Julien Hulot

D Aubert

R Standarovski

Ecoffet

published or not. The documents may come

Impact of the Earth's magnetic field secular drift on the low altitude proton radiation belt from years 1900 to 2050

1 Abstract-The effects of the space radiation environment on spacecraft systems and instruments are significant design considerations for space missions. In order to meet these challenges and have reliable, cost-effective designs, the radiation environment must be understood and accurately modeled. The low altitude proton environment varies slowly in time due to the secular drift of the Earth's main magnetic field and due to the evolution of the solar cycle. The purpose of this paper is to extend the OPAL model capabilities by introducing a prediction of the Earth's main magnetic field model up to year 2050. Impact on low altitude spacecraft radiation specification for next space missions is then assessed.

Index Terms-radiation belts, trapped protons, South Atlantic Anomaly forecast

I. INTRODUCTION

PECIFICATION of the high-energy radiation belt proton environment remains an outstanding issue for both present and future low altitude spacecraft design and analyses [START_REF] Xapsos | Near-Earth Space Radiation Models[END_REF]. In the late 90s' Huston [START_REF] Huston | A new model for the low altitude trapped proton environment[END_REF] proposed a first high energy trapped proton model where the solar cycle modulation was fully included. In 2014, the Onera Proton Altitude Low (OPAL) model [START_REF] Boscher | A new proton model for low altitude high energy specification[END_REF] (now part of the Global Radiation Earth ENvironment -GREEN-model) dedicated to altitudes below 800 km was issued to describe the > 80 MeV trapped protons in the Earth's radiation belts [START_REF] Xapsos | Near-Earth Space Radiation Models[END_REF]. The model accounts for the secular drift of the Earth's main magnetic field based on the International Geomagnetic Reference Field (IGRF) and National Oceanic and Atmospheric Administration (NOAA) data from 1980 to 2012 and for the solar cycle modulation impact of the proton flux. Currently two main initiatives to propose new global specification models for the Earth radiation belts are ongoing: Aerospace Electron 9/Aerospace Proton 9 (AE9/AP9) [START_REF] Ginet | AE9, AP9 and SPM: New models for specifying the trapped energetic particle and space plasma environment[END_REF] [START_REF] Johnston | Recent updates to the AE9/AP9/SPM radiation belt and space plasma specification model[END_REF] and GREEN [START_REF] Sicard | GREEN: the new Global Radiation Earth ENvironment model (beta version)[END_REF]. In the present study we extend the capabilities of the OPAL model by accounting for both the full IGRF-12 model between 1900 and 2015, and the predicted evolution of the Earth's main field up to 2050. We first describe the magnetic field models being used and the way the main field is being forecasted up to 2050 (section II). We next describe the methodology used to characterize the evolution of the low altitude proton radiation belt, comparing these updated OPAL predictions to those of the AP8min model [START_REF] Sawyer | AP-8 trapped proton environment for solar maximum and solar minimum[END_REF], and discuss this evolution, illustrating its impact on spacecraft specification (section III) and finally conclude (section IV).

II. THE EARTH'S INTERNAL MAGNETIC FIELD

The Earth's internal magnetic field is known to vary slowly in time. The typical time scale is on the order of months and longer: this is the so-called secular variation.

Consequently, the Earth's main field is defined in terms of a sequence of time-dependent Gauss coefficients 𝑔𝑔 𝑙𝑙 𝑚𝑚 (𝑡𝑡) and ℎ 𝑙𝑙 𝑚𝑚 (𝑡𝑡), such that the magnetic potential V in a source-free region reads

𝑉𝑉(𝑟𝑟, 𝜃𝜃, 𝜑𝜑, 𝑡𝑡) = 𝑎𝑎 ∑ ∑ � 𝑎𝑎 𝑟𝑟 � 𝑙𝑙+1 [𝑔𝑔 𝑙𝑙 𝑚𝑚 (𝑡𝑡) cos 𝑚𝑚𝜑𝜑 + 𝑚𝑚=𝑙𝑙 𝑚𝑚=0 𝑙𝑙=𝐿𝐿 𝑇𝑇 𝑙𝑙=1 ℎ 𝑙𝑙 𝑚𝑚 (𝑡𝑡) sin 𝑚𝑚𝜑𝜑] 𝑃𝑃 𝑙𝑙 𝑚𝑚 (𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃), (1)
in which (r,θ,φ) are spherical coordinates, t is time, a=6371.2 km is the average radius of the Earth, and 𝑃𝑃 𝑙𝑙 𝑚𝑚 represents the Schmidt quasi-normalized associated Legendre functions of degree l and order m. L T is the truncation of the spherical harmonic expansion. The 𝑔𝑔 𝑙𝑙 𝑚𝑚 and ℎ 𝑙𝑙 𝑚𝑚 are expressed in nT. The International Association of Geomagnetism and Aeronomy (IAGA) released the 12 th Generation International Geomagnetic Reference Field (IGRF-12) in December 2014 [START_REF] Thébault | International Geomagnetic Reference Field: the 12th generation[END_REF]. It provides Gauss coefficients for years from 1900 to 2010 with a five year time resolution (1900.0, 1905.0, etc.), preliminary Gauss coefficients for year 2015 and a linear annual predictive secular variation model from 2015 to 2020. For dates until 2000 the truncation is at L T =10, but from 2000 the truncation is at L T =13. The forward extrapolation giving the preliminary Gauss coefficients is truncated at L T =8. For dates between the model epochs, coefficient values are given by linear interpolation.

For years after 2015, a forecast is required to model the Impact of the Earth's magnetic field secular drift on the low altitude proton radiation belt from years 1900 to 2050 S. Bourdarie, A. Fournier, A. Sicard, G. Hulot, J. Aubert, D. Standarovski and R. Ecoffet S Earth's main field. Our physics-based forecast rests on the forward numerical integration of the coupled Earth (CE) numerical dynamo model of Aubert et al. [START_REF] Aubert | Bottom-up control of geomagnetic secular variation by the Earth's inner core[END_REF], which can reproduce some of the salient features of the geomagnetic secular variation. We apply a framework akin to the inverse geodynamo modeling framework introduced by Aubert [START_REF] Aubert | Flow throughout the Earth's core inverted from geomagnetic observations and numerical dynamo models[END_REF] and subsequently used by Fournier et al. [START_REF] Fournier | A candidate secular variation model for IGRF-12 based on swarm data and inverse geodynamo modelling[END_REF] for proposing an IGRF-12 linear annual predictive secular variation model from 2015 to 2020: in these studies magnetic observations at a single epoch are assimilated in order to define an initial condition for subsequent integration (beyond the single epoch) of the CE dynamo model. Aubert [START_REF] Aubert | Geomagnetic forecasts driven by thermal wind dynamics in the Earth's core[END_REF] refined this initialization process in order to take the uncertainties of the observations and modeling into account, by means of an ensemble approach. He defined an ensemble of initial conditions compatible with the uncertainties, which were next used to define an ensemble of forward simulations. The spread of the ensemble of forward simulations so obtained allowed Aubert [START_REF] Aubert | Geomagnetic forecasts driven by thermal wind dynamics in the Earth's core[END_REF] to assess the uncertainty impacting a forecast of the main field for epochs 2015-2115. Here we refine this strategy a little further, and consider two epochs for analysis instead of one single epoch. In this sequential assimilation framework, the numerical integration starts at epoch 1840.0, and a first ingestion of observations occurs at epoch 1865.0, followed by a second analysis at epoch 2015.0. The first ingestion, even though it only involves data of an arguably lesser quality than at more recent times, is beneficial for the assimilation. Having a first analysis allows us to try to estimate (and correct) the forecast bias, by inspecting the quality of the prediction over the 1930-2015 time period (over which observations are of better quality), prior to the second analysis.

