Reiner Rummel

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Abstract. In 1988 the interdisciplinary role of space geodesy has been discussed by a prominent group of leaders in the fields of geodesy and geophysics at an international workshop in Erice, (Mueller I I, S Zerbini, 1989). The workshop may be viewed as the starting point of a new era of geodesy as a discipline of Earth sciences. Since then enormous progress has been made in geodesy in terms of satellite and sensor systems, observation techniques, data processing, modelling and interpretation. The establishment of a Global Geodetic Observing System (GGOS) which is currently underway is a milestone in this respect. Wegener served as an important role model for the definition of GGOS. In turn, Wegener will benefit from becoming a regional entity of GGOS.

What are the great challenges of the realisation of a 10 -9 global integrated observing system? Geodesy is potentially able to providein the narrow sense of the words -"metric and weight" to global studies of geo-processes. It certainly can meet this expectation if a number of fundamental challenges, related to issues such as the international embedding of GGOS, the realisation of further satellite missions and some open scientific questions can be solved. Geodesy is measurement driven. This is an important asset when trying to study the Earth as a system. However its Satellites opened new horizons for geodesy and no other discipline is known to me that has benefited more profoundly from space techniques. Positioning, gravity field determination, Earth rotation monitoring and geodetic remote sensing can be done much more accurately, completely and efficiently from space. Geodesy became truly global and three dimensional. Oceans, a "terra incognita" of the classical times turned with satellites into an area of great geodetic activity. Classical geodetic techniques did not allow the accurate measurement of zenith angles, due to atmospheric refraction. From space the vertical dimension of the Earth's surface can be determined almost as accurately as the horizontal components. Progress of space geodesy was fast and had a great impact. Hand in hand with the rapid development of geodetic space techniques geosciences became more and more interested in geodetic work.

The Erice workshop about the interdisciplinary role of space geodesy. Twenty years ago some of the most outstanding geodesists, Earth scientists and physicists were invited to a workshop in Erice/ Sicily. It dealt with the interdisciplinary role of space geodesy and was organized by Ivan I MUELLER and Susanna ZERBINI (1989).

At this workshop the role of space geodesy for Earth sciences was carefully analysed and recommendations formulated for the future. The introductory chapter to the book by W M KAULA is especially worthwhile to read. He discusses five selected fields of Earth science and the possible role of space geodetic techniques for them. The five fields are (1) Earth rotation and core-mantle interaction, (2) mantle convection, (3) regional tectonics and earthquakes, (4) ocean dynamics and (5) Venus-Earth differences. The workshop in Erice marks the beginning of the era of space geodesy as being a discipline of Earth sciences.

Developments of the recent past.

In recent years the general emphasis of Earth sciences has moved towards Climate Change and Earth System Science.

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Awareness grew that we need a much better understanding of the Earth as a system, of solar radiation as its driving force, of the thermal back radiation and how it is affected by even tiny changes in chemical composition of the atmosphere, and last not least of the impact of man. One fundamental deficiency became particularly evident in the course of the preparation of the last report of the Intergovernmental Panel on Climate Change (Climate Change, 2007) and has been addressed in several articles in Science and Nature, see [START_REF] Hogan | Warming Debate Highlights Poor Data[END_REF] and the articles quoted there: There is a clear lack of observations (ibid, 2005). Space geodesy is able to provide important new and unique data to Global Change research by measuring mass and energy transport processes in the Earth system. Ben [START_REF] Chao | Geodesy is not Just for Static Measurements Anymore[END_REF] wrote:" After three decades and three orders of magnitude of advances, space geodesy is poised for prime time in observing the integrated mass transports that take place in the Earth system, from the high atmosphere to the deep interior of the core. As such space geodesy has become a new remote sensing tool, in monitoring climatic and geophysical changes with ever increasing sensitivity and resolution." One can claim that geodesy, by merging geometry, Earth rotation, gravity and geoid, is in a position to provide "metric and weight" to Earth system research. Before this background the establishment of the Global Geodetic Observing System (GGOS) is the right step at the right time. The underlying concept is simple and well described by the scheme shown in figure 1 and due to ROTHACHER, see (RUMMEL et al., 2005; see also PLAG & PEARLMAN, 2007). objective is to realize this with a relative precision level of 10 -9 in one unified Earth fixed reference system and to keep this system stable over decades. Where does such a demanding requirement come from? In geosciences one usually deals with estimates accurate to only a few percent. Global change parameters are small und their temporal changes are slow and even smaller. In general they cannot be observed directly but have to be derived from a combination of several measurement systems and models. In order to be able to analyze them as a global process they have to be scaled relative to the dimension of the Earth. Let us take an example. Sea level at an arbitrary tide gauge may vary by a few meters, due to tides and storm surges. Measurement of sea level change with a precision of a few mm requires therefore a relative precision of 10 -3 at this particular station. Local sea level monitoring can be transformed into a global monitoring system by satellite systems such as altimetry and GPS. Only then a global process can be deduced from local tide gauge records. In order to achieve cm-or mm-precision with satellite systems globally, orbit determination and altimetric measurements have to be delivered with a relative precision of 1 ppb.

In order to meet the goals set for GGOS a series of rather fundamental geodetic problems have to be dealt with. The three pillars of geodesy, geometry, Earth rotation and gravity have to be expressed in one and the same Earth fixed reference system with millimetre precision and stability (of the frame) has to be guaranteed over decades. This requires the space as well as the ground segments to function as one homogeneous entity as if all observations were done in one observatory encompassing the Earth. Each observation contains a superposition of a variety of effects, related to ionosphere, atmosphere, oceans, ice shields and solid Earth. In order to employ them for Earth system research strategies have to be developed for their separation and quantification by analysing their spatial, temporal and spectral What are the geodetic priorities and how can geodesy take advantage of nongeodetic space activities? Let me formulate a number of questions.

Several GNSSs will be available in parallel in the near future, the GPS, GLONASS, GALILEO, COMPASS and the associated augmentation systems. What can we gain from their combined use, what for example from their improved clocks? If one could establish inter-satellite ranging, one would get an orbiting precision polyhedron. What would we gain from such a constellation? Let us assume geodesy would push for a third LAGEOS (e.g. counter rotating as proposed by Professor BERTOTTI a long time ago). Would it further strengthen our terrestrial reference system, e.g. its long term stability and the low gravity harmonics? It would certainly be an important bridge to gravitational physics.

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After the great success of GRACE further gravimetric satellite missions are urgently needed to secure continuity of the measured time series, if mass transport should remain a central gravimetric theme. How should such missions look like? Compare also, KOOP and RUMMEL, 2006. In parallel the development of significantly improved geophysical "background" models of ocean tides, and coupled atmosphere-ocean circulation must have high priority on the geodetic agenda. They would serve the dealiasing and separation of geophysical effect. Only then one could fully benefit from improved technological concepts such as inter-satellite laser link, drag free system, proof mass-to-proof mass measurement and satellite configuration flights.

Would mini-satellites be useful, e.g. for atmospheric sounding or for a satellite based synchronization of two or several techniques, such as GPS, DORIS, VLBI and laser ranging?

