Journal of Atmospheric and Solar-Terrestrial Physics · a Institute of Environmental Systems Research, University of Osnabrück, Osnabrück, Germany b Karlsruhe Institute of Technology

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Particle precipitation: How the spectrum fit impacts atmosphericchemistry

J.M. Wissing a,n, H. Nieder b, O.S. Yakovchouk a,c, M. Sinnhuber b

a Institute of Environmental Systems Research, University of Osnabrück, Osnabrück, Germanyb Karlsruhe Institute of Technology (IMK-ASF), Karlsruhe, Germanyc Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia

a r t i c l e i n f o

Article history:Received 1 October 2015Received in revised form11 April 2016Accepted 12 April 2016

Keywords:Solar particle eventAtmospheric ionizationParticle precipitationIonization rateSpectrum fitPower lawParticle spectrumAIMOSAtmospheric Ionization Module OSnabrueck3dCTM

x.doi.org/10.1016/j.jastp.2016.04.00726/& 2016 Elsevier Ltd. All rights reserved.

esponding author.ail address: [email protected] (J.M. Wissing).

e cite this article as: Wissing, J.M., espheric and Solar-Terrestrial Physics

a b s t r a c t

Particle precipitation causes atmospheric ionization. Modeled ionization rates are widely used in atmo-spheric chemistry/climate simulations of the upper atmosphere. As ionization rates are based on particlemeasurements some assumptions concerning the energy spectrum are required. While detectors measureparticles binned into certain energy ranges only, the calculation of a ionization profile needs a fit for thewhole energy spectrum. Therefore the following assumptions are needed: (a) fit function (e.g. power-law orMaxwellian), (b) energy range, (c) amount of segments in the spectral fit, (d) fixed or variable positions ofintersections between these segments. The aim of this paper is to quantify the impact of different as-sumptions on ionization rates as well as their consequences for atmospheric chemistry modeling.

As the assumptions about the particle spectrum are independent from the ionization model itself theresults of this paper are not restricted to a single ionization model, even though the Atmospheric IonizationModule OSnabrück (AIMOS, Wissing and Kallenrode, 2009) is used here. We include protons only as thisallows us to trace changes in the chemistry model directly back to the different assumptions without theneed to interpret superposed ionization profiles. However, since every particle species requires a particlespectrum fit with the mentioned assumptions the results are generally applicable to all precipitating par-ticles.

The reader may argue that the selection of assumptions of the particle fit is of minor interest, but wewould like to emphasize on this topic as it is a major, if not the main, source of discrepancies betweendifferent ionization models (and reality). Depending on the assumptions single ionization profiles may varyby a factor of 5, long-term calculations may show systematic over- or underestimation in specific altitudesand even for ideal setups the definition of the energy-range involves an intrinsic 25% uncertainty for theionization rates.

The effects on atmospheric chemistry (HOx, NOx and Ozone) have been calculated by 3dCTM, showingthat the spectrum fit is responsible for a 8% variation in Ozone between setups, and even up to 50% forextreme setups.

& 2016 Elsevier Ltd. All rights reserved.

1. Introduction

The impact of large solar energetic particle events on the at-mosphere, in particular on Ozone destruction, has been described,analyzed and modeled in many studies (e.g. Crutzen et al., 1975;Heath et al., 1977; Jackman et al., 2000; Randall et al., 2005). Nu-merous ionization models have been built to estimate the impactfrom precipitating particles (e.g. Roble and Ridley, 1987; Hardyet al., 1989; Callis, 1997; Callis et al., 1998; Callis, 1998; Jackmanet al., 2001, 2005; Fang et al., April 2002; Schröter et al., 2006;Wissing and Kallenrode, 2009). All of these models use their

t al., Particle precipitation:(2016), http://dx.doi.org/10

individual set of parameters as selection of particle detectors, sa-tellites, energy range, spatial coverage, spatial resolution (if any),temporal resolution, internal algorithms and others. However, asall ionization models are based on particle measurements they allcan be split up according to the following scheme:

The particle data originate from measurements that representthe particle flux in a specific energy range. Particle data from

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1 Barycentric energy for a power law spectrum:

J.M. Wissing et al. / Journal of Atmospheric and Solar-Terrestrial Physics ∎ (∎∎∎∎) ∎∎∎–∎∎∎2

different channels have to be combined by a fit in order to inferthe continuous energy spectrum. Using an atmospheric energydeposition algorithm (e.g. Bethe–Bloch, range-energy relations orMonte-Carlo) this energy spectrum can be transposed into anenergy deposition profile. A constant factor allows to transposethis profile into an ionization rate profile.

We are interested in the accuracy of ionization models. Thecentral part of an ionization model is the energy deposition al-gorithm. Using Monte-Carlo simulations based on Geant4 this partof the ionization model has an error of just a few percent assumingthat the number of incidents is high enough to take care of sta-tistical variations. Looking at “heavy” particles (protons and alphaparticles) Bethe–Bloch calculations do not differ significantly.Therefore the energy deposition algorithm is not a significantsource of error in the energy ranges considered in this paper.

The quality of the particle data itself will not be discussed inthis article. Particle data will be used as is. Anyhow, it is knownthat particle detectors are affected by crosstalk of other particleenergies or species (for details see e.g. Yando et al., 2011) and thatradiation causes damage (Asikainen et al., 2012) that adds upduring time of operation. In addition different geostationary sa-tellites with the same set of detectors (like the often used GOESensemble) can measure fluxes that vary by an order of magnitudeat the same time, depending on their recent location.

In this paper the input particle precipitation should be realisticand identical in each comparison. Therefore we use particlemeasurements from the GOES and POES satellites from NOAA.However, as this paper concentrates on internal methods, we payno attention to particle origin or spatial variations (e.g. polar capsize with increasing geomagnetic activity as given in Leske et al.(1995, 2001)). The identical input data and the same energy de-position algorithm as given by AIMOS (Wissing and Kallenrode,2009) allows us to concentrate on the model variations caused byassumptions in the spectrum fit only. As we will see, the as-sumptions on the spectrum fit are responsible for typical char-acteristics in the ionization profile and may also cause large dis-crepancies. These discrepancies are in the order of 25% to factor 2(including 75% of the profiles, depending on setup) and thereforemore dominant than any other aspect of the ionization model.

For specific periods the results of different ionization modelshave also been compared in e.g. Reagan et al. (1981). However acomparison of single time intervals may lead to wrong conclusionsas the particle spectrum may show a strong variation and spectralfunctions may not be ideal for every spectral shape. Thus thevariation range is huge. In order to assess the impact of differentassumptions and their statistical relevance, we make model runsover 2 months with the 3dCTM and estimate their effects on at-mospheric chemistry. Ozone, NOx and HOx will be analyzed to findcharacteristic follow-ups of the spectrum fit.

The paper is structured as follows: in Section 2 we describe thedata and models. The effects of different amount of segments inthe spectral fit are discussed in Section 3. As an increased numberof segments (and therewith the amount of fit functions) willproduce a fit that is closer to the single input channels we will alsocall this “quality of fit”. Next Section 4 will focus on the energyrange and its effect on the ionization profile of a distinct altituderange. As the energy spectrum often can not be approximated witha single function, the spectrum will be combined by multiple fitsfor smaller energy ranges. In Section 5 we will investigate if itmatters how the total energy spectrum is divided into thosesmaller parts. For this we compare fits with fixed positions of theintersections and those with variable ones. Both types are used inionization models. Last but not least the fit function itself has atremendous impact on the results. Section 6 will outline the dif-ference between a Maxwell–Boltzmann spectra as e.g. used inJackman and McPeters (1985), Callis and Natarajan (2001) and a

Please cite this article as: Wissing, J.M., et al., Particle precipitation:Atmospheric and Solar-Terrestrial Physics (2016), http://dx.doi.org/10

power-law spectra as used in e.g. Schröter et al. (2006), Wissingand Kallenrode (2009).