In practice, an ensemble of N e = 80 members (i.e. 80 predictions) turns out to be sufficient to properly describe the uncertainties affecting our forecasts. Our prediction is therefore defined by an ensemble of 80 sets of Gauss coefficients 𝑔𝑔 𝑙𝑙 𝑚𝑚,𝑒𝑒 and ℎ 𝑙𝑙 𝑚𝑚,𝑒𝑒 , 𝑒𝑒 ∈ 1, … . , 𝑁𝑁 𝑒𝑒 , sampled at discrete epochs 𝑡𝑡 𝑖𝑖 (2015.0, 2016.0, …, 2050.0). The truncation is a posteriori set at L T =6. This is well below the native resolution of the CE model (L=133), but is consistent with the uncertainties affecting the predictions and proves sufficient for the purpose of this study (see below).

Introducing the mean of the ensemble

𝑔𝑔̅ 𝑙𝑙,𝑖𝑖 𝑚𝑚 = 1 𝑁𝑁 𝑒𝑒 ∑ 𝑔𝑔 𝑙𝑙 𝑚𝑚,𝑒𝑒 (𝑡𝑡 = 𝑡𝑡 𝑖𝑖 ) 𝑁𝑁 𝑒𝑒 𝑒𝑒=1 (2) ℎ � 𝑙𝑙,𝑖𝑖 𝑚𝑚 = 1 𝑁𝑁 𝑒𝑒 ∑ ℎ 𝑙𝑙 𝑚𝑚,𝑒𝑒 (𝑡𝑡 = 𝑡𝑡 𝑖𝑖 )
𝑁𝑁 𝑒𝑒 𝑒𝑒=1

(3) at each discrete time 𝑡𝑡 𝑖𝑖 , we also defined the distance of an ensemble member to the mean as:

𝑑𝑑 𝑒𝑒 = � � � ��𝑔𝑔 𝑙𝑙,𝑖𝑖 𝑚𝑚,𝑒𝑒 -𝑔𝑔̅ 𝑙𝑙,𝑖𝑖 𝑚𝑚 � 2 + �ℎ 𝑙𝑙,𝑖𝑖 𝑚𝑚,𝑒𝑒 -ℎ � 𝑙𝑙,𝑖𝑖 𝑚𝑚 � 2 𝑖𝑖 𝑚𝑚 𝑙𝑙 ∀ 𝑒𝑒 ∈ 1, … . , 𝑁𝑁 𝑒𝑒 (4)
This distance was used to identify the ensemble member with the smallest d e, which we considered as the best reference main field prediction (called IPGP-forecast hereafter where IPGP stands for Institut de Physique du Globe de Paris). The rationale to pick an ensemble member rather than the arithmetic mean for the IPGP-forecast is that the trajectory of the member is indeed a solution of the nonlinear dynamo problem (in contrast to the mean of the ensemble, which is not a dynamically consistent solution). Note that the (minimum) d e found for the IPGP-forecast is equal to 919.6 nT while the largest d e among the 80 members of the ensemble is equal to 2683.8 nT.

The parameters of a tilted eccentric dipole [START_REF] Fraser-Smith | Centered and Eccentric Geomagnetic Dipoles and their poles, 1600-1985[END_REF] best fitting the IGRF-12 or IPGP forecasts versus time from 1900 to 2050 are shown in Fig. 1. Clearly, those parameters do not evolve linearly with time. From 1900 to 2050, the magnetic field module at the magnetic equator and at 1 Earth's radius from the center of the dipole (B o ) is decreasing while the offset of the dipole with respect to the Earth's center always increases. Note also that the tilt of the dipole with respect to the Earth's rotation axis remained almost constant between 1900 and 1950 but has been decreasing since 1950. The Earth's main magnetic field intensity at 800 km altitude is given in Fig. 2 for years 1900 (top), 1970 (middle) and 2050 (bottom). The shape and location of the South Atlantic Anomaly (SAA) evolve with time. This anomaly drifts to the west and its surface (for a given iso-contour) expands with time. Note that the magnetic field map of year 1970 obtained from IGRF-12 is very close to the Jensen & Cain [START_REF] Jensen | An interim geomagnetic field[END_REF] field model being used in AP8min. In contrast, one can see that in the future (e.g. 2050, as shown in Fig. 2 bottom panel) the topology of the SAA is expected to be significantly different from that seen in 1970.

III. LOW ALTITUDE TRAPPED PROTONS

Because energetic protons are trapped by the Earth magnetic field at low L (the McIlwain parameter [START_REF] Mcilwain | Coordinates for mapping the distribution of magnetically trapped particles[END_REF]) shells, the topology of radiation belts is very much driven by the magnetic field itself. At low altitude, where the magnetic field is dominated by the Earth's internal field, proton radiation belts will be sensitive to its secular drift. Boscher et al. [START_REF] Xapsos | Near-Earth Space Radiation Models[END_REF] showed that taking into account the effect of the drift of the SAA over a given time range on the trapped particle distribution at a given L shell (L<2.5) and altitude is equivalent to consider the change in the maximum equatorial pitch-angle (angle between the particle velocity vector and the magnetic field at the magnetic equator) that can be measured at the same L and altitude over the same time range.

To compute the Maximum equatorial Pitch-Angle (MePA) found at a given L, altitude and time, the following approach was implemented:

• A longitude-latitude map of L shells is first computed with a 1° resolution at the given altitude (Fig. 3). In the north hemisphere hole (high latitude data gap in Fig. 3), particles bouncing there have a mirror point located in the upper atmosphere in the south hemisphere (in the loss cone), i.e. they cannot bounce any more and are therefore not trapped. In such condition it makes no sense to compute a Lshell value. • A primary value of equatorial pitch-angle versus L is deduced (Fig. 4); • A high resolution map of L shells is next computed with a resolution of 0.1° within ±10° around the first MePA location • A high precision MePA versus L is finally deduced. The drift of the MePA at three given altitudes (600, 800 and 1200 km) from year 1900 to year 2050 is shown in Fig. 5 at L=1.5 and in Fig. 6 at L=2. Clearly, on such a long timerange (150 years) this drift is not a linear function of time. Note, however, that from 1978 to 2012 the linear assumption made by Boscher et al. [START_REF] Xapsos | Near-Earth Space Radiation Models[END_REF] is fully compliant with these new results. The y scale in Fig. 5 and in Fig. 6 being the same, it is clear that at all altitudes the MePA drift becomes more pronounced as L decreases. The impact of relying on a truncation at L T =6 for the IPGP prediction, whereas IGRF-12 was computed up to L T =10, has also been investigated. To this purpose, the MePA was recomputed using IGRF-12 with truncation degrees L T equal to 2, 4 and 6, and compared to the reference results obtained with L T =10. The results for L=1.2 at an altitude of 500 km are shown in Fig. 7. Clearly, an IGRF-12 field model truncated at L T =2 is insufficient to compute an accurate value of MePA. Increasing L T improves the accuracy. At L T =4, results are already found to be decent for low L (1.2 to 1.5) and good for higher L values. At L T =6 they are found to be very good for all L. The mean deviations over 1900-2015 in the 1.1-2 L and 500-1200 km altitude ranges are shown in Fig. 8 for L T =4 and in Fig. 9 for L T =6. While in the first case a maximum mean MePA deviation of 1.5% can be found, it drops always below 1% in the second case. Relying on a spherical harmonic expansion of the Earth's internal magnetic field up to L T =6 thus appears to be sufficient to describe trapped particles at low altitudes. This new long-term assessment of the MePA drift versus L shells (1<L<2.5) and altitudes (400 km<altitude<1400 km) has next been implemented in the OPAL model [START_REF] Xapsos | Near-Earth Space Radiation Models[END_REF]. It will be released to the public via the GREEN-p model [START_REF] Sicard | GREEN: the new Global Radiation Earth ENvironment model (beta version)[END_REF] and implemented in the OMERE tool [16].