The GNSS signal emitters and receivers are distributed over three spatial layers: the GNSS satellites at high altitude, a large number of low Earth orbiters (LEO's) equipped with GNSS receivers between 300 and 1000 km altitude and many permanent receiving stations on ground. Could this add, literally, a further dimension to GNSS atmospheric sounding and to the modeling of the wet troposphere? Several space agencies are preparing missions to our moon. A lander mission could be used to deploy geodetic laser transponders. This would greatly facilitate and improve lunar laser ranging and strengthen its role among the geodetic space techniques and for gravitational physics. In addition, the far-side gravity field of the moon is still not known very well; thus any mission opportunity for satellite lunar gravimetry would be welcome.

What are the technological building blocks of future space geodetic missions? A new generation of ultra-high-precision clocks in space and on ground, such as optical clocks, active transponders for tracking systems, GNSS reflectometry and new types This leads to the question about the challenges and opportunities of future space geodesy. The three traditional enemies are non-gravitational forces acting on satellites, atmospheric refraction and local ties.

Uncertainties and gross errors in local ties between measurements systems sound like a trivial question of diligence and organisation but strangely enough this problem

is not yet globally resolved. Great progress has been made in measuring and modelling local tropospheric effects for the various ground receiver systems.

However a uniform and consistent approach for all techniques is still not routine and should be pursued with high priority. Modelling of the satellite environment (residual air drag and solar radiation) is still far from solved and should also be given high priority. Possibly, low Earth orbiters without accelerometers might be used for gravity field monitoring in the future.

What about clocks, time measurement, synchronisation and transfer? The great progress of the past in space geodesy can be intimately linked to a corresponding progress in the measurement of travel times and time keeping. Important new developments have lead to optical clocks (and counters) at a precision level of 10 -18 in the laboratory. Precisions better than 10 -16 can and will have important implications for geodesy. The materialisation of a global unified height system could be achieved using the relativistic dependence of time on the gravitational potential. Time synchronisation at this level of precision via satellites would open several new perspectives for geodesy. Time measurements made by satellites might be considered as real observables and not only as a device for "tick marking" measurements. One could start dreaming of the direct measurement of gravitational A c c e p t e d M a n u s c r i p t potential differences between satellites as well as between satellites and ground stations.

During the pioneering days of satellite geodesy direction measurement with cameras to satellites against the stellar background was one of the primary techniques. With the advent of laser and radio tracking range and range rate replaced angular measurements which always suffered from the effect of atmospheric refraction. But are angular measurements really obsolete for ever? Should one not think about new concepts of angular measurement, e.g. with synchronised twin laser telescopes, and about what their impact would be?

Finally, considering all this amazing progress one can wonder whether there is not a natural limit of precision beyond which further progress of geodetic space techniques does not make sense anymore because the ever increasing precisions cannot anymore be reproduced in nature. Is 10 -9 already such a limit or 10 -10 ? Concluding remarks. In the quoted book "The interdisciplinary role of space geodesy" (MUELLER and ZERBINI, 1999), KAULA wrote on page 9: "…Theoreticians get the impression that experimenters operate according to problem definitions that are a decade or more obsolete, while experimenters probably think that theoreticians are sporadic in their attention and underestimate technical difficulties. Better communication is particularly important now that measurement capabilities can yield valuable constraints, provided that they are applied in sufficient detail". This is a remark about the relationship between theory and experiment. KAULA, being both an outstanding geodesist and geophysicist, saw that there was a problem in this relationship at that time. Traditionally geodesy is very "measurement and technique driven". Even during the definition phase of GGOS the underlying rationale started from the observing system and not so much from the Earth science problems that could be addressed with such a system. Such an approach may be logical but it is

  s c r i p t guideline must be: "What are the right and most important observables to deal with the open scientific questions?" Key words: geodesy, satellite geodesy, global observing system, global geodetic observing system Historical introduction. Since about 150 years geodesy can be regarded as an independent discipline of science. BAEYER's memorandum about the size and figure of the Earth "Über die Größe und Figur der Erde" (1861) may be seen as a starting point, even though important geodetic work had been done before by famous scientists such as NEWTON, LAPLACE, GAUSS, BESSEL. But their work was not referred to as geodesy and they did not regard themselves as geodesists. BAEYER's initiative resulted in an extension and unification of existing triangulation and levelling networks covering central Europe. This work was then expanded to the whole of Europe, before its transition to an international effort with the aim to determine the global figure of the Earth. It was one of the first international projects in science and the root of what is today the International Association of Geodesy (IAG), cf. (TORGE, 2001). Last year, in 2007, 50 years of space age was celebrated. With the launch of Sputnik 1 on October 4, 1957 (and shortly after of Sputnik 2) modern space age began. Already these two satellites had a fundamental effect on geodesy. Almost instantaneously a large part of 100 years of diligent geodetic work dedicated to the determination of the figure of the Earth became out-dated. From measuring the precession of satellite orbits the Earth's flattening could be determined much more accurately than with classical astro-geodetic work, compare e.g. King-Hele, 1992.

Figure 1 GGOS

 1 Figure 1

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  s c r i p t characteristics. Satellite measurements represent time series along their orbit. Via the Earth's rotation and the choice of the satellite orbit elements these time series are related to a spatial and temporal sampling of the Earth. The reconstruction of the temporal and spatial geophysical phenomena poses a complicated problem of aliasing and inversion. The current investigations of the global water cycle or of the ice mass balance in Greenland and Antarctica from GRACE gravimetry are exactly problems of this type. The inclusion of terrestrial and airborne data, such as surface loading, ocean bottom pressure, tide gauges, gravimetry or altimetry may certainly help. However, this step is not easy either, because terrestrial measurements are affected by local influences and exhibit a spectral sensitivity quite different from that of satellite observations. Probably the most effective support to de-aliasing and separation of geophysical phenomena is the inclusion of prior information, such as models of solid Earth and ocean tides, atmosphere, oceans, ice, hydrology or glacial isostatic adjustment, however only if they are introduced consistently for all techniques of the observing system. Important work towards these goals is currently underway and we see geodetic techniques used much more widely in the various Earth disciplines.WEGENER developed over the years from an almost mono-disciplinary project to regional multi-disciplinary activity combining a large variety of geodetic and nongeodetic measurements techniques and involving all geo-disciplines relevant to its objectives. It is therefore an excellent example on how GGOS could operate on a global scale.A look into the future. With an enormous pace space geodesy has made fantastic progress over the past 50 years. Do we have to fear this development to slow down in the near future? Let me try to look into the future..

  what general boundary conditions will space geodesy have to operate in the years to come? Global Change activities are mostly organized on an intergovernmental level in international programs such as INSPIRE, IGOS or CEOS.GGOS must therefore strive to be integrated into such programs in order to attain the necessary impact and recognition. It is advisable that geodesy tries to activate its national governmental agencies towards this goal, in particular those agencies supporting already for years the geodetic scientific services under the umbrella of the International Association of Geodesy (IAG). Global Change is discussed nowadays in terms of so-called essential climate variables (ecv's). GGOS has to analyze in what way it can contribute to the determination and monitoring of the identified ecv's. To a large extent the major Earth oriented satellite programs of NASA and ESA are defined already for the next 5 to 10 years. If missions are missing which are essential for the progress of space geodesy, GGOS has to develop a strategy on how to get such missing elements approved by one of the space agencies.

  s c r i p t of accelerometers may soon become available for space geodesy. These could have a tremendous impact on the development of geodesy.

  s c r i p t essentially wrong. Experiments have to be derived from theory and new hypotheses from the experiments; to be successful an intimate relationship between the two must exist. From this I conclude that geodesy and geodesists have to get much deeper into Earth sciences. Geodesists have to have a profound understanding of the geophysical problems. Only then the fantastic tools of modern space geodesy will develop their full potential for the understanding of our Earth as a system. This poses a great challenge to geodetic education and science.

