magnetospheric particles with high spatial and temporal resolution. Spectra of precipitating particles and the interaction of these particles with the atmosphere are modeled in a conventional fashion (power law spectra, Monte Carlo simulation for the interaction). The new features of the model are as follows:
 1. The combination of solar and magnetospheric particles.
 2. The consideration of all particle species in both populations.
 3. Last but not least, the construction of 2-D precipitation maps allows a full 3-D ionization model. The latter allows for comparison with, e.g., electron densities obtained with radio scattering instruments and can be used to validate the model.
 The model has been tested by comparison to calculations of spectra and ionization rates in other models and found to be in good agreement with them. A continuous set of ionization rates from 2002–2005 is available at aimos.physik.uos.de.
 The model also has been applied to data during quiet times, a solar particle event and the complex series of SEPs and shocks in October/November 2003. Within the complex temporal and spatial variations in ionization rates, some relevant features can be identified. During a solar particle event the ionization in the mesosphere (and most likely also in the stratosphere) mainly is due to protons while with increasing height the ionization by solar electrons dominates (lower thermosphere). While solar electrons correctly have been neglected in the study of stratospheric effects of precipitating particles they must be considered in atmospheric models extending to greater heights. The situation is different, if particles stem from geomagnetic disturbances, in this case shocks following solar energetic particle events. Here the relative importance of particle precipitation inside the polar cap and the auroral oval depends on geomagnetic activities and the spectrum of the solar energetic particles. At least in the lower thermosphere, both particle populations can lead to comparable ionization rates. In the mesosphere, ionization by magnetospheric electrons often exceeds that by solar electrons; it also can exceed that by solar protons. Consequently, the consideration of both particle populations with all particle species modifies the estimated ionization rates. These modifications are not large enough to nullify earlier studies but they are large enough to be considered in comparisons between atmospheric models and measurements of atmospheric constituents.
 This work was supported by the Deutsche Forschungsgemeinschaft DFG under contracts DFG-Ka1297/6-1 and DFG-Ka1297/8-2. We are grateful to the many fellow researchers from the CAWSES community who discussed the model and used first results, in particular, Jens Kieser, Holger Winkler, Miriam Sinnhuber, and Hauke Schmidt.
 Wolfgang Baumjohann thanks the reviewers for their assistance in evaluating this paper.