In Fig. 10, we show the predicted longitude-latitude maps of trapped proton flux with E>82 MeV at 800 km altitude for epochs 1900, 1970 and 2050 when using the updated OPAL model. For comparison, we also show 2050 predictions when using AP8min. As expected, between 1900 and 2050 the SAA has drifted to the West and the overall shape of the SAA has changed while the peak flux is almost comparable. Note however, that the shape of the SAA from the perspective of trapped proton flux does not exactly reflect the shape of the SAA as seen in the field intensity (compare Fig. 10 and Fig. 2, in particular for epoch 1900, when the SAA low field intensity overlapped with the dip-equator, leading to a distinct signature in the proton flux SAA). Note also that the forecasted SAA from OPAL in 2050 exhibits significant deviations in location and shape from that provided by AP8min. This is attributed to the lack of magnetic field secular drift compensation in AP8min as it depends on the Jensen & Cain field model from year 1970. Of course those deviations become larger and larger as epoch difference from 1970 increases.

Detailed comparisons between OPAL predictions and insitu measurements from Polar Operational Environmental Satellites (POES) [START_REF]POES data[END_REF] are shown in Fig. 11 to Fig. 14. Fig. 11 shows the >82 MeV proton fluxes at 800 km altitude in a longitude-latitude map from POES-06 (top panel) and from OPAL (middle panel) in 1979. Note that POES-06 data were projected down to 800 km altitude considering constant L, B/B eq . One can see the very good match between in-situ data and the OPAL model prediction.

The ratio between >82 MeV proton flux measured by POES-06 and OPAL prediction is given in the bottom panel. In most of the SAA, this ratio is close to 1. Largest deviations (dark red and dark blue) are found at the outer edge of the SAA where proton fluxes are expected to be low. The distribution of these ratios is plotted in Fig. 12 for fluxes >100 cm 2 s -1 . As can be seen, 28.7% of points are within 5% error, 55% of points are within 10% error and 81.2% of points are within 20% error. The spread of the distribution around 1 is attributed to statistical uncertainties in the Space Environment Monitor 2 (SEM2) instrument count rates (see irregularities in the top panel of Fig. 11). Both ends of the distribution is linked to systematic errors which are found at the outer edge of the SAA where fluxes are low. Similar plots using POES-19 for comparison are shown for year 2010 in Fig. 13 and Fig. 14. Again, the OPAL model matches very nicely the in-situ data (for fluxes >100 cm 2 s -1 it is found that 31% of points are within 5% error, 55% of points are within 10% error and 80.4% of points are within 20% error). Note in particular that the OPAL model properly accounts for the westward drift of the SAA between 1979 (Fig. 11) and 2010 (Fig. 13). To illustrate the impact of the OPAL predictions on spacecraft specifications, the yearly averaged >82 MeV proton flux a sun-synchronous spacecraft would encounter at an altitude of 800 km has been computed between 1900 and 2050 (Fig. 15). For predictions beyond 2015, a conservative approach was used and a very weak solar cycle (via the F10.7 radio flux) was considered (see orange curve in Fig. 15). The >82 MeV proton fluxes from the OPAL model normalized to AP8min at 800 km altitude exhibit a global trend over more than a century: the trapped proton flux decreases due to the secular drift of the magnetic field (see Fig. 1). This decrease is not linear with time and strongly depends on the offset and tilt of the eccentric dipole best describing the Earth's core magnetic field. -The amplitude of the energetic proton flux modulation is linked to the solar cycle amplitude. The global decrease of energetic proton flux (on the very long term, i.e. several solar cycles) is linked to the secular drift of the Earth's core magnetic field. -The >82 MeV proton flux is expected to be lower than predicted by AP8min in future years.

Fig. 1 .

 1 Fig. 1. Parameters of a tilted eccentric dipole best fitting IGRF-12 (or IPGPforecast) versus time between 1900 and 2050.

Fig. 2 .

 2 Fig. 2. Magnetic field intensity (nT) at 800 km altitude for year 1900 (top), 1970 (middle) and 2050 (bottom). The red dashed line indicates the magnetic equator. The resolution of the grid is 360×180, i.e. 1° in longitude and latitude.

Fig. 3 .

 3 Fig. 3. Longitude-latitude map of the Lshell parameter at 825 km altitude from IGRF-12 in 2010. The resolution of the grid is 360×180, i.e. 1° in longitude and latitude.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Deduced equatorial pitch-angle at 825 km altitude for various L shells from IGRF-12 in 2010 in the southern hemisphere.

Fig. 6 .

 6 Fig. 6. Drift of the MePA computed at L=2. for three altitudes from year 1900 to 2050; IGRF-12 is used for the time period 1900-2015 (dashed line) while the IPGP-forecast is used for the time period 2015-2050 (solid line).

Fig. 7 .

 7 Fig. 7. Drift of the MePA computed at L=1.2 and an altitude of 500 km between 1900 and 2015, using IGRF-12 truncated at LT=2, 4, 6 and 10.

Fig. 8 .

 8 Fig. 8. Mean deviations of MePA values computed using IGRF-12 truncated at LT=4 with respect to MePA values computed using IGRF-12 truncated at LT=10 over the 1900-2015 time range.

Fig. 9 .

 9 Fig. 9. Mean deviations of MePA values computed using IGRF-12 truncated at LT=6 with respect to MePA values computed using IGRF-12 truncated at LT=10 over the 1900-2015 time range.

Fig. 10 .

 10 Fig. 10. Trapped proton flux [cm -2 s -1 ] with E>82 MeV at an altitude of 800 km predicted from the updated OPAL model in 1900 (top panel), 1970 (second panel from top) and 2050 (third panel from top) and predicted from AP8min in 2050 (bottom panel). The dashed black line indicates the magnetic equator. The resolution of the grid is 180×90, i.e. 2° in longitude and latitude.

Fig. 11 .

 11 Fig. 11. >82 MeV protons flux (cm 2 s -1 ) provided by POES-06 at 800 km altitude in 1979 (top panel), and predicted by OPAL (middle panel); also shown the ratio between OPAL predictions and POES-06 measurements (bottom panel). The resolution of the grid is 180×90, i.e. 2° in longitude and latitude.

Fig. 12 .

 12 Fig. 12. Distribution of the ratio of OPAL predictions to POES-06 measurements for the >82 MeV flux in 1979.

Fig. 13 .

 13 Fig. 13. >82 MeV protons flux (cm 2 s -1 ) provided by POES-19 at 800 km altitude in 2010 (top panel), and predicted by OPAL (middle panel); also shown the ratio between OPAL predictions and POES-19 measurements (bottom panel). The resolution of the grid is 180×90, i.e. 2° in longitude and latitude.The yearly averaged >82 MeV proton flux obtained from the NOAA-POES satellites (06, 08, 10, 12, 15 and 19) at the same altitude is also reported on this plot. Note that flux values are normalized to AP8min. As mentioned in[START_REF] Xapsos | Near-Earth Space Radiation Models[END_REF], low altitude proton fluxes are modulated by the solar cycle, i.e. F10.7 radio flux, with a time lag depending on the energy, the amplitude of the peak flux being anti-correlated to the F10.7 radio flux. Because the F10.7 radio flux cannot be reliably predicted beyond the current solar cycle it is then challenging to accurately extrapolate trapped proton flux out to 2050.