Figure 1 :

 1 Figure 1: Geodetic space techniques determine the shape of the Earth, Earth rotation

Figure 1 :

 1 Figure 1: Geodetic space techniques determine the shape of the Earth, Earth rotation

Figure 1

 1 Figure 1

Acknowledgement: Several coffee time discussions with Gerhard Beutler and Urs

Hugentobler are gratefully acknowledged.


Paolo Ghigna
email: paolo.ghigna@unipv.it.

Sonia Pin

Adolfo Speghini

Marco Bettinelli

Taiju Tsuboi

"Unusual Ln 3+ substitutional defects": The local chemical environment of Eu 3+ and Er 3+ in nanocrystalline Nb 2 O 5 by Ln-K edge EXAFS

The local chemical environment of the trivalent lanthanide cations in Nb 2 O 5 nanopowders doped with 1 mol % of Eu 3+ and Er 3+ , prepared via a Pechini approach, has been studied by means of EXAFS at the Ln-K edge. It can be demonstrated that the lanthanide ions enter the Nb 2 O 5 structure as substitutional defects with respect to Nb, giving rise to a very large amount of disorder: both Eu 3+ and Er 3+ ions substitute Nb in the 9-fold coordinated site, with clustering of oxygen vacancies around the substitutional defects. Valence Bond calculations have been used to validate the Ln-O distances obtained by the EXAFS fitting. The Er 3+ doped nanocrystalline Nb 2 O 5 sample shows efficient luminescence in the near infrared region around 1.5 μm. The emission and excitation spectra are affected by significant inhomogeneous broadening, in agreement with the presence of strong disorder around the dopant ions in nanosized Nb 2 O 5 .

A c c e p t e d m a n u s c r i p t 1. Introduction

Luminescent niobium based compounds doped with trivalent lanthanide ions (Ln 3+ ) have been the subject of considerable attention in the past decades. For instance, LiNbO 3 has proved to be a very important host for Ln 3+ ions, with widespread applications in the field of optoelectronics and light emitting devices [1,2], and strontium barium niobate (Sr x Ba 1-x Nb 2 O 6 ) (SBN) and barium sodium niobate Ba 2 NaNb 5 O 15 (BNN) [3], activated with Ln 3+ ions, are very promising materials in the field of photorefractive memories [4] and linear and self-frequency converter solid state laser materials [5,6]. It is important to note that in all these crystals the location of the Ln 3+ in the lattice is not obvious, as the trivalent lanthanide ions cannot easily replace the constituent cations (Li + , Na + , Sr 2+ , Ba 2+ , Nb 5+ ) due to evident size and/or charge mismatches. It is worth noting that for these niobate hosts the doping Ln 3+ ions have a different charge with respect to the host cations (Li + , Sr 2+ , Ba 2+ and formally Nb 5+ ) and also a different ionic radius (the Sr 2+ and Ba 2+ cations are larger while the Li + and Nb 5+ are smaller than the Ln 3+ ions [7]). Also simple oxides like TiO 2 or Nb 2 O 5 , in which a single cation is present, are characterised by similar problems due to large mismatch of both charge and ionic radii between the doping Ln 3+ ions and the host constituent cations. However, recent investigations by our research group have demonstrated the feasibility of the synthesis, using solution methods, of both TiO 2 [8] and Nb 2 O 5 [9] doped with lanthanide ions. Recently, in a paper dealing with the local chemical environment of Ln 3+ dopants in anatase TiO 2 the incorporation of lanthanide ions in such class of hosts as been referred to as "unusual Ln substitution" [10]. By using a local structural probe such as EXAFS at the Ln-K edges, it has been demonstrated that the lanthanide ions enter in the anatase structure as substitutional defects with respect to Ti, but that the amount of disorder created by the substitutional defects is very large. Indeed, the Ln-O and Ln-Ti distances have been found to increase by as much as 0.45 Å, with respect to what is found for the Ti-O and Ti-Ti distances in pure anatase [10]. Aim of this paper is to extend this kind of study to Nb 2 O 5 . As a matter of fact, samples considered in this paper retain the T-Nb 2 O 5 crystal structure [11]. This structure is orthorhombic (space group Pbam) and Nb can be in a distorted octahedral

Experimental details

Samples preparation

Nanocrystalline powders of Ln 3+ doped Nb 2 O 5 were prepared by a sol-gel Pechini approach as described elsewhere [9]. The molar ratio between the niobium and the Ln 3+ ions was kept 99:1. Xray powder diffraction patterns collected on a Brucker D8 diffractometer, in the Bragg-Brentano geometry and using a Cu X-ray tube, confirmed the single phase nature of the reaction products. All the diffraction pattern could be indexed using the orthorhombic structure of T-Nb 2 O 5 [11].

Moreover, from the broadening of the diffraction peaks and electron microscopy images, the average size of the nanoparticles was estimated to be about 25 nm [9].

EXAFS

Extended X-Ray Absorption Fine Structure (EXAFS) spectra were collected at the Er and Eu-K edges at the BM-29 beamline of ESRF. The data collection was made at 20 K in fluorescence mode using a Si (511) monochromator. For the measurements, a selected amount of sample (ca. 0.3 g) was thoroughly mixed with cellulose in an agate mortar and pressed to form a pellet. The data analysis was carried out taking advantage of the FEFF8 code [12]. The EXAFS extraction has performed by the use of ATHENA code. The EXAFS fitting was performed by means of the IFEFFIT interface [13]. The goodness of fit (GOF) is given by the R-factor parameter which is scaled to the magnitude of the data itself

R = ∑ ∑ = = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ N i data data N i i i f f 1 2 2 1 2 2 ) Im( ) Re( ) Im( ) Re( χ χ

A c c e p t e d m a n u s c r i p t

measured data on concentrated samples, R ≤ 0.02. The accuracy of amplitude and phase-shifts calculated by the program have been checked by fitting the spectrum of powdered lanthanide oxides, and comparing the fitted radial distances with crystallographic values, that have been recovered with an accuracy better than 0.01 Å.