All sections include a discussion of the impact on atmosphericchemistry modeling represented by calculations of 3dCTM. Thelast chapter will sum up the results.

2. Data and models

The particle data which are used as input data set originatesfrom the Polar Orbiting Environmental Satellites (POES 17/18) andthe Geostationary Operational Environmental Satellites (GOES 11).GOES measures protons from 4 to 500 MeV using the SEM in-strument (NASA, GOES I-M DataBook, 1996). The POES satellitesare flying at 850 km altitude measuring particles with MEPED andTED instruments down to 150 eV (Evans and Greer, 2004).

This paper focuses on different aspects of the particle spectrumfit. Parts of an ionization model, here AIMOS, are used to infer theparticle count rates in the polar cap as well as the atmosphericforcing. The following paragraph (2.1) describes the AIMOS model.However as the spectrum fit was modified the ionization modelhad to be adjusted accordingly. Changes of the main setup aredescribed in the respective sections of the paper.

As we also present the effects of different ionization forcings onatmospheric chemistry (NOx, HOx and Ozone), we use 3dCTM. Adescription is given in Section 2.2. Section 2.3 gives an overviewon the particle flux during our investigation period and how itcompares to a multiple year distribution. It also explains why acombination of several instruments is reasonable.

2.1. Ionization model: AIMOS

The original setup for the AIMOS has been given in Wissing andKallenrode (2009). It originally includes a spatial resolution, allmain particle species (protons, electrons and alphas) and an en-ergy range from low energetic magnetospheric particles up to highenergetic solar particles.

However as we are interested in the effect of the spectrum fitwe will make a more basic approach prescinding from spatial re-solution and different particle species. We will limit ourselves toprotons precipitating homogeneously inside the polar cap (60°poleward) as it has been done in (e.g. Jackman et al. (1980, 2005)).The advantage is that the follow-ups of the spectrum fit will not besuperposed by other effects, as e.g. electron bremstrahlung thatcan not be traced back to the corresponding particle energy ormodel specific characteristics about spatial mapping of the lowenergetic particle precipitation. Nevertheless the forcing can stillbe considered as more or less realistic. The advantage in usingAIMOS here is that we get mean values for the polar cap derivedfrom two different POES satellites.

Since the low energetic POES TED data is available as differ-ential flux only, we choose the same for the other instruments. Ifnot described separately in the corresponding setup the particlechannels are POES TED (proton band 4, 8, 11 and 14) covering154 eV–9.457 keV, POES MEPED (mep0P1, 2, 3, 4 and 5), covering30 keV–6.9 MeV and GOES SEM (z_p2, 3, 4, 5, 6 and 7) covering 4–500 MeV. The individual energy thresholds are given in Table 1.Using differential channels unfortunately adds some uncertaintyto the particle spectrum, because we need to find the barycentricenergies1 of the differential channels (¼the energy at which thedifferential flux is the same as the measured flux), which thendefine the slope of the spectrum. Unfortunately the barycentricenergies also depend on the spectral slope.





Table 1Energy thresholds of the used proton channels.

Satellite Instrument Channel Energy range (MeV)

POES TED proton band 4 0.000154–0.000224proton band 8 0.000688–0.001000proton band 11 0.002115–0.003075proton band 14 0.006503–0.009457

MEPED mep0P1 0.03–0.08mep0P2 0.08–0.24mep0P3 0.24–0.8mep0P4 0.8–2.5mep0P5 2.5–6.9

GOES SEM z_p1a 0.8–4z_p2 4–9z_p3 9–15z_p4 15–40z_p5 40–80z_p6 80–165z_p7 165–500

a z_p1 is used in Section 6 only.

J.M. Wissing et al. / Journal of Atmospheric and Solar-Terrestrial Physics ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3

To solve this we used a fitting method from AIMOS with aniterative algorithm that determines the slope of the spectrum fromthe barycentric energy and vice versa till a steady state is reached.This is done in first case for a single spectrum function. If thecorrelation coefficient of the fit and the barycentric energies doesnot meet our requirements, the same is done for two segments ofthe spectrum (up to 5 or whatever the setup describes). The choicewhich energy channels belong to a segment is made in a bruteforce method by trying all and selecting by correlation coefficient.The intersection point of neighboring spectral fits defines the en-ergy borders of these segments, which therefore are variable inenergy (except for the setups where they are fixed). In most cases(but not in all) this results in a spectrum that uses the highestpossible number of segments.

If not announced differently we will use a fit function that is

based on power laws: ( )Φ Φ( ) = ·γ−

EplEE0

0. While E0 is usually set to

1 MeV, the flux Φ0 at E0 and γ result from the fit and the energyrange will be divided into up to 5 segments. The resulting functionis designed to cover a wide energy range and even allows tocombine different particle sources in one spectra such as magne-tospheric and solar particles. As far as variations of this fittingfunctions are used the effects of these different assumptions willbe focused in the discussion.

The particle population's angle distribution is assumed to beisotropic. The average energy deposition of a particle in a mono-energetic particle beam is calculated by the Monte-Carlo Simula-tion Geant4 (Agostinelli et al., 2003). The assumed fit function iscombined with the mono-energetic particle's energy depositionsin order to get the accumulated energy deposition profile of the

(footnote continued)

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Barycentric energy for a Maxwellian spectrum:

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E1 and E2 describe the lower and upper energy thresholds. γ and E0 are power-lawand Maxwellian fit parameters that determine the steepness of the spectrum.


whole particle precipitation. According to Valentine and Curran(1958) and Porter et al. (1976) 35 eV is required to create one ionpair. Therefore the atmospheric energy deposition of a spectra canbe transformed into an ion pair production rate.

Atmospheric parameters like composition and density are ta-ken from HAMMONIA (Schmidt et al., 2006).

2.2. Description of 3dCTM chemistry-transport model

The three dimensional chemistry and transport model (3dCTM)used in this issue is a further developed version of the B3dCTM(Wissing et al., 2010; Funke et al., 2011), which is based on thechemistry code of SLIMCAT (Chipperfield, 1999) and on thetransport code of the CTM-B (Sinnhuber et al., 2003). It evaluatesthe chemical composition of the atmosphere on 47 pressure levels,using a grid spacing of 3.75 degrees in longitude and about2.5 degrees in latitude. Chemical reactions are driven by reactionrate constant data from JPL2006 (Sander et al., 2006). Tracertransport is computed using prescribed windfields from externalsources such as LIMA (Berger, 2008). Advection is calculated usingthe second order moments scheme described in (Prather, 1986).The 3dCTM uses a chemical family approach in the stratospherebut not in the mesosphere; details are given in (Sinnhuber et al.,2012). Compared to the development state described there, mainimprovements were made regarding the production of NOx fromboth particle ionization and photoionization. The production ofNOx depends now on the atmospheric state, using the productionrate database presented in Nieder et al. (2014), allowing for rea-listic NOx-production due to ionization in different backgroundconditions.

2.3. Data selection

The two main aspects of the data selection are: which periodshould be investigated and which energy range is important for us.Both questions will be addressed in this section.

Our aim is that our findings may be applicable to more or lessarbitrary time periods. Therefore the first question is if we cansimply use one (or one for each activity level) mean spectra for theparticle forcing. However, two arguments forbid this option:(a) the chemical response of the atmosphere is not linear, meaningthat putting average ionization rates instead of fluctuating oneswith the same average is not the same. For non-linearity of theNOx-production see Sinnhuber et al. (2012) and Nieder et al.(2014). The non-linear behavior of OH-production has been shownin Verronen et al. (2011), even though it refers to electron pre-cipitation. And (b) different assumptions for the fit function willnot only affect the mean, but probably also the variation (range) insingle spectra. Thus we are interested if the atmosphere com-pensates this variation in time or by vertical transport. Conse-quently we always end up with an ensemble of spectra.