Fig. 14 .

 14 Fig. 14. Distribution of the ratio of OPAL predictions to the POES-19 measurements for >82 MeV flux in 2010.

  Fig. 15 leads us to conclude that: -AP8min generally underestimates proton fluxes at energies > 82 MeV and at 800 km altitude. This is true even during the time period when proton data being used to produce AP8 model were measured (see the hatched polygon in Fig. 15, deduced from [18]): a maximum factor between 1.3-1.4 is found right after the 1964 solar minimum. -the >82 MeV proton fluxes found between 2011 and 2015 are compliant with conclusions from [19], where it was found that AP8min was underestimating both the Total Non-Ionizing Dose (TNID) measured by ICARE-NG onboard SAC-D by 10.7% [19], and the cumulated Single Event Upset (SEU) number from Error Detection And Correction (EDAC) code implemented onboard the CRYOSAT-2 altimeter by 16% [19]. -OPAL slightly underestimates >82 MeV proton fluxes at 800 km after 2013 (by about 10%). Note that OPAL was developed in 2013 and that recent POES data during the current weak solar cycle were therefore not yet available. So far this 10% discrepancy is attributed to the F10.7 dependence of the model rather than to the Earth's core magnetic field. It is suspected that our assumption of a dependence on F10.7 with an energy dependent lag time is not yet sufficient: to further refine the model, the time derivative of F10.7 should also be considered (while during the extended solar minimum period from 2007 to 2009, the F10.7 index remained almost constant and very low, the >82 MeV proton flux was still increasing. Because OPAL only depends on F10.7 and not on its time derivative, this feature cannot be captured by the model).

Fig. 15 .

 15 Fig. 15. Yearly averaged >82 MeV proton flux a sun-synchronous spacecraft at an altitude of 800 km would encounter. Results are normalized to AP8min predictions. Dots refer to proton flux obtained from the NOAA-POES satellites (06, 08, 10, 12, 15 and 19) normalized to APmin predictions. The red indicates the reference, i.e. AP8min, and the blue line refers to AP8max normalized to AP8min predictions. IV. CONCLUSIONS The secular drift of the Earth's main field has been implemented in the OPAL (and GREEN-p) model and is now available from years 1900 to 2050. Note that it can be implemented in any new specification model, like AP9 for example. A slow decrease of energetic low altitude proton fluxes along time is predicted, reflecting the secular drift of the Earth's core magnetic field. The solar cycle modulation introduced in the OPAL model reproduces POES flight data with high fidelity during the active solar cycles 21, 22 and 23. During the weak solar cycle 24, OPAL predictions are underestimating POES data by about 10%. This discrepancy will be investigated in the near future and is attributed to the F10.7 dependency during weak solar cycles. Keeping in mind this limitation, it is found that: -AP8min underestimates energetic trapped proton fluxes by about 30% in the 1970s and by 20% in the 1980s to 2000s years on average over a full solar cycle. -This deviation is expected to be smaller in the near future and to reverse after 2025, when AP8min would then overestimate energetic trapped proton fluxes.


Alessio Antonini
email: alessio.antonini@open.ac.uk

Francesca Benatti
email: francesca.benatti@open.ac.uk

Edmund King
email: edmund.king@open.ac.uk

François Vignale
email: francois.vignale@univ-lemans.fr

Guillaume Gravier

Modelling Changes in Diaries, Correspondence and Authors' Libraries to support research on reading: the READ-IT approach 1

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Diaries, correspondence and authors' libraries provide important evidence into the evolution of ideas and society. The archives and collections that form the cultural heritage of Europe contain plentiful examples of these types of sources. A significant topic in many of these sources is the discussion of what their creators read. The study of the cultural heritage sources that discuss reading is connected to understanding changes of perspective and values through the interaction between their creators and other people. These changes become significant from two perspectives: how on a personal level events and changes in society are reflected on the changes and evolution of a person, and on a comparative level across times and different societies.

The READ-IT project has the aim of addressing macroscopic questions [START_REF] Hitchcock | Big Data, Small Data and Meaning[END_REF] about the shaping of the identity of European readers [START_REF] Baillot | Exploring the digital heritage of reading: the READ-IT project[END_REF], and more specific questions about the impact of reading on the shaping of an era, confronting historical events, defining the identity of a population or the construction of a public discourse. As diaries, correspondence and authors' libraries are important sources of evidence for different types of research enquiries, READ-IT aims to facilitate collaboration and multidisciplinary research through the sharing of annotated resources.

READ-IT (Reading Europe Advanced Data Investigation Tool) is a 3-years (2018-2020) transnational, interdisciplinary R&D project funded by the Joint Programming Initiative for Cultural Heritage that will build a unique large-scale, user-friendly, open access, semantically-enriched investigation tool to identify and share ground-breaking evidence about 18th-21st century Cultural Heritage of reading in Europe (https://readit-project.eu/). This contribution is framed within the first-year activities of READ-IT aimed to build a convergence between different case studies and research teams on a shared conceptualisation of the phenomenon of reading, which will be used to inform the development of the technical tools.

To facilitate research on shared sources, READ-IT activities include the definition of a data model for annotating cultural heritage sources that could be used as meta-language across disciplines. By having annotations defined within a shared conceptual framework, researchers from different fields will be able to identify and retrieve data from the READ-IT pool of sources and to share their work with the community of Humanities researchers. This process will increase the visibility and usability of cultural heritage sources for research. Thus, the main challenge for modelling the reading experience in READ-IT is to be able to define a set of shared concepts with a universal value, such as defining a way to capture changes within diaries, correspondence and authors' libraries as sources of evidence for reading experiences.

Previous similar Digital Humanities projects, such as UK-RED, LED and EU-READ, had a strong focus on supporting collaboration between researchers in annotating and managing resources. READ-IT aims to support research by addressing the phenomenon of reading. The focus on changes and the evidence of change in the sources has been addressed in READ-IT as a set of requirements driving the modelling of the reading experience. Specifically, we investigate:

• What are the changes in the reading testimonies reported in diaries, correspondence and authors' libraries?

• What are the concepts in common between these three types of sources and how can these be represented?

• How can we study these changes through the use of shared annotated sources?

In this contribution, we present how the study of reading in diaries, correspondence and authors' libraries has been addressed in previous models of reading and compare the READ-IT model with the concepts and approaches adopted in relevant conceptualisations such as FRBR and LED. Specifically, we present the physical changes in the circumstances of reading, the changes to the reader as a person and as part of a society, and the changes in the medium providing access to the content and discuss how these phenomena can be encoded in the READ-IT data model. Lastly, we discuss how the proposed annotation system can be used to study change at individual and collective scale.

The rest of the paper is structured as follows. Section 2 presents the model of reading and the correspondence between its main concepts and the concepts of FRBR (IFLA, 2009) and LED [START_REF] Adamou | Crowdsourcing Linked Data on listening experiences through reuse and enhancement of library data[END_REF]. Section 3 introduces the three case studies about the study of diaries, correspondence and authors' libraries. Section 4 illustrates how the READ-IT model can be used to address changes in the three case studies. Lastly, Section 5 present a discussion about the potential contribution of using the READ-IT model in addressing this family of case studies and sources, its current limitations and final remarks about future challenges.