Luminescence

The luminescence emission and excitation spectra were measured using a Spex Fluorolog-3 spectrofluorimeter equipped with a 450 W xenon lamp. The spectrofluorimeter consists of two monochromators, one for the excitation and the other for the detection of the emission. The slit width of the emission monochromator was fixed to band pass of 0.2 nm to obtain highly resolved luminescence emission spectra, while a narrow slit width (band pass of 0.2 nm) was selected for the excitation monochromator to obtain highly resolved luminescence emission spectra. The infrared emission signal was measured by a liquid-nitrogen cooled Jobin-Yvon DSSX-IGA010L InGaAs photodiode with sensitivity in the range 800-1650 nm. incorporation in the Nb 2 O 5 structure. In the EXAFS FT, moreover, just one peak, i.e. at distances around 2 Å, is apparent in both spectra and can be attributed to oxygen atoms (nearest neighbours).

Results and discussion

The best fits, according to the structural models reported in Tab. 1, are shown in Fig. 2 and3 as dotted lines for the Eu-K edge spectrum and the Er-K edge spectrum, respectively. According to the data reported in Tab. 1, the local chemical environments of Eu 3+ and Er 3+ in the Nb 2 O 5 host structure are impressively similar. It should be noted that the models used for the EXAFS fitting implicitly assumed that the Ln 3+ ions enter into the Nb 2 O 5 host as substitutional defects on the Nb position. An additional comment is worth here on the fitting procedure that has been applied in this work. The large amount of disorder that is found in the samples reduces the k range in which observable EXAFS oscillations are found. This evidence makes the EXAFS analysis problematical, especially due to the heavy correlations between the coordination numbers and σ 2 . It is possible to overcome these limitations, by noticing that the coordination distance is much less affected, as it determines the frequency of the EXAFS oscillations. Therefore the coordination distances can be quite accurately found out by a first EXAFS fitting using "dummy" coordination numbers. Next, these distances can be used to estimate, by the well established Bond -Valence Sum method [14],

the coordination numbers that give the best agreement between the calculated charges on the Ln 3+ ions and the formal (III) oxidation state. The use of the Bond -Valence Sum method to restrain the number of variables in the EXAFS data analysis has been widely discussed by Newille [15]. Then, it is possible to test that these coordination numbers give a reasonable fit for the σ 2 parameters, and a further test can be performed by checking that the fitted values for the distances do not change in this final fit. Using the Ln 3+ -O distances reported in Tab 1, and 7 as the coordination number, the calculated charges on both Eu and Er are 2.63. On the other hand, using for both Eu and Er a coordination number of 8, the calculated charge is 3.00, which is in better agreement with the formal (III) oxidation state. The present results, therefore, suggest that the most probable location of The spectra shows that excitation in the 2 H 11/2 level gives rise to luminescence terminating on the 4 I 15/2 ground state and originating from the excited levels 4 I 9/2 (860 nm), 4 I 11/2 (980 nm) and 4 I 13/2

(1520 nm). The sharp band located at about 1230 nm is most probably due to an unidentified impurity. The Er 3+ excited states below 2 H 11/2 are populated by multiphonon relaxation bridging the energy gaps separating successive levels. This agrees with the relatively high energy phonons found in the Raman spectrum of nanocrystalline Nb 2 O 5 (cut-off wavenumber of about 700 cm -1 [9]) and the relatively small energy gaps above 4 I 13/2 . On the other hand, the gap separating the latter level from 4 I 15/2 is larger (about 6600 cm -1 ) and therefore the 4 where where I(λ) is the luminescence intensity and I max is the intensity at the peak maximum. In the present case, eff λ Δ =44 nm, a value not far from the ones measured for this transition in conventional oxide glasses (e. g. 57.1 nm in Sr(PO 3 ) 2 glass [17] and 32-51 nm for a series of sodalime aluminosilicate glasses [18]). The high value of eff λ Δ is a definite proof of a strong disorder around the luminescent ion.

Conclusions

The

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A c c e p t e d m a n u s c r i p t 4 (

 4 coordination number 6) or pentagonal bipiramid (coordination number 7) environment. Further Nb centres are randomly locate in the cell in a nine-fold coordination. For this reason, the structure is quite complicated and the location of the lanthanide ions in the cell could be a challenging task.

Fig. 1 A c c e p t e d m a n u s c r i p t 6 vanish

 16 Fig.1shows the Eu-K edge XAS spectrum of the sample investigated in this work. The statistical

A c c e p t e d m a n u s c r i p t

  Fig.4shows the room temperature emission and excitation spectra of the Nb 2 O 5 :Er 3+

  I 13/2 → 4 I 15/2 band dominates the emission spectrum. The excitation spectrum indicates that NIR luminescence of nanocrystalline Nb 2 O 5 :Er 3+ can be excited efficiently in the visible region. The profile of the 4 I 13/2 → 4 I 15/2 band clearly shows the presence of inhomogeneous broadening, as several relatively sharp peaks are superimposed to an underlying broad bandshape. Significant broadening is also present in the other features present in the emission and excitation spectra. These observations confirm the luminescence results obtained for nanocrystalline Nb 2 O 5 :Eu 3+ [9]. The general behaviour shown by the optical spectra of nanosized Nb 2 O 5 :Ln 3+ is clearly due to the presence of significant disorder around the dopant ions, in agreement with the EXAFS results discussed above. The broadening can be quantified through the estimation of the effective linewidth

Fig. 1 .Fig. 2 .

 12 Fig. 1. -Raw fluorescence data at the Eu-K edge for Nb 2 O 5 :Eu.

Fig. 3 .

 3 Fig. 3. -Eu-K edge EXAFS spectra (upper panel) and EXAFS Fourier Transform (lower panel) of

Fig. 4 .A c c e p t e d m a n u s c r i p t 13 Tab. 1

 4131 Fig. 4. -Room temperature luminescence excitation (λ em =1516 nm) and emission (λ exc =525 nm) spectra of nanocrystalline Nb 2 O 5 :Er 3+ .

Fig. 1 EA c c e p t e d m a n u s c r i p t 15

 115 Fig. 1

7 A c c e p t e d m a n u s c i p t 16

 716 Fig. 2

Fig. 4

 4 Fig. 3

  local chemical environment of the trivalent lanthanide cations in Nb 2 O 5 nanopowders doped with 1 mol% of Eu or Er with respect to Nb, prepared via a Pechini route, has been studied by means of EXAFS at the Eu and Er-K edge. It can be demonstrated that the Ln 3+ cations enter the Nb 2 O 5 structure as substitutional defects with respect to Nb: the most probable site occupied by the Ln 3+ cations being the nine-fold coordinate one randomly located in the unit cell. In addition, it is quite probable that oxygen vacancies, formed for charge compensation of the Ln" Nb defects, cluster around the substitutional defects. These findings are compatible with the large amount of disorder that is found around the Ln 3+ cations. The values obtained for the Ln-O distances have been validated by means of Bond Valence calculations. Luminescence spectra of the Er 3+ doped sample shows significant inhomogeneous broadening, that indicates a large amount of static disorder, in agreement with the EXAFS findings.