The next question is if different activity levels should be con-sidered on their own, e.g. grouped in quiet, medium (storm) orextreme (solar particle event (SPE)) levels. Even though it mightmake sense to examine a quiet period on its own, the atmosphericeffects of a longer solely extreme (SPE) period would be useless assuch would never occur in reality. Also it would be hard to ex-amine such a period as time delayed transport would mix up withinstant production. Thus a useful setup needs to include differentactivity levels.

Our conclusion is that we should look for a period in which thefluxes in all activity levels are good representatives for averageproton flux in terms of median spectrum and its variation range.Also it is reasonable to look for a period in which the activity levelsare separated well enough to allow backtracing of chemical effectsto the corresponding activity.





Fig. 1. Median and interquartile range of the proton flux for Nov/Dec 2006 and


There is no common agreement on what is e.g. a quiet period.In some cases geomagnetic indices are used, but since the chem-istry model in this paper simulates the atmospheric impact from16 to 130 km it sounds reasonable to focus on the more energeticpart of the spectrum and group the particle spectra based on amedium (z_p2 4–9 MeV from GOES) and a high energetic protonchannel (z_p6 80–165 MeV from GOES). Therewith we define aquiet level that has no significant contribution of middle and highenergetic particles, a medium or “storm” level that has an in-creased contribution of medium energy particles but no high en-ergetic impact and an extreme level that shows strong high en-ergetic particle flux which clearly indicates a SPE. In detail thelevels are given here:

2004–2007: For simplicity the median and upper and lower quartiles of each

QuMe

2 This is also thelower quartile at 500

Please cite thisAtmospheric an

reason why the median for one exMeV.

article as: Wissing, J.M., etd Solar-Terrestrial Physics

channel have been fitted by multiple power-law spectra. Note the vertical lines thatindicate the upper energy range of the TED instrument and the lower threshold of
z_p2 ( )−m s sr MeV2 1 z_p6 ( )−m s sr MeV2 1
the GOES SEM instrument. The amount of 2 h periods entering the different activitylevels is indicated by the “#”-symbol.
iet <500 <10
dium
≥500 <10 reme ≥10 Ext
As far as our experience goes these flux levels are useful todescribe what is commonly known as quiet level, storm level andSPE, thus these terms are used synonymously, especially when weare discussing the impact on chemistry.

Using these activity levels, we analyzed 4 years of satellite data(2004–2007, including 17491 two-hours' spectra) and compared itwith our two months' investigation period November/December2006 (720 spectra).

Fig. 1 shows the median spectral slope and its interquartilerange (spread of the distribution that omits the lowest and highest25%) for the three different activity levels within our investigationperiod and during 2004–2007. Actually the figure shows a spec-trum fit (using 5 segments) to the upper and lower quartiles and tothe median since it became completely unreadable including allthe lines for every energy channel for all six setups.2

Two aspects become obvious in the Fig. 1: (a) the median fluxspectrum as well as the interquartile range of the two months'period agrees very well with the 4 years' values. In so far we cannote that we have a correct forcing, even including the typicalvariance that also occurs in the long-term observation. And(b) there is no variation in the spectral slope at the transitionbetween POES TED and MEPED as well as between POES MEPEDand GOES SEM. All changes in the spectral gradient are within theTED instrument or within the GOES SEM instrument.

While (a) indicates that our investigation period is a good re-presentative for the average flux – and that our results may also beapplicable to other periods, (b) shows that there statistically is nobreak in the spectrum where two different instruments or evenwhere instruments from different satellites are bound together.

To whom it might confuse that POES MEPED and GOES SEMshow such a good match even without any flux mapping, giventhat altitude, orbit, view points and opening angles differ and justnominal geometric factors are known: Actually there is an intrinsicflux “mapping”. According to Bornebusch et al. (2010) the particleflux increase by a narrowing magnetic flux tube (e.g. from ageostationary orbit down to 800 km altitude of POES) is fullycanceled out by the particles that are mirrored back due to theincreased magnetic flux. This is of course theoretically and basedon an isotropic pitch angle distribution (which is not measured),but it means that GOES data in first assumption is already “fluxmapped”, which is also the justification for a number of other

treme setup falls below the

al., Particle precipitation:(2016), http://dx.doi.org/10

ionization models which use GOES data as is.Of course this does not mean that the flux of the instruments

itself are correct or the transitions are always matching (localvariations may apply as well), nor that the isotropic pitch angledistribution is a proper assumption. However, the intention of thispaper is to show the impact of the fit function parameters used in(existing) ionization models. Since TED, MEPED, GOES SEM arecommonly used and there is no ionization model known by theauthors that does not use isotropic pitch angle distribution theseassumptions look reasonable for this paper.

Consequently, due to the smooth transition between the in-struments, we (a) see no problem in combining the different in-struments into one large energy range and (b) we do not see abenefit by separating the instruments as the desired input forchemistry models is a full altitude covering ionization rate. Also aseparation into instrument-range segments would produce energygaps and thus ionization gaps at certain altitudes and increase thedegrees of freedom at the energy thresholds of each instrument.Either does not help to identify the impact of the fit functionparameters on chemistry. In fact, currently chemistry modelershave the option to include ionization rates from one more or less“full-range” energy spectrum or to include magnetospheric parti-cles from one model, solar particles from another and GCRs from athird one, which creates gaps or overlaps in the ionization profilewherever the energy thresholds of the separate models do notexactly match. End even in case that they match a fixedintersection is created which affects the results as described inSection 5.

Coming back to the activity levels. A closer look at the in-vestigation period in Fig. 2 reveals that it consists of more than amonth relatively quiet period including a shorter medium (storm)activity in between, while in December 2006 two SEPs hit theEarth (extreme periods), each followed by a medium period. Fi-nally we see a quiet period again.

The interesting aspect is that there is a relatively clean se-paration between the different activity levels, which allows totrace back the chemical follow-ups to the corresponding activitylevel and still looking at a natural setup. Thus the activity levelsmedium and extreme are marked in the chemistry plots.

A final remark should be made about the reliability of the usedsatellite data. As already noted particle detectors are sufferingfrom long-term degradation. Thus it makes sense to use satellitesshortly after launch. In fact that is a little more delicate here than itmight be in other examinations since we use data from 3 differentsatellites. Thus all of them being just launched is a little bit toooptimistic. But we selected the investigation period to be in 2006,because this is the first year when AIMOS uses a new set of POES





Fig. 2. Overview of the activity levels in the investigation period Nov/Dec 2006together with Ap and DST indices. There is some agreement of the geomagneticindices with our activity levels, but as both indices are not sensitive to high en-ergetic particles we decided that it is best to use the measured flux levels for de-termination of the activity level.


satellites, namely POES-17 (launch date 15.10.2002) and POES-18(launch date 30.08.2005).

Fig. 3. Different amount of segments for the same data. Top: spectral functions andthe energy channels that have been fitted. Bottom: resulting atmospheric ioniza-tion rate.

3 It should be added, that whenever we talk about magnetospheric, solar orgalactic cosmic particles in this paper, we do not assign them with exact energyranges. Instead they are characterized by typical precipitation patterns that indicatetheir source. GCRs for example are blocked by when a coronal mass ejection passesEarth, which is nicely seen in Fig. 4 (top or middle). Magnetospheric particlescorrelate with geomagnetic indices and ionize the atmosphere around 110 km andthe solar particles are connected to the solar particle events and may ionize allregions of the atmosphere.