The READ-IT model of Reading

The READ-IT model of reading had been developed adopting a design research approach, considering the different perspectives of the research disciplines as stakeholders and the data model as a meta-language (object of the design research) aimed to support their collaboration and the interoperability of the outputs of their research activities [START_REF] Antonini | The role of philosophical analysis in the design[END_REF]. The approach adopted combines the theoretical analysis of reading [START_REF] Bortolussi | Psychonarratology[END_REF][START_REF] Craig | Developing a Philosophy of Reading: Piaget and Chomsky[END_REF][START_REF] Davies | Aesthetics and literature[END_REF][START_REF] Gerrig | Experiencing Narrative Worlds -On the Psychological Activities of Reading[END_REF][START_REF] Gibson | Authors, speakers, readers, and mock readers[END_REF][START_REF] Eco | Lector in fabula: la cooperazione interpretativa nei testi narrativi[END_REF] with the analysis of the sources of reading experiences (e.g. diaries, correspondence, author's libraries) to identify the key concepts and relations of the anatomy and dynamics of the reading phenomenon. The development of the model is being framed in an agile-like process of incremental update and evaluation. Currently, the model is at a consolidating stage after two cycles of development and validation, but it will be further updated to incorporate emerging requirement from the READ-IT case studies [START_REF] Vignale | Reading in Europe -Challenge and Case Studies of READ-IT Project[END_REF].

The current version of the model of reading (V1.5) combines three different perspectives on reading: 1) as an action, 2) as a process and 3) as an experience. By adopting these three lenses, the phenomenon of reading has been deconstructed in its foundational elements, and then reconstructed in a unifying theory of reading based on an cognitivist ecological view of reading [START_REF] Gibson | The Ecological Approach to Visual Perception[END_REF][START_REF] Hutchins | Cognitive Ecology[END_REF] with a strong focus on a) the reader's personal perspective and b) the embodiment of the action in a physical and social environment [START_REF] Dourish | Where the action is[END_REF]. Summarising, the resulting model provides a new metaphor of reading as the act of keeping a balance between the physical and cognitive activities of reading and the external forces mediating or interfering with the reading (reading as niche).

Reading as Action.

As action, the Reader is the actor of the action, while the Content (e.g. Moby Dick) has the role of object of the action and the Medium (e.g. book) has the role of means facilitating or impending the action mediating the interaction between the actor and object. The act of reading configures three distinct types of interactions between Reader, Medium and Content: Reading as Process. The act of reading is a dual-track process involving (a) a physical process of manipulating a Medium with the aim of perceiving the text encoding of the Content and (b) a cognitive process of elaboration of the Content aimed at rebuilding its meaning and consolidating concepts and ideas within the Reader's memory. Furthermore, concerning the semiotic analysis of text, reading performs (i) an analytical reading aimed at rebuilding the author's intended meaning and (ii) a performative reading of the situation aimed at "filling the gap" with personal experience and knowledge. In this frame, we consider different types of engagement of the Reader as the number of processes, see Fig. 2: a) dedication, the engagement in the physical process, perception of the content b) commitment, the engagement in the cognitive process, semiosis of meaning i. focus, the engagement in the analysis of the meaning within the content (proposition analysis) ii.

transportation (performance) [START_REF] Eco | Lector in fabula: la cooperazione interpretativa nei testi narrativi[END_REF][START_REF] Gerrig | Experiencing Narrative Worlds -On the Psychological Activities of Reading[END_REF], the engagement in the situation evoked by the content enriched by the memory and experience of the reader (situation analysis) Fig. 2. On the left, the conceptual model of the process of reading connecting perception, analysis and performance with the experience of reading as change of state of mind. On the Right, the schema encoding the process of reading as a Temporal Entity characterised with the four type of engagement and two type of cognitive processes.

A Reading Process is a Temporal Entity as it is characterised by a time and duration, Fig. 2. The instances of Reading Process are time related, e.g. follows, precedes.

As an intermittent activity, Reading is carried out as sessions (Reading Session). Furthermore, during each session, the effects of the interaction with the content are multiple as the reader navigates situations and arguments (Reading Experience). In READ-IT, we address the dynamics of the reading process by defining the concepts of (Fig. 3):

• Reading: a collection of reading sessions of the same work (first or one of multiple reading), sharing a context, such as being part of the same activities, addressing the same aims or approached with an overall state of mind • Reading Session: a chain of Reading Experiences, an interaction between event and action delimited by the opening and closing of a reading resource • Reading Experience: the cognitive activity of reading in a physical context Reading, Reading Sessions and Reading Experiences are Reading Process(es) and therefore Temporal Entity(ies) as well. Thus, a Reading can precede or follow another Reading, Reading Sessions and Reading Experiences can be sequentially ordered. Furthermore, Experiences are part of Sessions, and Sessions are part of Readings, and, on the other side, a Reading is the situation of several Sessions, which are situation of the Experiences of reading.

Reading Processes are situated in a physical and social environment. We encode the external situation using the concept of Event, characterised by Place and Conditions, comparison relations, e.g. better than, similar to, and temporal relations as well. We defined Reading Process a specialisation of Event to encode an important pattern of reading experiences: description of acts of reading by comparing with other reading experiences. The comparison of Reading Processes can be between different Reading(s), but also between the different type of processes of reading (cognitive and physical, analysis and situation). On the left, a conceptual scheme representing how the changes in the reader's state of mind is the result of the readermedium-content interactions, mediated by the environment conditions and co-occurring events, and how the resulting state of mind can be the premise of a new reading session. On the Right, the schema encoding the temporal relations between reading process and states of mind of the reader, and the relations between reading resources and state of mind and the reader

FRBR

The Functional Requirements for Bibliographic Records (FRBR) is a standard for the representation of bibliographic resources. FRBR provides a conceptual framework of four main concepts: work, expression, manifestation and item (IFLA, 2009), see Fig. 5 (left), representing a form of consensus on the anatomy of reading contents. Moreover, the adoption of FRBR enables the connection of the reading model with a wide range of book catalogues, such as the French National Library. On the other hand, FRBR addresses the phenomenon of content production (e.g. versions, translations), societal aspects of books (e.g. editions and censorship) and the physicality of books, but it does not include elements related to the use of contents (i.e. reading).

The READ-IT concept of Content is represented in FRBR by the two concepts of work and expression: the creative work as conceived in the author's mind and its realisation through one specific form (expression). In FRBR, the READ-IT concept of Medium is captured by the two concepts of manifestation and item: the first is the form of the physical embodiment of the expression, e.g. the first edition of La Montagna Incantata, translation of Ervino Pocar published by Acquerelli, while the item is one of the instances of the manifestation, e.g. my personal copy stolen from my father. Moreover, FRBR defines also the relations (has a subject) between a work and other concepts, such as work, person, corporate body, concept, object, event, place, expressions, see Fig. 5 (right). In this regard, these FRBR relations can be used to connect a Reading Experience with concepts, objects, event or places topics of a Content.

UK-RED

The Reading Experience Database (RED) was devised by Simon Eliot in 1993. It stemmed from the realisation that a topic as vast as the history of reading needed as large and representative a corpus of evidence as possible to support research in the field, and that this corpus could be a database made up of contributions collected from individual researchers [START_REF] Eliot | The Reading Experience Database, or, what are we to do about the history of reading?[END_REF]. RED was officially launched at The Open University in 1996 and, with the support of funding from the UK Arts and Humanities Research Council (AHRC), relaunched as a public-facing, searchable web resource in June 2007 [START_REF] Halsey | Reading the Evidence of Reading: An Introduction to the Reading Experience Database, 1450-1945[END_REF]. Since its inception, RED has encouraged crowdsourcing: volunteer contributors have been able to input new contributions directly into a web-based version of the contribution form. RED currently has over 34,000 unique records, many of them contributed by interested members of the public. As a collaborative tool, RED was mostly focused on the management of contributions (sources and annotations). On the "experience" aspect of reading, RED provided an 'evidence field', a free-text box in which contributors were asked to enter the evidence recording the reading experience (e.g. a transcription of a diary entry, or part of a letter, or a reader's marginalia). Then, the contributor could provide information about the personal, spatial, and temporal relationships underlying the reading experience, such as the reader's name and vital statistics, the title and format of the text being read, and the date and place where the reading experience took place.