Nb 2 O 5 doped Eu 1% Pechini

	Atom	n	r (Å)	σ 2 (Å 2 )/ BVS	R
	O	7	2.41(1)	0.010(2) / 2.63	0.008
			Nb 2 O 5 doped Er 1% Pechini
	Atom	N	r (Å)	σ 2 (Å 2 )/ BVS	R
	O	7	2.35(2)	0.010(4) / 2.63	0.008
			Nb 2 O 5 doped Eu 1% Pechini
	Atom	n	r (Å)	σ 2 (Å 2 )/ BVS	R
	O	8	2.41(1)	0.010(2) / 3.00	0.008
	Atom O	Nb 2 O 5 doped Er 1% Pechini r (Å) 2.35(2) A c c e p t e d n 8 m a n u s c r i p t σ 2 (Å 2 )/ BVS R 0.010(4) / 3.00 0.008
					14

Acknowledgements

This work has been supported by the European Synchrotron Radiation Facility (ESRF, experiment CH 1965 at the BM29 beamline). The BM29 staff, and in particular Simone de Panfilis, is gratefully acknowledged for help during the XAS data collection.


J Legrand

Impact of Regional Reference Frame Definition on Geodynamic Interpretations

Keywords: Geodesy, Reference Frame, Methodology, GNSS, Velocity Field, Geodynamic

Ten years (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006) of weekly GNSS solutions of 205 globally distributed stations have been used to investigate the impact of the reference frame definition on the estimated station velocities. For that purpose, weekly regional solutions (covering the European region) and global solutions have been respectively stacked to obtain regional and global velocity fields. In both cases, the estimated long-term solutions (station positions and velocities) were tied to the ITRF2005 under minimal constraints using a selected set of reference stations. Several sets of global and regional reference stations were tested to evaluate first the impact of the reference frame definition on the global and regional velocity fields and later the impact on the derived geodynamic interpretations.

Results confirm that the regional velocity fields show systematic effects with respect to the global velocity field with differences reaching up to 1.3 mm/yr in the horizontal and 2.9 mm/yr in the vertical depending on the geographical extent of the network and the chosen set of regional reference stations.

Introduction

GNSS (Global Navigation Satellite Systems) is often used to produce 3D velocity fields aiming at geodynamic interpretations. Due to the expected small intra-plate deformations in most European regions, the accuracy of the estimated surface displacements must be at the sub mm/yr level in the horizontal and vertical components.

A c c e p t e d M a n u s c r i p t 3

The IGS (International GNSS Service) started its first reprocessing campaign in Feb.

2008 (Steinberger et al., 2008) and is presently reprocessing its global GNSS network data to deliver a set of consistent high quality GNSS products (e.g. orbits, clocks and earth rotation parameters) which will be used by regional GNSS densification networks during their reprocessing. Today, with the improving computing facilities and GNSS data analysis, it has become less demanding to perform a global analysis and regional networks may consider this approach. Within that context, we compared the regional approach to the global approach where global stations located on other continents were added to a regional GNSS network processing.

Historically, two major methods were used to express a GNSS position and velocity solution in a given realization of the ITRF (International Terrestrial Reference Frame): (1) by constraining the positions and the velocities of a selected ITRF subset of stations to ITRF values, (2) by aligning the solution to the ITRF using a 14-parameter Helmert similarity transformation under the minimal constraints approach for a selected set of stations. According to [START_REF] Altamimi | Discussion on How to Express a Regional GPS Solution in the ITRF[END_REF], the advantage of the first method is that the solution is well expressed in the ITRF frame, while its disadvantage is that the selected stations will have their coordinates entirely determined by the ITRF selected values. In comparison, the second method has the advantage of preserving the intrinsic characteristics of the solution and avoiding any internal distortion of the original network geometry. In this paper, we concentrate on the second method and study specifically the alignment of the solutions (regional or global) to the ITRF2005 (Altamimi et al., 2007a) using a 14-parameter similarity transformation under the minimal constraints approach.

In Legrand and Bruyninx (in press), global and regional solutions for station positions have already been compared and it was demonstrated that positions obtained through global solutions are less sensitive to the reference frame definition compared to regional solutions. [START_REF] Wöppelmann | Terrestrial reference frame implementation in global GPS analysis at TIGA ULR consortium[END_REF] investigated the influence of using different sets of reference stations to express a global solution in a given frame and concluded that the best results were obtained using a large global distribution of reference stations mitigating the individual problems at each of the reference stations.

In this study, we investigate the impact of the size of the GNSS network and the choice of the reference stations on the estimated velocities and the derived geodynamic interpretations. For that purpose, we elaborated several long-term solutions by varying the geographical extension of the network and the reference stations used in the alignment to the same reference frame.

Geodynamic interpretations are often based on GNSS velocities fields stemming from a regional network processing. However, to detect sub-mm/yr motion it is fundamental to pay attention to the GNSS data processing strategy and particularly the reference frame definition. To address that problem, we focused on the Western part of Europe where geodynamics require sub-mm/yr precision for both horizontal and vertical velocities. We used the velocity solutions from our global and regional

Data Set and Methodology

The computation of a velocity field from GNSS data consists of several steps.

Weekly Coordinate Solutions

In a first step, weekly positions of continuous observing GNSS stations are estimated. Ten years (1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006) of weekly GNSS solutions produced by ULR (Université de la Rochelle) as its contribution to TIGA (Tide Gauge Benchmark Monitoring Project of the IGS) have been used throughout this paper. The ULR solutions are in the SINEX format, and provide station coordinates together with their covariance information for 225 globally distributed continuous GNSS stations (Figure 1) from which 205 stations have more than 3.5 years of data. The same parameterization and observation modeling were used over the whole 10-year period, estimating station coordinates, satellite orbits, earth orientation parameters, and zenith tropospheric delay parameters every 2 hours. IGS absolute phase centre corrections for both the tracking and transmitting antennas were applied (see [START_REF] Wöppelmann | Rates of sea-level change over the past century in a geocentric reference frame[END_REF] for further details on the GNSS reprocessing). Each weekly solution was aligned to the ITRF2005 using minimum constraints with seven transformation parameters (translations, rotations and scale) with the CATREF software package (Altamimi et al., 2007b). To study the differences between global and regional solutions, regional weekly solutions have been created from the ULR global weekly solutions by extracting 60 GNSS stations located in Europe, all included in the EUREF Permanent Network (EPN) [START_REF] Bruyninx | The EUREF Permanent Network; a multidisciplinary network serving surveyors as well as scientists[END_REF].

Cumulative Position and Velocity Solution

In a second step, the weekly positions (and their covariance information) were combined to estimate site positions and velocities expressed in a chosen reference frame. Global and regional velocity fields were obtained by stacking both sets of weekly solutions. The stacking was performed with CATREF and tied to the ITRF2005 under minimal constraints using 14 transformations parameters (translations, rotations, scale and their rates) using a selection of ITRF2005 reference stations.

The quality of the alignment of the long-term solution on ITRF2005 depends on the selected set of reference stations; these stations should be of high quality. Their selection is based on the following criteria:

residuals of the similarity transformation between the solution and the ITRF2005: In this study, we distinguish two reference frame definition strategies: (1) a first case considering a set of global well distributed reference stations; (2) a second case with regional distributed reference stations.

Effect of Reference Frame Definition on Absolute Velocity Fields

To evaluate the impact of the reference stations on the global and regional velocity fields, several sets of reference stations were tested when expressing the cumulative solution in the ITRF2005.