3. Amount of segments/quality of fit

Any ionization model that uses particle measurements needs acontinuous particle spectrum to calculate the ionization profile. Asparticle data consist of discrete differential energy channels, theiradequate representation should be a fit through the characteristic(barycentric) energy of each channel. Apart from the kind of func-tion that should be used (see Section 6 and e.g. Mewaldt et al. (2005)for more details), the main aspect is probably the amount of seg-ments that are fitted by a separate function. Given that a shock ac-celeration assumes a power-law spectrum, and the whole energyrange may be affected by a superposition of shock mechanisms, acombined spectrum of piecewise power-law functions may be ap-plicable. We will use a combination of 1, 3 and 5 power-law fits here.

It seems reasonable to consider a fit as “better” if it shows abetter mathematical correlation with the points that it should fit.Since a division into smaller segments always results in a bettercorrelation with the original points, we can consider the 5-seg-ment fit as obviously the best. Of course that does not mean that itnecessarily produces the best results in a chemistry model, but ifmeasurements would be correct, physical as well as chemical in-teractions entirely known and models a perfect representation ofthe entire atmosphere, then the 5-segment version would defi-nitely be the best option.

We would like to note that the 5-segment version or even a fitwith the maximum number of n-1 segments (referring to n energychannels) may not necessarily be the best representation of thereal particle spectrum flux as single channels are likely to becontaminated (or e.g. the sensitivity of a channel may not be equalthroughout the whole energy range, leading to a shifted bary-centric energy) and the effect of single outliers will be reduced bya smaller number of fit functions.

Fig. 3 shows the spectrum fit and the resulting ionization rateprofile for a typical quiet day 2-hour interval. As expected theagreement is worse using just one segment, leading to an error ofhalf an order of magnitude in the lower atmosphere compared tothe other fits. A more realistic (and in some ionization modelsused) version is a fit of 3 segments. Apart from a small surplus at15 MeV (always compared to the 5-segment fit) it looks like a goodagreement. But we need to keep in mind that the spectrum fit ispresented in a double-logarithmic graph. Consequently evensmallish differences in the plot representing the spectral fit havesignificant effects on the ionization rate. The ionization rate profile


reveals that this “small” surplus is responsible for an increase ofabout 70% at a certain altitude (here 70 km).

As single time intervals are not necessarily representative Fig. 4shows the ionization rates for the different amount of segmentsfor November–December 2006. Starting with the 5-segment fitionization rates, we can see magnetospheric particle ionizationaround 130 km, high energetic contribution from galactic cosmicrays (GCR)3 producing a local maximum around 30 km. Missingionization below about 16 km is due to the restriction: particleenergy <500 MeV. Two solar particle events (SPEs) occur betweendoy 340 and 350, leading to strong ionization in all but especiallymiddle altitudes between 50 and 100 km, both followed by For-bush decreases (missing GCR precipitation).

Comparing the 3-segment ionization rates with the 5 segmentversion we can see good qualitative agreement with the justmentioned features but a quantitatively less pronounced magne-tospheric maximum. In contrast, the 1-segment method offers acompletely different ionization profile, lacking the GCR part, un-derestimating the magnetospheric maximum and significantlyshifting the solar energetic particle (SEP) maximum to altitudesbelow 50 km.

For a more comprehensive view see Fig. 5. Here the





Fig. 4. Amount of segments: comparison of ionization rates for November–De-cember 2006. (The colored web version may allow an easier interpretation of thecontour plots. This also applies for the following chemistry plots.)

Fig. 5. Amount of segments: comparison of ionization rates for the different setupsfor November–December 2006. The 50% shading is equivalent to the interquartilerange.

Fig. 6. Amount of segments: median ionization rates and interquartile ranges inrelation to the activity level.


discrepancies between the 3-segment version and our referencescenario, the 5-segment version, are given in shadings (respec-tively 1 vs. 5-segment version, in dotted regions). In detail, theionization rates of the different versions have been divided by eachother for every 2 h interval (meaning a quotient of 1 would be aperfect agreement) and the colors (dot sizes) indicate the quo-tients that include 25, 50, 75, 90 and 100% of the intervals aroundthe median. All intervals of the two months period, November–December 2006, have been used.

To include 90% of the ratios of 3 and 5-segment fit functionsionization rates, a variation (error) range of 50% is needed. Theerror range of the 1 segment version is not much worse – but themedian shows systematic over- and underestimations at distinctaltitudes, as there is the less pronounced magnetospheric ioniza-tion (factor 0.6 compared to the 5 segment version), a factor1.4 overestimation at 70 km and the missing GCR ionization (re-duced to a factor 0.5–0.6 in 20 km). The 3 segment version showsthe same tendencies but much smaller deviations to the 5 segmentversion.

In the following setups we will just deal with the


comprehensive view as it includes all necessary information aboutthe ionization rate in one graph.

As discussed above, the investigation period can be divided intodifferent activity levels. Fig. 6 shows the median ionization ratesand their interquartile range. Square signs indicate quiet time, dotsmedium (storm) and stars the extreme (SPE) periods. Obviouslythe number of segments has a nonuniform impact at differentactivity levels. While e.g. the 1-segment version underestimatesthe low latitude ionization rate (the GCRs) during quiet time, itsignificantly overestimates the solar particles on the same altitudeduring the extreme period (SPE). Going to the more realistic3-segment variant, it underestimates the ionization rate above110 km in all scenarios, and it overestimates the ionization ratesbetween 60 and 100 km during quiet time.

Given these differences based on the amount of segments, wewould like to introduce the term “quality of fit” which basicallymeans how many segments are used per magnitude in particleenergy. As it can be seen in Fig. 6 where we used the 1, 3 or5 segments for the same energy range, the quality of fit is animportant aspect for the description of an ionization model. Incontrast, Fig. 11 (see next section and just consider the regionbelow 90 km) shows that ionization rates that originate fromdifferent energy ranges but having the same quality of fit are verysimilar (in median and even interquartile range).

3.1. Chemical follow-ups

Since we want to assess the impact of different amount ofsegments for atmospheric chemistry modeling, the 3 versionshave been simulated in 3dCTM. Fig. 7 shows the NOx absolute





Fig. 7. Amount of segments: impact on NOx absolute volume mixing ratio for the5-segment case in Section 3 as well as for the extended energy range in Section 4.

Fig. 9. Amount of segments: impact on NOx, 1-segment compared to the 5-seg-ment case: up to (�)90%.


volume mixing ratios resulting from 5 segments (as well as anextended energy range setup that will be discussed later) for thetwo month period (the white line separates November and De-cember). Typically the highly ionized upper atmosphere (above100 km) shows a higher absolute NOx volume mixing ratio thanthe lower atmosphere.

Also the NOx ratio between 70 and 90 km increases slightlyduring the relatively quiet time before the SPE, which indicates adownward propagation of NOx. With onset of the SPE (extremeactivity level starts at doy 341, indicated by the red (black in thegrayscale version) color bar in the lower part of the figure) themixing ratio above 50 km enhances by one order of magnitude.

The NOx follow-ups for the 3 and 1-segment versions areshown relative to the 5 segment results in Figs. 8 and 9. As con-centrations typically vary intensively (e.g. on 8 orders of magni-tude for NOx), mainly depending on altitude and activity level, anddifferences between the setups (which are in the order of a few10%), ratios to our reference scenario turned out to be the bestoption to identify and to quantify the differences.

Starting with the 3 segment version (Fig. 8), there is a clear NOx

underestimation above 80 km for most of the time, except for theperiod of the solar particle event. The underestimation reaches upto �40% on the upper altitude border. Given that we have adownward transport of NOx in these altitudes, heights down to80 km are affected. During the onset day of the SEP precipitationhowever, the altitude around 110 km even shows a NOx increase ofup to 50%. Another systematic feature is the small NOx over-estimation at 80 to 90 kmwhich is visible in the first 10 days of thesimulation only. It originates from the higher ionization rates ofthe 3 segment version in this altitude, but in the later phase it iscloaked by the lower amount of downwelling NOx in this version.