READ-IT presents an opportunity for creating a more comprehensive, representative, and technically sophisticated iteration of the RED idea. Transnational in scope and unlimited in time frame, it will enable the comparison of reading habits and practices across time and across national boundaries. It will allow for the modelling of a range of forms of evidence beyond the purely textual. It will have a much more secure and less labour-intensive system for entering and reviewing new contributions. Finally, it will present users with multiple avenues into the data beyond a simple, linear list of search results, utilising new innovations in UI to make the most of the rich data within.

LED

The Listening Experience Database (LED) is a semantically enriched, machine-readable dataset about music events and records of the experiences of listeners [START_REF] Adamou | Crowdsourcing Linked Data on listening experiences through reuse and enhancement of library data[END_REF]. Rather than on text, LED focuses on audio contents, but the overall objective is similar to READ-IT: the study of experiences. Moreover, in term of type of content, LED and READ-IT overlap in relation to collective reading, audiobooks and any form of reading aloud.

In LED, the concept of listening experience is defined as a subtype of event and an action with an agent and a subject, a performance, situated in an environment, place and time, see Fig. 6 (left). Furthermore, LED provides a description of the Agent in terms of group, location, religion, social status, date of birth and of death. The scope of LED is the management of sources, of activities of collaborative annotation, see Fig. 6 (right), and the interoperability with existing catalogues of sources and of musical contents.

Reading in Diaries, Correspondence and Authors' Libraries

In this section we briefly discuss the relevance of diaries, correspondence and authors' libraries in understanding the evolution of ideas and values within a society and historical period. How have these documents reflected the way in which societies have adapted and changed as a result of historical events? In the first case, personal diaries kept during war time open a window onto how the act of reading helped soldiers cope with the horror of war through the creation of an alternative form of "literary camaraderie". In the second case, examining correspondence dealing with the experience of reading provides a unique view of how new ideas and topics enter and clash with common sentiments, ethics and ideals. It can also show how over time these new visions were rejected or integrated, from the eyes of the very actors at the centre of public discourse. Lastly, authors' libraries provide evidence of the influence of reading in shaping ideas in the form of traces, notes, comments (i.e. alterations) left by readers in their books.

3.1

Changes in Diary Keeping Practice

Personal diaries are an important source for understanding lived experience and cultural engagement across history. They can also be rich potential sources of evidence for reading. Patterns in diary keeping have not, however, always been constant through time. Before the late nineteenth century, keeping a diary was very much a middle-class or bourgeois practice. Diaries required literacy, the availability of at least some leisure time, and the possession of the money required to purchase them [START_REF] Elspass | The Use of Private Letters and Diaries in Sociolinguistic Investigation[END_REF]. These limitations mean that much of the evidence about reading preserved in historical diaries is heavily biased towards social elites. By the early twentieth century, however, diary manufacturers were starting to target consumers of more modest means. During the First World War, newspaper commentators and stationery industry advertising strongly encouraged soldiers and their families to keep personal diaries, a phenomenon that expanded the social reach of the practice of diary keeping substantially [START_REF] Lyons | A New History from Below? The Writing Culture of Ordinary People in Europe[END_REF][START_REF] Towheed | Introduction. In Reading and the First World War: Readers, Texts, Archives[END_REF]. This expansion of diary keeping into the working classes means that we have evidence about the daily lives and habits --including reading habits --of many thousands of ordinary people that would otherwise have been unrecorded. Diaries --and especially diaries kept by non-elite diarists --therefore form an important aspect of cultural heritage, a fact that is now starting to be recognised through the creation of specialist projects and repositories such as the Great Diary Project at London's Bishopsgate Library [START_REF] Moran | Private Lives, Public Histories: The Diary in Twentieth-Century Britain[END_REF].

Pre-war patterns in diary-keeping continued to operate to some extent during the First World War. As Jessica Meyer points out, many surviving British First World War diaries were kept by officers who were posted to relatively quiet sectors. It was obviously difficult to keep a diary in a busy or chaotic part of the front; any diaries kept in such areas were also liable to loss or abandonment due to action or the death of the diarist [START_REF] Meyer | Men of War: Masculinity and the First World War in Britain[END_REF]. However, a number of men in the ranks did keep diaries --often for the very first time in their lives --and these can give us a special insight into their experiences and, in some cases, what they were reading. An example of such a working-class diarist is Private William Hodgson of the King's Own Royal Lancaster Regiment. Hodgson was a territorial soldier during peacetime and he sporadically kept a diary while training in Britain in 1916 and after he was posted to the front in early 1917. On 26 November 1916, while at Aisne Barracks in Hampshire, he recorded in his diary: '9-30 Church Parade Watched the match between King's Own [Royal Lancaster Regiment] and Army Service Corps King's Own won 6-1. Took YMCA library book back: E F Benson's "Princess Sophia" and drew Jack London's "Call of the Wild"'. While in hospital in December 1916, he records in his diary reading London's 'White Fang', alongside novels by E. Phillips Oppenheim, Ethel M. Dell, Richard Marsh, and Baroness Orczy, though an attempt to 'find interest in reading' Charles Dickens's 'Great Expectations' failed [START_REF] Hodgson | King's Own Royal Regiment Museum[END_REF]). These would have been regarded as thoroughly unremarkable reading choices in 1916. However, they (and records like them) are extraordinarily valuable for historians of reading in the 21st century. They record the reading of mass-market fiction that was extremely popular at the time, but often derided or overlooked by the kinds of elite contemporary readers, critics, and cultural commentators whose opinions subsequently came to define our understanding of early twentieth-century literary culture. Looking to non-elite records, like the diary of William Hodgson, can give us an insight into popular reading cultures, but it can also suggest how those cultures helped sustain morale and entertain readers on both the home and fighting fronts during a period of worldwide crisis.

Changes in Correspondence: the correspondence of Ugo Foscolo, 1794-1824

Collections of letters held in archives and libraries form a rich part of the cultural heritage of Europe. Those produced by or addressed to writers and artists supply a critical source of reading experiences. By showing how books were received, interpreted and shared, these collections of letters provide crucial insights into the formation of European identities and mentalities. The correspondence of Italian poet Ugo Foscolo (1778-1827) provides a useful case study of the types of change encountered in this type of source of evidence of reading.

Vanhoutte and den Branden define the following elements in the formal description of a letter: the sender; the message; the recipient; references to the extra-linguistic reality (e.g. names, places, dates, etc.); the language of the letter [START_REF] Vanhoutte | Describing, Transcribing, Encoding, and Editing Modern Correspondence Material: A Textbase Approach[END_REF]. Most of these elements contain change, as exemplified by Foscolo's correspondence.

While the sender (Foscolo himself) is the same, his preferred name changed, from Niccolò to Ugo. There are numerous recipients to his letters, whom Foscolo addresses with varying degrees of trust and familiarity. The extralinguistic reality of the letters changes both through time, as Foscolo grows from adolescence to manhood, and most strikingly through place, as Foscolo moves through a number of Italian cities and then to France, Switzerland and Britain. Finally, the language of the letters changes according to the nationality of the recipient and the place and time of writing. Underlying these changes are the tumultuous political circumstances of Napoleonic Europe and the individual author's personal journey from his rebel patriotism to his service in the Napoleonic army to his reluctant collaboration with Restoration authorities to his final exile. These changes of social status certainly condition Foscolo's access to reading content and his disposition towards it.