Stability of the Networks

The impact of outliers (residuals of the similarity transformation between ITRF2005 and the solution exceeding the criteria presented above) in the reference stations and of reducing the number of reference stations (all of them responding to the above mentioned site selection criteria) was tested for the two networks. We observed that the velocities obtained by using different sets of the global reference stations differ below 0.2 mm/yr indicating that in general they behave in a stable way. However, the velocity fields obtained with the regional network were much more sensitive to the set of reference stations used (outliers and geometry) compared to the global network (see section 3.3). In the regional network, it was evidenced that the border stations are crucial for a proper datum definition, they could considerably impact the coordinates and velocities of the whole network. Moreover, the estimated coordinates and velocities of the border stations were extremely sensitive to the reference frame definition This means that in general, even if they are mandatory for the reference frame definition, the coordinates and velocities obtained for the border stations should be treated with care, or even not used at all in the geodynamic interpretation.

Regional and Global Sets of Reference Stations

Finally, for the global network, 83 geographically well-distributed IGS05 stations [START_REF] Ferland | IGSMAIL-5447: Proposed IGS05 Realization[END_REF], following the criteria defined in section 2.2, were selected as reference stations to express the solution used throughout this paper in ITRF2005 and obtain the V GLOB velocity field. The IGS05 consists of 132 IGS stations based on station performance, track record, monumentation, co-location and geographical distribution selected by the IGS Reference Frame Working Group for the IGS realization of the International Terrestrial Reference Frame. For the regional network, we selected two sets of reference stations (Figure 2), both following the criteria defined in section 2.2 and having a large probability of being used by users in Europe:

-Selection A: 23 reference stations consisting of all EPN ITRF2005 stations also part of the IGS05 -Selection B: 14 stations, subset of selection A with stations located only on the European continent The two associated regional velocity fields are V REGA (selection A) and V REGB (selection B).

FIGURE 2

A c c e p t e d M a n u s c r i p t 9

Comparison of the Velocity Fields

Figures 3 shows the comparison of the horizontal and vertical velocity fields derived from the global (V GLOB ) solution with the two regional solutions (V REGA and V REGB ) and shows that both regional velocity fields present systematic effects with respect to the global velocity field. As shown in Table 1, the velocity differences are significant with respect to the error ellipses and can reach up to 1.3 mm/yr in the horizontal and 2.9 mm/yr in the vertical components. In zones where the aim is to measure (sub)-mm/yr deformations, such an effect cannot be neglected.

FIGURE 3 TABLE 1

At the start of the computations, the stations in each weekly regional solution have the same coordinates as in the corresponding weekly global solution. Then, during the stacking, station coordinates and velocities are estimated together with a similarity transformation between each weekly solution and the reference datum. Especially in regional networks, these transformations will absorb common mode signals and will slightly change the estimated velocities (effect N 1 ). Finally, the stacked solution is tied to the ITRF2005 using minimal constraints applied upon different sets of reference stations. The minimal constraints method typically does not alter the network geometry. The choice of the reference stations used to express the long-term solution in ITRF2005 has an impact on the alignment and consequently also changes the estimated velocities (effect N 2 ). In general, these two effects (N 1 and N 2 ) are known as the network effect. The effect N 2 , which only 2. These transformation parameters have been estimated with all stations of the regional network; the correlations between the transformation parameters are the same for the two regional networks and are shown in Table 3. The translation rates are strongly correlated with the rotation rates (affecting only the horizontal velocities) and the scale (affecting only the vertical velocities). These transformation parameters explain more than 90% of the velocity differences. The systematic effects observed in the horizontal velocities (see Figure 3, left) are explained by the rotation rates and the translation rates. For the vertical component, the bias (Regional A) and the tilt (Regional B) observed in Figure 3 (right) are explained by the scale rate together with the translation rates. The residuals obtained after the similarity transformations are caused by the effect N 1 ; they are below 0.2 mm/yr in horizontal and 0.6 mm/yr in vertical (see Table 4) and are the same for the two regional networks. The effect N 1 is correlated with the size and the geometry of the whole network.

Summarized, the differences between the global and regional velocity fields are due to the combined effect of the size of the network and the selection of the reference stations and are called "network effect". The disagreement between the velocity fields is amplified when the reference stations cover a smaller geographical area (selection B). This effect is probably increased by the fact that in selection A, some reference stations belong to the American, the African or the Arabian plates; while for selection B, all the reference stations are located on the European plate. Adding reference stations from outside the European continent allows reducing the difference between the regional and global velocity fields.

Effect of the Reference Frame Definition on Geodynamic Interpretations

Impact on Euler Pole Rotation Estimation

Euler Pole rotations are usually used to model the mean rigid block rotation of a tectonic entity (e.g. tectonic plate, tectonic block). Consequently, Euler pole rotation is also used to estimate the residuals from the rigid block motion hypothesis in order to detect strain accumulation areas and/or intra-plate deformations. To quantify the impact of the reference frame definition on the Euler pole rotation estimation, the mean rigid block rotation has been estimated individually for the Western part of Europe from each of the three solutions.

In each case, the same 40 stations were used satisfying the following criteria:

continuously observed during at least 3 years; located on rigid parts of the European tectonic plate; post-fit velocity residual below 1.5 mm/yr, after the estimation of the rotation pole.

TABLE 5

The resulting rotation poles together with the Eurasian rotation pole published in ITRF2005 [Altamimi et al. 2007a] are given in Table 5. From this, it can be seen that the ITRF2005 rotation pole for Eurasia is closer to the rotation pole from Regional B than to the rotation poles from Regional A or Global. Indeed, the reference stations used to tie the Regional B solution to ITRF2005 are only located on the European plate and 12 of these 14 stations were used by [Altamimi et al. 2007a] to estimate the Eurasian rotation pole. As a consequence, due to the principle of the minimal constraints, the Regional B velocities of the European stations are closer to the ITRF2005 values than the two other solutions and finally the rotation pole from Regional B is closer to the rotation pole from [Altamimi et al. 2007a] than the others. Nevertheless, this does not remove the fact that regional solutions behave in an unstable way: any other choice of reference stations could lead to a different rotation pole for Europe. This is confirmed by Table 5 which shows that the three resulting rotation poles estimated from V REGA, V REGB and V GLOB differ significantly.

Consequently, the choice of the reference stations during the reference frame definition has a relevant impact on the estimated rotation pole.

Residuals from Rigid Block Motion Hypothesis in Western Europe

To test the impact of the network effect on the detection of non-rigid deformation, in each case, the modeled rigid block rotation was removed from the horizontal velocities to obtain the residual velocity fields. The order of magnitude of the residuals is the same for V REGA , V REGB and V GLOB . Nevertheless, we observe systematic effects when comparing them (see Figure 4). The RMS of the differences between V GLOB and V REGA is about 0.1 mm/yr and the differences reach up to 0.5 mm/yr. The RMS of the differences between V GLOB and V REGB is 0.2 mm/yr, but the maximal difference reaches 0.8 mm/yr. The velocity residuals of the two regional solutions are similar in the middle of the network, but the differences between the two sets of residuals are larger when getting closer to the edges of the regional networks.