Fig. 8. Amount of segments: impact on NOx, 3-segment compared to the 5-seg-ment case: up to (�)50%.


The first days of the 3dCTM run can be considered as initialization.For the 1 segment version (see Fig. 9) the effect is significantly

stronger, as expected from the comprehensive ionization rateFig. 5. First of all, the NOx underestimation in the upper atmo-sphere reaches even below a factor of 0.1 (�90%), again with amaximum at the upper altitude border and again with a smalloverestimation during the SPE onset (between þ20% and �60% inthe main event phase). Second, the negative effect especially afterthe event is visible down to 45 km. As before, the overestimationin mid altitudes (80–90 km) is cloaked as soon as it overlaps withthe lower amount of downwelling NOx. In addition there is anoverestimation at the lower boundary altitude of the ionizationmodel at 20 km during the main SPE phase (extreme activity le-vel). Referring to Fig. 4 this is due to a strong altitudinal shift of theionization maximum during that time, showing that the highenergetic tail of the energy spectrum during an SPE is decreasingstronger with energy than a single power-law fit of the wholespectrum suggests. However, the badly represented low altitudeionization rate maximum during quiet time (which originatesfrom GCR) seems not to be a problem for NOx chemistry modeling.It seems that ionization rates in this altitudes have to be orders ofmagnitude higher than they are during SPEs to have a significantimpact on NOx. Although it should be noted that the highest en-ergy range in this study is 500 MeV and therefore just a small partof the GCR spectrum is covered.

In sum, lesser segments lead to an underestimation of highaltitudinal ( > )50 km NOx mixing ratio. This effect is increasingwith rising altitude. Systematic over- or underestimations in thelower altitude which can be seen from the combined ionizationgraph (Fig. 5) have no direct impact on NOx or are cloaked bydownwelling. The completely different particle spectra during theSPE are also visible in the comparison of the NOx mixing ratios.While the 3-segment version shows just small differences, espe-cially in the second SPE, the 1-segment version show large de-viations during the whole simulation period (even though it isslightly improved during the first SPE but not the second one).Consequently we can conclude that the second SPE spectrumshows segments of different steepness, which might imply a su-perposition of multiple acceleration processes.

The Ozone impact of particle precipitation is mainly restrictedto the SPE when we see a depletion of roughly 50% between 70and 90 km (Fig. 10, top). The differences between the 5-segmentrun and the 1-segment version are in a similar order, reaching 50%overestimation of the 1-segment version at 75 km during the SPEonset (Fig. 10, bottom). Concerning the 3-segment version thepicture is similar, but reaching a 20% overestimation at 65–75 kmduring the onset only.

Given that the amount of segments has a tremendous impact,the following sections will deal with the same amount of





Fig. 10. Amount of segments: impact on Ozone plotted as logarithmic volumemixing ratio, (top) 5-segment, (bottom) 1-segment case compared to the 5-seg-ment case.

Fig. 11. Energy range: median ionization rates and interquartile ranges in relationto the activity level.


segments (fits) per magnitude in energy as we assume this willmake fits more comparable even if they do not cover e.g. the sameenergy range.

4. Energy range

Ionization models depend on satellite particle data. As theenergy range is limited according to detector specification andsatellites in use, all available ionization models use different en-ergy ranges – or in terms of ionization: they are suitable for dif-ferent altitude ranges. Focusing on protons the ionization by singleparticles shows a distinct characteristic, the Bragg Peak, whichmeans that most particle energy is deposited at the end of thepath, while there is almost no energy loss and therefore no sig-nificant ionization before (above) that. Consequently, the first es-timation is that ionization rates for specific altitudes should be thesame as long as the different ionization models cover the corre-sponding “core” energy range. In reality, however, we will see thateven the same model with the same power-law assumption differsdepending on whether we use the core energy range only or if weextend it without changing anything in the particle data that en-ters to the core altitude. This section will describe the main rea-sons and give a dimension of its impact on atmospheric chemistrymodeling.

We compare the three sets of ionization rates that differ inenergy range only: a small “core” proton spectrum 0.8–500 MeV, a“medium” 0.08–500 MeV and an “extended” one from 154 eV–500 MeV. All spectra are combinations of GOES and POES data forthe northern polar cap. The POES data includes TED channels(154 eV–9.457 keV with 4 subdivisions), mep0P1 (30–80 keV),mep0P2 and mep0P3 (80 keV–0.8 MeV) as well as mep0P4 andmep0P5 (0.8–6.9 MeV). The GOES channels are given by z_p2 toz_p7 (4–500 MeV in 6 subdivisions).

All spectra are fitted with multiple power laws. In order to get a


best fit, the positions of their intersections are variable. As wewant to focus on the effect of the different energy ranges only, the“quality of fit”, namely the quotient of amount of segments andenergy range were chosen to be similar, which we expect to endup in a comparable model accuracy.

Here we choose a combination of 2 segments for the core en-ergy range (POES mep0P4 and mep0P5 as well as the GOESchannels), the medium energy range with 3 segments (POESmep0P2 to mep0P5 as well as the GOES channels) and an ex-tended range (all POES and GOES channels) which will be fitted in5 segments. This results in 0.72 segments (fit functions) permagnitude for the small energy range, respectively 0.79 for themedium and 0.77 for the extended range. It should be noted thateven though we choose the same number of fits per magnitude inenergy, the fit over the extended energy range commonly is mostlikely the best because linear parts of the spectrum allow otherparts of the spectrum to be divided into smaller segments (e.g. inthe extended fit in Fig. 12, top, 10 channels are represented by onepower-law fit). The impact of variable intersections will be dis-cussed in Section 5.

In fact as Fig. 11 shows, the medians of all setups are very closetogether for the corresponding activity level and compared to theprevious setup (Fig. 6). Even the interquartile range is congruent.Thus the “quality of fit” seems to be a reasonable criteria to de-scribe the ionization models. Note that the profiles diverge above90 km as this is the upper altitude border of the core setup.

In a first guess the extension of the energy range, in this casedown to lower particle energy which ionizes in the upper atmo-sphere (thermosphere), should have no or just an insignificanteffect on the ion pair production in lower altitudes, especially asmedian and interquartile range are almost identical. However,different energy ranges may show severe differences in single io-nization profiles (see Fig. 12, bottom) even on the core altitudesthat are covered in all versions. The culprit can be identified easily:an enlargement of the energy range causes variations in the fittingfunction. Unfortunately, the logarithmic scaling in Fig. 12 (top)hampers to see the differences between the spectra. But since thedifferences in the spectra are directly proportional to the differ-ences in the ionization rate of the corresponding particle energy,we can directly look at the resulting ionization profiles in Fig. 12(bottom) which reveals 40% variation at 66 km altitude, respec-tively 200% at 20 km in this case.

As a first impression the reason might look too simple to beworth noting, but every recent ionization model is based on par-ticle measurements and uses energy fits. Therefore, variations dueto the fit function are an inherent and universal problem of allionization data.

A close look at the (northern polar cap) ionization of No-vember–December 2006 (see the comprehensive Fig. 13) gives anoverview of the long-term behavior of both truncated energyranges in relation to the extended one. For this, the ionization rate





Fig. 12. Top: the energy spectra shows only minor variations. But please note thedouble-logarithmic scale. The medium/extended range has been fitted using 3/5segments. Bottom: ion pair production according to the energy spectrum fitsshown on top. The deviation of both energy ranges is visible at mid altitudes (e.g.66 km).

Fig. 13. November–December 2006 2 h-ionization profiles from the extended andthe narrow energy range are shown in ratio. For detailed information look atSection 4.