Foscolo's case is far from extreme. The nature of the letter as a communicative act from one individual to another at a specific point in time and space involves changes in the circumstances and content of the evidence of reading it contains.

3.3

Changes in Authors' Libraries

Authors' libraries represent an important source of evidence on the reading processes of their owners [START_REF] Jackson | Marginalia and Authorship[END_REF]. Through marginal notes and underlining, readers record their thoughts within the very pages of the reading material.

The survival of such libraries tends to be limited to prominent historical and cultural figures and is therefore not always representative of the reading habits of a whole population. However, as authors write texts that are influenced by what they read and that in turn influence their readers, this type of cultural heritage collection deserves study.

Books as media are the physical interfaces between readers and contents and as such the host of traces of this interaction and target of the immediate effect of reading. In this regard, books from authors' collections provide a variety of insights ranging from dedications, comments and bookmarks to graphical signes expressing the reader's emotions, such as stupor or disagreement. In this frame, the personalisations (alterations) of books at the centre of a system of thoughts and relations of the reader that can become evident from identifying what, where and when these changes occur.

Modelling Changes in READ-IT

As previously discussed, Readers change during time and events in terms of their abilities, ideas, memories, aims. Furthermore, as result of reading, Medium change as well, on material level (e.g. annotations) and immaterial level in terms of emotion or value for the reader. The READ-IT model addresses these phenomena by discriminating between:

Reader and Person

An action is embedded in a specific context and so is the actor. As an actor of reading, a Reader acts being in a specific state of mind, by using their current abilities, skills and in a contingent personal and social situation. Understanding the state of the reader is a relevant aspect of the context in which the reading experience takes place and thus it is relevant to keep track of the reader's state at the time of reading. Therefore, we consider a Reader a diachronic description of one of the multiple states that a Person assumes during their life. On the other side, a Person is the cumulative result of all the status (Reader), a synchronic representation of a human being. In other words, a Reader is a description of a Person, see Fig. 7. A Reader is a specialisation of the class of Person, characterised by the dynamic (variable) features of a Person, such as their age at the time of reading, while the Person is described by the static (invariant) features of readers, e.g. Place of Birth. The Reader is a description of a Person at a specific moment in date or period. Thus, a Person is a collection of Reader(s) instances. Furthermore, Reader is specialisation of Temporal Entity, so that it is possible to describe the temporal aspect of the Reader as duration or time in which the described set of dynamic features were a description of a Person.

For example, the Person Ugo Foscolo changes as a Reader as he grows in age, changes name and moves to different countries. His occupation, social status and political allegiance change over time and place. His reading Habits change as he goes from being a student to being a soldier, a lecturer, a journalist or an exile.

War diaries provide us with examples of a different group of Readers: officers and common soldiers who turned to books as a means of psychological escape from the stresses of wartime. Many soldiers developed reading Habits, of which we can find traces in their diaries, indicating a change in attitude toward reading when measured against their reading habits and preferences before the war, changes which in many cases persisted after the war's end.

Reader's Dispositions

As argued, the current status of a Person, the Reader, has a great impact on the experience of reading. The reader's linguistic abilities, knowledge of topics or historical facts, their political and religious beliefs (Dispositions) are filters to the interaction with a Contents or a specific type of Medium, e.g. e-reader, manuscript, printed book.

In the READ-IT model, we specify the reader's Dispositions as a type of State of Mind grounded on the Reader (has disposition). In this frame, a Disposition could be related to ethical or aesthetical aspects of a Reading Resource, its value of within a social group or to the skill required to understand it, and a Disposition is oriented in approaching a specific Reading Process (e.g. a chapter), see Fig. 8. As a specialisation of State of Mind, a Disposition can involve Reading Resources (e.g. prejudice against an author or a topic). Furthermore, a Disposition is also a Temporal Entity, and thus characterised by a time and duration and temporal ordering relations. For example, as Reader Ugo Foscolo undergoes changes of social status and location, his Disposition towards a given Reading Resource e.g. Dante's Divine Comedy changes due to his political and personal circumstances, and whether he is reading for pleasure or in order to write an essay about Dante for a literary journal.

In the case of war diaries, it is possible to distinguish between diarists' attitudes toward reading before, during and after the war (Disposition). For instance, before the war, both diary-keeping and (to an extent) leisure reading were practices associated with middle-class people with time to spend in leisure activities, while during the First World War reading and keeping diaries became relatively common activities among soldiers as well as officers.

Alteration and Medium

With time and in relation with the reader's personal circumstances or social relationships, a Medium can assume a special value for the Reader that can also result in developing new forms of Disposition. As a valuable object (for the reader), a Medium can traverse epocs and events, passing from hand to hand through the generations and working as probes in readers' life. As result of time and usage, a Medium can be adapted or enhanced with notes and dedications, or damaged by time and events. The model of reading can capture a scenario in which an Alteration can be causing a Reading Experience for the Reader as the process involve an altered Medium. On the other hand, e.g. in case of taking notes, a Reading Process can be causing an Alteration (as part of the process), inscribing a trace of the reading in the physical or item Medium. In this regard, an Alteration can be related to a Content: an Alteration can be specifically aimed to alter or fix a specific interpretation or value of a concept or situation of the Content, see Fig. 9 (left).

A Reading Experience can involve an Alterations of Medium as the Alteration mediates the interaction between Content and Reader, see Fig. 9 (right).

For example, the libraries belonging to writers are often preserved as part of cultural heritage collections. These books often contain Alterations that can provide an indication of the changing Dispositions of the Reader, such as influences on their subsequent careers as writers. An example is the study of Herman Melville's marginal annotations (a form of Alteration) in his book collection, which has been used to show how his Reading Experience shaped his writing style [START_REF] Ohge | At the Axis of Reality: Melville's Marginalia in The Dramatic Works of William Shakespeare[END_REF]. A similar study could be conducted on other book collections preserved in cultural heritage repositories, such as for example, the books belonging to poet Thomas Moore held at the Royal Irish Academy in Dublin.

Premises and Outcomes

As argued, a Reading Process is situated in the reader's life and, therefore, extends beyond the moment of direct interaction with medium and content, see Fig. 10 (left). The contingencies of activities and expectations (Premise) provide a context that will be relevant for the results and closure of a reading (Outcome), see Fig. 10 (right). Premises and Outcomes are the mental Frame in which reading takes place as a result of the contingent personal and social situations relating to Reader's life, public discourse and the personal value of the Content or the personal and social relational system around the specific Medium. In this setting, the Frame of reading provides information about how purpose, expectations, value and relevance of the topics of reading change through time and events. Furthermore, the Frame of a Reading Process can be specified and then studied at the level of a whole Reading (i.e. from the begin to the end of a content) or at level of Session and through the temporal relations connecting reading experiences. For example, the Outcome of Reader Ugo Foscolo's reading of Dante changes depending on the Premise of his reading, such as reading for pleasure in Italy or in order to write a review of Dante for a literary journal in Britain.

Considering author's libraries, the graphic signs, such as underlining and marginal notes, left by authors can provide information about an author's reading goals, e.g. why they were studying a text (Premise, e.g. Aim and Activities), what they were looking for and what was their evaluation of a given passage of a text (Outcome, e.g. Self-reflection).

Discussion

From a technical level, the extension of the READ-IT model enables the annotation of a new range of aspects related to the dynamic of reading from the perspective of a single reader. The person-centred perspective we adopted is the result of the examination of sources reporting direct experience of reading. The value of these sources is beyond the individual but can be unlocked only by the systematic annotation of a vast number of sources, which is the purpose of the model of reading and of the technological work-strand of READ-IT.