The reference frame definition strategy therefore has a significant impact on the velocity estimation, and this has to be considered when sub-mm/year precision is required for a proper interpretation of the intraplate deformations.

FIGURE 4

Impact on GIA Model Estimation

In Northern Europe, the vertical motion is mainly due to the post-Glacial Isostatic Adjustment (GIA). According to previous studies the estimated vertical motion can reach 10 mm/yr in the Fennoscandian region [START_REF] Nocquet | Geodetic Constraints on Glacial Isostatic Adjustment in Europe[END_REF]. Additionally, the first order of the GIA effect on vertical velocities over Western Europe, is well A c c e p t e d M a n u s c r i p t 14 explained by a 4 th order polynomial function [START_REF] Milne | Space-Geodetic Constraints on Glacial Isostatic Adjustment in Fennoscandia[END_REF] with uplift in Northern Europe and transitions zones between uplift and subsidence below 56° of latitude. However, the transition between the GIA-induced uplift and subsidence zone is not well constrained due to the small velocities that have to be measured in the Western central part of Europe for regions below 56° of latitude.

The three vertical velocity fields (V GLOB , V REGA and V REGB ) have been used to construct velocity profiles along the European region subject to post-glacial rebound. The stations used for the vertical velocity profiles range from 45° to 71° of latitude and -5° to 35° of longitude.

We estimated the parameters of a 4 th order polynomial function from the vertical profiles of the global and two regional solutions to model the contribution of the GIA on the estimated velocities (Figure 5). As can be seen in Figure 5, the velocity of the station TRDS (Trondheim, Norway) is atypical. For that reason, the modeling was done with and without TRDS showing that TRDS influences dramatically the fit of the data and changes the 4 th order function parameters.

Table 6 demonstrates that the models from V REGA and V REGB exhibit a constant bias with respect to the modeling from the global solution V GLOB (up to 0.5 mm/yr). This is due to the impact of the reference frame definition on vertical velocities illustrated in Figures 3. The RMS of the difference between the model from V REGA (resp.

V REGB ) and the model from V GLOB can reach 0.3 mm/yr (resp. 0.5 mm/yr).

Consequently, when a velocity field is derived from a regional network, GNSS stations located far outside the studied region should also be integrated to minimize the effect of reference frame definition on the estimated site velocities. In agreement with the GIA models, subsidence is predicted (maximum subsidence of 0.2 mm/yr at 51.7° latitude) by the global solution, while the regional solutions do not show subsidence at all, but a minimum uplift of 0.3 mm/yr at that latitude.

Consequently, to detect mm and sub-mm/yr vertical velocities from GNSS data modeling, the regional approach is not appropriate. In our case, the transition between subsidence and uplift in northern Europe is important for example to investigate long-term sea level rise in the northern part of Belgium.

Conclusion

In order to express a GNSS solution in the ITRF, it is possible to constrain the positions and velocities of some sites to their ITRF values or to align the solution to the ITRF using a 14-parameter similarity transformation under minimal constraints.

In this study, we focused on the minimal constraints approach to express our GNSS solutions in ITRF2005 and we investigated the influence of the reference frame definition -in terms of reference station selection and network extension -on the estimated velocity field.

It was shown that based on identical sets of weekly positions as the basis, different velocity vectors (up to 1.3 mm/yr in the horizontal and 3 mm/yr in the vertical) can be estimated depending on geographical extent of the network (regional versus global). The obtained velocity differences are due to a network effect which depends A c c e p t e d M a n u s c r i p t 16 on the selection of the reference stations. The disagreement between the global and regional velocity fields is amplified when the reference stations cover a smaller geographical area. In the regional network, the border stations have the most unstable velocity estimates.

The Euler rotation poles estimated from the regional networks differ significantly from the rotation pole estimated from the global solution. After removing the rigid block rotation, the residual velocity fields show differences up to 0.9 mm/y. We also proved that, in contrary to the global solution and the GIA models, none of the regional solutions could predict subsidence around 52° latitude.

In conclusion, when expressing a GNSS solution in the ITRF2005 using minimal constraints, the network effect due to the size of the GNSS network and the choice of the reference stations has a significant influence on the estimated velocity field and consequently might cause wrong geodynamical interpretations. Consequently, when sub-mm/year precision is required for a proper interpretation of intraplate deformations or vertical velocities, a global approach should be considered. Table 1. Statistics of the differences between the global and regional velocity fields.

  the results of different commonly-used geodynamic modeling strategies, such as the estimation of Euler rotation poles, residuals from rigid block motion and vertical velocity profiles.

  FIGURE 1

o

  positions: below 7 and 15 mm in horizontal and vertical components, respectively o velocities: below 1.5 and 3 mm/yr in horizontal and vertical components, respectively station observation history: at least 3 years in the ITRF, as well as in the ULR time series

-

  optimal distribution of the reference stations over the network.

  estimates dependent on the chosen set of reference stations.

  choice of the reference stations, is fully explained by a similarity transformation whose parameters are shown in Table

-

  formal error of the estimated horizontal velocity (as result of the stacking) below 1.5 mm/y;

  FIGURE 5

FiguresFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig.2. Stations used for the reference frame alignment of regional solutions.

Fig. 3 .

 3 Fig. 3. Difference between global and regional velocity fields (mm/yr). Left:

Fig. 4 .

 4 Fig. 4. Differences between residuals from rigid block motion of the global solution

Fig. 5 .

 5 Fig. 5. Vertical profiles and best fit 4th order polynomial function for: a): global

  Figure1

Figure

  Figure 3 c bottom left

Figure

  Figure 3 c bottom right

TABLE 2 TABLE 3 TABLE 4 A

 234

	M a n u s c r i p t
	c c e p t e d
	11

Table 2 .

 2 Translation, scale and rotation rates between the global and regional velocity fields.

	Transformation
	parameters
	between
	VGLOB		-0.099	-0.162	0.004	0.057	-0.058	0.023	0.028
	and
	VREGA	±	0.025	0.033	0.024	0.034	0.010	0.009	0.008
	VGLOB		-0.153	-0.483	0.093	0.059	-0.169	0.046	0.061
	and
	VREGB	±	0.025	0.033	0.024	0.034	0.010	0.009	0.008

X T  (cm/yr) Y T  (cm/yr) Z T  (cm/yr) S  (10 -9 /yr) X R  (mas/yr) Y R  (mas/yr) Z R  (mas/yr)

Horizontal (

mm/yr) Vertical (mm/yr)

	Table
		-0.216	0.018
	VREGA -VGLO VREGB -VGLO	Mean ±RMS S  -0.511 -0.034 -0.682 Max Mean of 1σ Error Ellipses 0.3 ± 0.4 0.9 0.03 X -0.092 0.884 -0.008 0.000 R  -0.826 0.080 0.685 0.000 R  0.6 ± 0.7 1.3 0.03 Y R  0.088 -0.740 -0.002 0.000 -0.388 -0.041 Mean ±RMS 0.3 ± 0.5 0.086 0.1 ± 1.0	Max 1.2 2.9	Mean of 1σ Error Ellipses 0.04 0.04
		Z
			M a n u s c r i p t
	A c c e p t e d
					2

X T  Y T  Z T  S  X R  Y R  Y T  -0.088 Z T 

Table 3 .