Fig. 14. Impact of the energy range on NOx: (top) medium divided by extendedenergy range, (bottom) core divided by extended energy range.


of the extended spectra has been divided by the ionization rates ofeach of the truncated spectra. A factor of 1 would indicate an exactmatch.

Most prominent in Fig. 13 is the upper energy threshold of thecore and medium spectra, producing the lateral shift at 90 km for800 keV, respectively 105 km for 80 keV. Consequently belowthese altitudes the ionization rate ratios can be compared. In fact,the spread is much less than in Fig. 5. But the following chemistrydiscussion will show that the upper part is not negligible. In thecore altitude 90% of the ratios are within a variation range of 25%,with the biggest variations at the upper and lower altitudes whilethe center of the core altitude (at around 35 km) shows variationsof less than 10%.


In sum this implies three things: (a) The median ionization rateis not affected by setting an energy range if the “quality of fit” ispreserved. (b) The spread of the ionization rates is similar in allsetups. (c) But every single modeled ionization rate profile has animplicit statistical error of up to 25% compared to the same 2 hinterval in the other setups (just because an energy range needs tobe set).


The setup of the chemistry simulation is similar to Section 3.1but using the ionization rates with core, medium and extendedenergy range. We again used the 3dCTM chemistry model.

From Figs. 11 and 13 we would expect that the influence of theinherent variations will minimize on longer time periods. There-fore we simulated the November–December 2006 period andcompared NOx, HOx and Ozone impacts. Given that all forcingcovers the core altitude up to about 90 km, this is the regionwherethe atmospheric effects should be more or less similar. Ad-ditionally, the medium and especially the extended energy rangewill insert a higher ionization in the levels above 90 km. Thus thissimulation will on the one hand show the impact of the inherentvariation inside the core altitude and on the other hand it will givean estimate how precise low- and middle-top models can be incomparison to high-top models.

The extended energy range is the same as the 5-segment setupin the quality of fit section, therefore the NOx absolute volumemixing ratio of the extended energy range has already been shownin Fig. 7 and discussed in the first paragraph of Section 3.1.

If we compare these results to the medium (Fig. 14, top) and thecore (Fig. 14, bottom) energy range versions three aspects areseen: (a) As expected, there is a strong underestimation of the NOx

ratio above the nominal altitude range. In the medium energyrange version NOx drops to 10% above 125 km, in the core versionit reaches this level already at 105 km. (b) There is a lack of NOx inthe altitude restricted versions below 110 km that builds up duringquiet time. Looking at the first 20 days of the simulations, theshape looks like a lack of downwelling NOx due to the missingcontent in the higher atmosphere. However, there is an interestingfeature at about 90 km. Here we see a local NOx minimum in both





Fig. 15. HOx: (top) medium/extended energy range, (bottom) core/extended energyrange.

Fig. 16. O3: (top) medium/extended energy range, (bottom) core/extended energyrange.


comparisons: in the medium range version we lack about 60% ofthe NOx, while the core range version even lacks 70% in the periodbefore the SPE onset. According to Fig. 13 the ionization ratemedian of the core version is somewhat 5% lower than the ex-tended range version, which might support a smaller local sourceat 90 km, an even deeper insight is provided by Fig. 11 (for quietperiod) that reveals a lower local ionization rate for the truncatedspectra above 72 km. Therefore we can only conclude that not onlythe lack of downwelling NOx from altitudes above 105 km is re-sponsible. (c) During the SPE the NOx ratio is pretty much thesame in the core altitudes (except below 30 km), indicating thatthe NOx directly produced inside the core altitude dominatesduring these periods and magnetospheric sources can be


neglected. However, this only holds during the onset phase of theSPE as the rapidly downward extending lack of NOx on doy 342–348 shows. A feature that is seen in the core version only is a 10–20% NOx overestimation at the lower altitude border during theSPE, which is a local effect of the ionization rates. As most of NOx

features are cloaked by downward transport, we will have a lookat the local effects with HOx (Fig. 15) and Ozone (Fig. 16).

Starting with HOx, the truncated spectra differ during the SPEperiod only. Altitudes below 75 km (down to the model boundary)are affected. There is no systematic over- or underestimation but astochastic variation by about 720%. Interestingly the biggestvariations occur in the medium energy range run in the main SPEphase, a period when the core energy run shows no deviation,which underlines the stochastic behavior. Due to the limited life-time of HOx there is no long lasting effect that impacts the at-mospheric chemistry run.

For Ozone the picture is quite similar. Deviations to the ex-tended spectra are mostly found during the SPE phase and atlower altitudes than the NOx differences. Here the height between50 and 90 km is affected. The quantitative effect is much smallerthan in the HOx case, reaching about 73–4%. Even though thereseems to be a systematic and long-lasting (up to 10 days) under-estimation in the truncated spectra, which is propagating down-wards, the impact of SPEs itself seems to be stochastic and mightalso be overestimating.

Given that HOx and Ozone differences are almost exclusivelylimited to the SPE period and altitudes below 75 km for HOx andbelow 90 km for Ozone, the impact of low energetic particles(<800 keV, for HOx even <80 keV) can be regarded as insignificant.The stochastic impact of both species represents the typical var-iation of the spectrum fit due to a changed energy range.

Historically we use those particle data (satellite/channels)which are available as long as the energy range covers the altitudeof the ionization model. Given that there is a descent of NOx a firstimprovement is to use high top models that include even lowestparticle energies that might cause ionization. But even though thiswould remove the top border aspect, the spectrum fit variationscan not be eliminated (just minimized by better spectral mea-surements). In this setup (characterized by 6 orders of magnitudein energy, 5 power-law fit functions and a realistic ionizationmodel) the resulting error range is about 720% for HOx and 73–4% for Ozone during the SPE plus a significant and accumulatingNOx deviation above 72 km. This is an intrinsic problem of all io-nization models that cannot be suppressed. Anyhow, the impacton atmospheric chemistry models (and climate simulations)strongly depends on species and time-frame and in contrast to thestrong and long lasting impact on NOx, HOx and Ozone do notshow a significant variation outside of the SPE.

The thermospheric NOx is dominated by electrons, not protonsas considered here. However, as for the electrons also an energyrange has to be defined, we would expect a similar error range forthe ionization rate and chemical follow-ups as for the protons butless limitation to SPEs as electron precipitation is mostly definedby geomagnetic disturbance. Additionally the higher amount ofdownwelling NOx might cover features below.

5. Fixed and variable intersections

A (sufficiently large) particle spectrum normally does not havea constant slope. The physical reason can be, for example, differentparticle populations that experienced diverse acceleration me-chanisms like shock accelerated SEPs, auroral particles and galacticcosmic rays. Another example could be a superposition of differentshocks. Therefore it is reasonable to divide the particle spectruminto segments that can be fitted individually. However, the





Fig. 18. Fixed and variable intersections: median ionization rates and interquartileranges in relation to the activity level.


disposition of these segments is not standardized in ionizationmodels. Consequently we will have a look at the impact of the twomost common setups.

Setup (a) is the fixed energy intersection. In this case we alwaysuse the same particle energies to divide the particle spectrum. Theadvantage of this version is that the fitting algorithm is straightforward and usually one or several of the mid energy channels aretaken to define the intersection energies. Setup (b) is the variableintersection. Here we adjust the position of the intersections inorder to get the best fit of the whole spectrum. This calculation ismore complex as it is an iterative method and needs correlationcoefficients to be calculated in each step as well as new bary-centric energies that depend on the actual slope of the particlespectrum. But after all, the resulting function represents the ori-ginal spectrum significantly better than the fixed version, which isthe reason why we will take the variable intersection method asour reference scenario.