From a theoretical perspective, the phenomenological approach to the phenomenon of reading as human experience does have limitations on the ability to address functional and societal aspects of reading. Indeed, reading has a fundamental role in shaping society, as a pervasive technology (text) and set of skills required to use this technology (writing and reading). The possession of these skills is nowadays considered almost an assumption of being part of European society and is placed at the centre of education systems. However, this is a very recent social innovation, and yet not universal (either in or outside Europe). In this frame, the ability to read, the level of skill, the competencies with technical or theological text, the access to books and to the places where these abilities where cultivated and taught are central topics for understanding the different meanings of reading during most of human history. The person-centred view of reading is the result of the current ubiquitous presence of reading, which assumes that access to skills and text is not an issue anymore for the vast majority of the population. In this new context of democratised reading, the focus is on the aesthetics and ethics of contents and on the role of reading in the formation of personality and ideas, as we assume that reading has indeed a role in the life of each and every person.

The question of the value and effects of applying this contemporary perspective of reading to historical sources is not trivial and deserves further investigation. On the other hand, from a pragmatic perspective, the historical sources on reading experiences are limited to the elite of society, the few people with both the skill and the access to contents. Thus, limits of the relevance of this approach in understanding society evolution in history is not specifically related to the person-centred approach, but on the availability of sources. Furthermore, the content and factors of reading experiences in historical sources are not indeed different qualitatively from contemporary sources.

Conclusions

In this contribution we presented and discussed the technical solutions developed within the frame of the READ-IT project aimed at enabling the study of changes to readers and to the medium of reading in historical sources. We grounded the technical solutions on three real case studies addressing the study of three different sources: diaries, correspondence and authors' libraries. By considering the features related to change in these three types of sources, we introduced four extensions to the READ-IT data model aimed to enable the representation of changes of the Reader and of the Medium:

1. The reader is considered as a description of a person, in a specific time and situation, which enables the study of how the age, skills, religion, political positions, and all variable aspects of a person life can contribute to the reading experience 2. The reader's dispositions as a specific state of mind grounded in the abilities, skills, social groups, age and all aspects of the reader which influence their approach to a content or a type of medium 3. Alteration of media as physical modification of the object granting access to the content, which provides evidence of the use of a reading resource 4. The frame of a reading characterised by specific premises and outcomes of the activity, as a particular state of mind specifically causing and caused by reading

The development of the model of reading we present is tightly related to the development of the READ-IT case studies and requirements emerging from research activities. Furthermore, the model of reading in READ-IT is a first attempt to address the construction of a general theory of reading, thus it is far from reaching a consensus in the different academic communities interested in the study of reading. In this context, we recognise that the work presented is at an intermediate (or early) stage of a long process of iterative improvement and slow convergence on a set of common concepts. Nevertheless, we do believe that the effort of extending the scope of conceptual models to the core of the research topics is a necessary step to address the interdisciplinary macroscopic scale questions which READ-IT targets. Indeed, a common and yet imprecise theory can enable the collaborative construction of a common resource on reading envisaged by UK-RED, beyond the current limits set by the different theoretical framework of disciplines, language and perspectives.

In relation to the value of the sources presented in defining a European cultural heritage, the work presented contributes by providing the means to amplify the effort of individual research groups working on identifying and documenting the historical and cultural phenomena shaping European identity from the analysis of sources. Indeed, the concepts and relations of the model of reading will support the convergence of individual contributions in a common discourse about reading in Europe, and therefore support and promote a holistic European perspective on cultural heritage.

Fig. 1 .

 1 Fig. 1. On the left, the three-fold interaction of reading: (A) Reader with Medium, (B) Reader in accessing to the Content through the Medium, (C) Reader with the Content. On the Right, the schema encoding the three interactions.

Fig. 3 . 4 .

 34 Fig. 3. On the left, a conceptual schema representing the dynamic of readings, relating Readings, Sessions and Experiences in terms of sequence and of inclusions. On the Right, the schema encoding Experience, Session and Reading as specialisation of Reading Process, and Event. Reading as Experience. We consider an Experience a piece of evidence of a change of State of Mind of the Reader, as a result of the interaction of the Reader with Content and Medium, see Fig. 4. With State of Mind we encode all evidences related to a cognitive state of the Reader, such as Emotion, Remembrance or Self-reflection. A Reader's State of Mind could be involving a Medium or a Content (Reading Resource) motivated by personal and social circumstances, such as a gift to the Reader. Thus, a Reading Resource could have a special meaning for the Reader.

Fig. 4 .

 4 Fig. 4.On the left, a conceptual scheme representing how the changes in the reader's state of mind is the result of the readermedium-content interactions, mediated by the environment conditions and co-occurring events, and how the resulting state of mind can be the premise of a new reading session. On the Right, the schema encoding the temporal relations between reading process and states of mind of the reader, and the relations between reading resources and state of mind and the reader

Fig. 5 .

 5 Fig. 5. On the left, the relations between work, expression, manifestation and item in FRBR, reproduction of the original schema from IFLA (2009). On the Right, in FRBR a work can have has a subject a set of concepts, reproduction of the original schema from IFLA (2009).

Fig. 6 .

 6 Fig. 6. On the left, the ontological model of listening experience in LED, reproduction of the original schema from Adamou (2018). On the Right, the management workflow of entity data, reproduction of the original schema from Adamou (2018).As a follow-up of LED, in READ-IT we moved the focus of the model from the management of sources and research activities to the object of the research: the reading experience. In this regard, READ-IT introduces the concepts of State of Mind of the Reader, and defines and Experience within the situation of a broader view as an articulation of Sessions and Experiences and Readings defining an ecology of experience of the Reader. Thus, experiences are multiple during a same session and several sessions are interconnected providing the possibility to study the dynamic evolution of the experience.

1 .

 1 Reader and Person 2. State of Mind and Disposition 3. Medium and Alteration 4. Reading Process and Reading Frame, and State of Mind, Outcome and Premise

Fig. 7 .

 7 Fig. 7. On the left, a conceptual schema representing the different status of reader of a person. On the left, the schema encoding the Reader as a Temporal Entity describing a Person.

Fig. 8 .

 8 Fig. 8. Schema encoding Disposition, specialisation of State of Mind, and the relations with Reading Resource and Reading Process.

Fig. 9 .

 9 Fig. 9. On the left, Reading Resource and Alterations are Temporal Entities, an Alteration is altering a Medium and related to a Content and a Reading Process can be causing an Alteration. On the right, an Alteration can be causing a Reading Experience.

Fig. 10 .

 10 Fig. 10. On the left, a Reading Session is a Foreground Activity, performed through Foreground and Background processes (i.e. Reading Process), while Reading, as a whole, extends beyond a Session as a Background Activity. Both Foreground and Background Activities generate Outcomes. The inclusion of states of mind outside reading sessions specifically relates to the extension of reading beyond sessions, as background activity. On the right, the states of mind related (premises and outcomes of reading) to the background activities are encoded with the concept of Reading Frame. In modelling reading, we consider Premises and Outcomes as the characterisation of the Reading Frame in which a Reading Process take place. Premise and Outcome are specialisation of State of Mind causing a and being a result of the Reading Process. Premise and Outcome are Temporal Entities as well, thus it is possible to express temporal relations

This work was partially supported by Reading Europe -Advanced Data Investigation Tool (READ-IT) is funded by the JPI Cultural Heritage project under the European Union Horizon

Research and Innovation programme (grant agreement No 699523).