Since both versions are generally in use, we will analyze howionization rate and chemical follow-ups are influenced by usingfixed or variable intersections. For this we will make typical as-sumptions: the energy range is 0.8–500 MeV, based on NOAAGOES measurements of November and December 2006. The par-ticle spectrum will be divided into 3 segments. The fixed version(a) will have intersections at 10 and 50 MeV. The resulting spectraare converted into ionization rate profiles by the same algorithmtaken from AIMOS.

A first look at a (as we will see a very characteristic) spectrumsample (Fig. 17, top, during the SPE) reveals the intrinsic problemof fixed intersections. Here the second highest energy channel isabout an order of magnitude too low for a constant slope in thethree highest channels. If we assume this to be a correct mea-surement (which might be justified by the transition to galactic

Fig. 17. Fixed (solid line) and variable (dashed) intersections: spectrum (top) andionization rate profile (bottom).


cosmic rays that cause an increase at higher energies) than thisoverestimation of the fixed intersection version yields a similarfactor 10 surplus in the ionization rate profile as well.

As every proton particle energy has its specific Bragg-Peak al-titude, we can directly map the fitted spectra (Fig. 17, top) to theionization profile (bottom). The overestimation at the secondhighest channel matches with the overestimation at 20–50 km. Athigher particle energies the fit functions cross, leading to lowerionization in the fixed version. However, even though this is aneffect of the different fitting methods, it has to be treated with careas we do not know how the spectrum continues at higher en-ergies. Other characteristic features are the good agreement of theionization rates around 60 km which originates from the particleenergies between about 10–25 MeV. As we see in the spectrumthis is where both fits have their first intersection. Finally theoverestimation in the altitudes 66–95 km can be traced back to theslightly higher fixed version spectrum fit. Everything above 95 kmcan be discarded as the lowest particle energy is 0.8 MeV.

When splitting the period into the three activity levels (seeFig. 18) we can see that fixed intersections boost the ionizationrates of all activity levels and on all altitudes. The median as wellas the interquartile range is shifted to higher ionization rates by upto a factor of 2.5. During quiet periods below 70 km the agreementis better, which leads to a significantly smaller deviation duringthe whole investigation period.

The comprehensive Fig. 19 gives the ionization rate ratio offixed/variable intersections. It clearly shows that the features givenin the example (Fig. 17) are very typical for most of the time. It alsopoints out that the overestimation at 20–50 km appears regularly,while Fig. 18 shows that this can be linked to medium (storm) andextreme (SPE) periods. To include 90% of the ratios at these alti-tudes a 60% overestimation has to be taken into account. Anotheraspect is a slight general overestimation of about 5% as indicated

Fig. 19. Fixed and variable intersections ionization overview November–December2006.





Fig. 20. Fixed/variable intersections: (top) NOx, (middle) HOx, (bottom) Ozone.


by the red (light-gray in the grayscale version) shaded area (25% ofall ratios around the median) and an increasing overassessmentabove 70 km, reaching 30% at the 95 km (top boundary).


The already discussed discrepancies between 20 and 50 km inFig. 17 (bottom) can be directly linked to the HOx surplus (up to50%) in the fixed version at the same altitudes during the SPEperiod in Fig. 20 (middle). Also at 65–70 km we observe a smallHOx overestimation of about 5–10%.

Even though the HOx increase is significant, it is limited to theSPE. Given that a high flux of high energetic particles is missing,other periods show a difference of less than 5%, regardless how theshape of the spectrum looks like.

For Ozone the picture is relatively similar (Fig. 20, bottom). Adifference between the two versions is just seen during the SPE,when energetic particles have a direct impact on the middle at-mosphere. Qualitatively the fixed version shows a discrepancy ofup to �8%, centered at 70 km. At first glance this is surprising in sofar as the ionization rates show their best agreement in this


altitude (see Figs. 18 and 19). The reason is that the HOx-cycle isvery effective between 70 and 80 km altitude and that the relativeHOx-growth peaks in this altitude. Below this altitude HOx num-bers are already high so that the relative increase is small. Giventhat the fixed version shows a HOx increase around 65 km, this isthe reason for the Ozone decline.

A completely different matter is seen in the case of NOx, seeFig. 20 (top). Here the discrepancies are limited to the periodoutside of the SPE and to high altitudes. Given that 0.8 MeV is thelow energy limit, all particle impact above 95 km can be con-sidered as bias and should be ignored. But even then the over-estimation of the fixed version reaches 75–100% in high altitudes.A little surprising is that we do not see a NOx difference during theSPE period even though Fig. 18 indicates a significant ionizationdifference. This could eventually be an already saturated atmo-sphere so that a factor 2 more ionization does not make a differ-ence any more.

Of course we cannot make a general statement on the quality ofall fixed and variable setups, since a different selection of the in-tersection positions will impact the fit tremendously, but we hopeto draw the readers' attention to the point that it probably matters,because by using fixed intersections the information gets lostwhere exactly the slope changes. In this setup we observed ioni-zation rate differences of more than factor 2, NOx overestimationsof up to factor of 2, HOx overestimation of 50% and Ozone un-derestimations of up to 8% – with the same particle measurements,both using power-law fits, the same energy deposition model andthe same chemistry model. Given that we can minimize the im-pact of different slopes in a particle spectrum we suggest usingvariable intersections.

Furthermore we will not disregard that the fixed intersectionsmay have advantages as, e.g., the stability. The variable positions ofintersections are defined by a barycentric energy fit and compar-ison of correlation factors. Since very crude particle spectra mayneed a couple of fit functions on a small energy band the rest ofthe energy range will be less accurate than it might be using fixedintersections.

Last but not least we have to keep in mind that the fit functionis not the exclusive criteria of fixed intersections. Within themeasuring process the limited amount of energy channels on asatellite has a comparable impact on the spectra.

6. Particle spectrum fit function: power-law vs. exponential

The main premise for a spectrum fit function is that the spec-trum should be accurately represented, meaning that no char-acteristic information should be removed or added. However, aparticle spectrum over many orders of magnitude can be verydynamic and is normally just fragmentary described by a fewdetector channels. Consequently there are many options to com-bine various kinds of fit functions, amount of segments andstepped, instant or smooth crossovers (see e.g. Mewaldt et al.,2005). We want to keep the comparison as simple as possible,leaving out smooth crossovers and concentrate on fundamental fitfunctions: (a) the power-law fit (straight line in a log-log graph)and (b) the exponential fit (straight line in a linear-log graph). Bothfunctions have a physical background: the exponential functionrepresents the high energetic tail of the thermal spectrum as givenby the Maxwell–Boltzmann particle distribution (Roble and Ridley,1987). Consequently it is labeled as “Maxwell” in the figures. The

formula is: Φ ( ) = −E CeexpE

E0 where C and E0 result from the fit.The power-law spectrum has its justification in the theoretical

description of the shock acceleration (Fermi, 1949).Also, both fit functions are used in existing ionization





Fig. 21. Comparison of different particle spectrum functions for quiet time. Thehigh energetic tail of the Maxwell–Boltzmann spectrum (exponential) is given by adashed line, the power-law by a solid line: (top) spectrum fits, (bottom) ionizationrate profile.

Fig. 22. Powerlaw–Maxwell ratio of ionization Nov–Dec 2006.

Fig. 23. Power-Law vs. Maxwellian: median ionization rates and interquartileranges in relation to the activity level.


models, e.g. exponential spectra in Jackman and McPeters(1985), Callis and Natarajan (2001) and the power-law spectraare used in e.g. Schröter et al. (2006), Wissing and Kallenrode(2009).

Note that a realistic spectrum should be a superposition ofboth, namely the Kappa-distribution (Gosling et al., 1981). Sincethe Kappa-distribution is generally not used in ionization models,we want to discuss the effect of both elementary spectra used inionization models and their impact on atmospheric chemistry.

As every impact besides the fit function should be suppressedin this section we will use the same particle data (GOES-11, SEMincluding z_p1, 0.8–500 MeV) and the same energy depositionalgorithm (GEANT4, Monte-Carlo, as used in AIMOS). The energychannels will be fitted on three fixed segments: 0.8–10 MeV, 10–50 MeV and 50–500 MeV. This is a quite realistic setup for an io-nization model as e.g. Jackman et al. (1980), Jackman et al. (2005)uses three exponential fits on the segments 1–10 MeV, 10–50 MeVand 50–300 MeV.

As in the previous setups the model period includes Novemberand December 2006, resulting in 720 single profiles.

Power-law and exponential fit cannot achieve a perfect con-gruence. In fact, if the intersections are at fixed positions in bothfits, the power-law fit (see Fig. 21, top) will typically exceed theexponential one at these intersections while it is vice versa in themidrange between them. Given that the slope of the spectrumimpacts the barycentric energies of the channel (the point wherethe function should reach the measured differential flux) this isnot a strict rule but depends on the slope. The tendency howeveris always seen.

For fixed intersections these characteristic maxima and minimarecur at their corresponding altitude in the ionization profile (see


Fig. 21, bottom and the comprehensive plot in Fig. 22). For oursetup the power-law ionization rate exceeds the exponential oneat: approx. 67 km (corresponding to 10 MeV) and 45 km (50 MeV)as well as at the borders of the energy range 96 km (0.8 MeV) and18 km (500 MeV). In between the exponential fit shows large butnot necessarily larger ionization rates at approx.: 78 km (ca.4.5 MeV), 59 km (20 MeV) and 35 km (120 MeV).

Fig. 22 shows an exponential ionization rate maximum at78 km that sticks out from the others. The reason is that the lowestGOES channel often is enhanced by trapped particles (that are notprecipitating) during quiet time (see Fig. 21) that significantlyboosts the count rates. This outlier is a strong handicap for a goodspectrum fit. Indeed it forces a strong increase in the spectrumslope and therefore produces a maximum in the exponential fit.During SPE periods in contrast, the lowest channel is not especiallyenhanced and smoothly connects to the spectrum slope given bythe higher channels, see Fig. 24. Therefore the resulting ionizationprofiles are more similar than during quiet time.

Fig. 23 shows that even though the SPE period is not affected bythe low channel outliers, the general behavior is similar. Themedian of the power-law setup always exceeds the exponentialsetup except for about 78 km altitude. At 45 and 67 km altitudethe excess is largest. At the upper and lower altitude range is rises.

Please note that the problematic channel z_p1 has been re-placed by channels from the POES MEPED instrument in all othersections which produces combined spectra with smooth transi-tions as shown and discussed in Section 2.3.

Given that SPE periods do not show these outliers and that theparticles we are looking at occur in atmospherically effectivenumbers just during a SPE, we will continue with the chemicaleffects.





Fig. 24. Comparison of different particle spectrum functions during SPE. High en-ergetic tail of the Maxwell–Boltzmann spectrum (exponential) and power-law:(top) spectrum fits, (bottom) ionization rate profile.

Fig. 25. Ratio of exponential/power-law chemistry follow-ups: (top) HOx, (bottom)O3.



Given that our energy range starts at 0.8 MeV we will skip NOx

and concentrate on HOx and Ozone. Likewise to the previous setups,the direct impact on Ozone and HOx is restricted to SPE periods assufficient flux of high energetic particles is needed. Starting withFig. 25 (top) we see the HOx ratio of the exponential and the power-law run. It shows two clear negative peaks (�40%) at approx. 25 km(low altitude border) and 45 km. Comparing to Fig. 22 this nicelyagrees with the relative minima in the exponential spectra.

The O3 differences in Fig. 25 (bottom) consist of two maincharacteristics. First a minimum of up to 4% at 78 km in the ex-ponential version that corresponds to the ionization rate max-imum at the same altitude. As we are in the SPE period the alreadydiscussed outliers are not responsible here. Second there is anOzone maximum (4%) at 67 km as result of the local ionization rateminimum. This Ozone maximum obviously has a long-lasting ef-fect (about 0.5–1% during the following 20 days) including a slightdownward movement.

In sum we can say that the decision of the kind of fit functionmay add characteristic to/remove natural information from thespectrum that can be responsible for about 40% HOx and 4% Ozonedifference during SPEs.

6.1.1. Exponential spectrum with fixed intersections vs. power-lawwith variable intersections

Since the power-law spectrum with variable intersections wasmore accurate than the one we just used, the reader might askhow that compares to the exponential fit. Implicitly this compar-ison has already been done as we compared both versions to the


power-law with fixed intersections.If we have a look at the main features in Figs. 20 and 25, the

HOx plots are almost negatives of each other. While the ex-ponential run in 25 has about 40% less HOx at 25–45 km than thefixed power-law run, the latter one has 40–50% more HOx than thevariable power-law run. Or in short, exponential and variablepower-law should agree in HOx quite well.

For Ozone the picture is more complicated. We concentrate onthe two altitudes with the biggest deviations (67 and 78 km). At67 km the exponential run gives 4% more than the fixed power-law, which has 8% less than the variable power-law version. Thusthe exponential run gives about 4% less than the variable power-law on 67 km.

At 78 km however, the prefix changes and both deviations addup: the exponential run has 4% less than the fixed power-law andthat one 5% less than the variable power-law. In sum we get about9% less Ozone at 78 km for the exponential run in comparison tothe variable power-law.

Even though this comparison does not exactly match the modelspecifications it might be of interest for users of e.g. AIMOS (power-law, variable intersections, difference 5 fits instead of 3 but on awider energy range) or the Jackman model (exponential fit, fixedintersections, difference energy range slightly smaller: 1 MeV–300 MeV instead of 0.8 MeV–500 MeV).

7. Summary

The final statement of this paper is that all assumptions that wehave to make for the spectrum fit have characteristic implicationsfor the ionization rates and therefore for the modeled chemistry.

Our impression is that a multiple power-law fit with variableintersections and “enough” segments is a good candidate to de-scribe the precipitating particle flux, but there is no perfect set of






assumptions for a particle fit because of the limitations of theobserved particle fluxes.

Variable intersections have the benefit that they can adopt todifferent knees in the spectra. Using fixed intersections will causeoverestimations or underestimations (in comparison to the pre-vious) to appear at altitudes corresponding to the particle energyat the intersection (and vice versa in between). A high number ofsegments may result in a “perfect” fit of the measured values, butdisagrees with the idea of a constant slope spectra (as result of asingle acceleration process) and increases the impact of singlemeasurement errors. The energy range normally is restricted bythe detectors on a satellite, but our results show that disregard of achannel at the end of the spectrum adds a 25% variation to the(unchanged) rest of the spectrum. This consequently is an un-certainty that applies to all ionization rates.

We suggest to use the “amount of segments per magnitude ofparticle energy range” as characteristic for the accuracy of theresulting fit, as we noticed a similar median and interquartilerange in the ionization rate if this applies.

Every direct comparison of a single time step that uses eitherdifferent energy ranges, different fitting functions or number/po-sition of intersections is problematic as the internal variation ofthe fitting function will be on the order of a factor of 2 (referring toionization in some specific altitudes within our comparison ofdifferent energy ranges as shown in Fig. 13).

Consequently our main concern is not to suggest a set of as-sumptions, but to focus the attention of modelers, that satellite-(spectrum) based ionization rates always have some inherentuncertainty.

Acknowledgment

This work was supported by the Deutsche Forschungsge-meinschaft DFG under contract WI 4417/2-1. The authors aregrateful to NOAA for providing POES and GOES data and for thesupport from ISSI (Bern).

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