 3 Correlations between the translation, scale and rotation rates estimated in

Table 2 .

 2 The correlations larger than 0.5 are shown in grey.

Table 4 .

 4 Statistics of the velocity residuals after the estimation of the translation, scale and rotation rates shown in Table2.

	Pole estimation strategy	Longitude (°)	Latitude(°)	W (°/Ma)
	Global solution	-102.02 +/-0.82	53.02 +/-0.56	0.252 +/-0.002
	Regional solution A	-100.51 +/-0.91	53.35 +/-0.59	0.251 +/-0.002
	Regional solution B	-97.77 +/-1.00	55.15 +/-0.58	0.256 +/-0.002
	ITRF2005 [Altamimi et al. 2007a]	-95.98 +/-0.97	56.33 +/-0.55	0.261 +/-0.003

Table 5 .

 5 The rotation poles estimated from V REGA , V REGB and V GLOB solutions and comparison with the Eurasian rotation pole from ITRF2005 published in[Altamimi et al. 2007a].

		Horizontal (mm/yr)	Vertical (mm/yr)
		Mean ±RMS	Max	Mean ±RMS	Max
	VREGA -VGLO	0.0 ± 0.06	0.2	0.0 ± 0.14	0.6
	VREGB -VGLO	0.0 ± 0.06	0.2	0.0 ± 0.14	0.6

Table 6 .

 6 Mean biases and RMS between modeled functions from V REGA or V REGB solutions and global solution

		With	Without	With	Without
		TRDS	TRDS	TRDS	TRDS
	Mean bias	0.3	0.2	0.5	0.5
	RMS	0.3	0.3	0.4	0.4

VREGA -VGLO ( mm/yr)

VREGB -VGLO (mm/yr)

Acknowledgements

The research of J. Legrand was supported by the grant MO/33/019 of the Belgian Science Policy.


Janis Vanacker
email: janis.vanacker@ugent.betel

"Why do you break me?" Talking to a human tree in Dante's Inferno

The author of this essay focuses on Canto 13 of the Inferno which describes the encounter between Dante and Pier delle Vigne, the suicide who has been changed into a tree. To this day critics do not agree on the classical source which has been a model for this episode. Several Ovidian tales (the tales of Daphne, the Heliads, Dryope and Erysichthon which occur in the Metamorphoses) and one passage in the Aeneid (the Polidorus episode narrated in book 3) have been considered a source of inspiration. The question can be resolved by a more profound and more systematic examination of both Canto 13 and its possible sources. Some of the most important issues studied are: the relationship between the changing character and the character that does not change; the conduct of the person transformed into a tree and the meaning of metamorphosis in the story. The author concludes that, although there are many structural resemblances between Canto 13 and the Polydorus episode, Dante clearly took a few essential elements from Ovidian myths.

Introduction

This essay examines Canto 13 of the Inferno which narrates the encounter between Dantepilgrim, his guide Virgil, and Pier delle Vigne, the damned soul who has been transformed into a thorn-bush. As many scholars have already pointed out, this episode is clearly inspired by classical authors: whereas the metamorphosis of a human body recalls Ovidian transformations, other details in the encounter can be related to the Aeneid. Despite the obvious intertextual links with Ovid and Virgil, one can notice a lack of precision and consensus in the identification of the tales rewritten by Dante. Therefore we want to find out whether or not there is a particular tale or myth which had a decisive influence on the depiction of Dante"s selva dei suicidi.

Entering the second ring of the seventh circle

Before we concentrate on the Latin sources behind the thorn-bush episode, it may be useful to consider the passage itself. At the beginning of Canto 13 Dante and Virgil enter the second ring of the seventh circle after having crossed Phlegethon, the river of blood, with the help of the centaur Nessus. The first aspect that catches our attention is the landscape which contrasts sharply with the location depicted in Canto 12: compared to the first ring where the setting was dominated by boiling blood (cf. Inf. 12, 101; "la proda del bollor vermiglio" 1 ), this place is totally different since all references to bloody fluids (Inf. 12, "sangue", "riviera", "Tamisi", "bulicame") have disappeared. The new landscape is described as an uncivilized and darkish wood whose venomous vegetation causes death instead of engendering new life (Ubaldini 2005, pp. 134-135):

(…) un bosco che da neun sentiero era segnato. Non fronda verde, ma di color fosco; non rami schietti, ma nodosi e "nvolti; non pomi v"eran, ma stecchi con tòsco. non han sí aspri sterpi né sí folti quelle fiere selvagge che "n odio hanno tra Cecina e Corneto i luoghi cólti. (Inf. 13, 2-9) (…) a forest not marked by any path. No green leaves, but those of dusky hue-not a straight branch, but knotted and contorted -no fruit of any kind, but poisonous thorns. No rougher, denser thickets make a refuge for the wild beasts that hate tilled lands between the Cècina and Corneto.

Note that, by using the anaphoras "non/ ma" in lines 4-6, the author suggests two landscapes at the same time: he calls to mind a classical locus amoenus ("fronda verde"; "rami schietti"; "pomi") and its perfect reversal ("perfetto rovesciamento", Ubaldini, 2005, p. 134). The contrast between the two scenes could not be more evident: the juxtaposition emphasizes the rough and gruesome character of the forest that Dante and his guide are about to enter.

This wood is the place where the hideous Harpies live: these hybrid creatures have the body of a bird of prey and the face of a woman. The howling of these strange monsters is the first of the bizarre sounds that Dante can hear in this locus horridus 2 . At this point Virgil expresses a warning that prepares both his companion and the reader to a confrontation with the unusual: "(…) sí vederai/ cose che torrien fede al mio sermone" (Inf. 13,(20)(21) 3 . All of a sudden the pilgrim perceives plaintive cries coming from all sides, but he is unable to see the human beings expressing these lamentations. Encouraged by his guide, Dante picks a branch from one of the thorn-bushes ("un gran pruno", Inf. 13, 32). The bloodstained trunkthe allusion to the blood reminds of canto 12 -reacts immediately and shouts: "Perché mi schiante?" (Inf. 13, 33) 4 . This human behavior is repeated in the next verses when the stem repeats his question (Inf. 13, 35: "ricominciò a dir: "Perché mi scerpi?") 5 . Dante, who is frightened by this unexpected reaction, drops the twig and remains silent, whereas Virgil 1 "the vermilion boil", see also Inf. 12, 47-48: "la riviera del sangue in la qual bolle/ qual che per vïolenza in altrui noccia" ("the river of blood that scalds/ those who by violence do injury to others"); Inf. 12, 117: "quel bulicame" ("that boiling stream"). 2 Inf. 13, 13-15: "Ali hanno late, e colli e visi umani,/ piè con artigli, e pennuto "l gran ventre;/ fanno lamenti in su li alberi strani". ("They have broad wings, human necks and faces,/ taloned feet, and feathers on their bulging bellies./ Their wailing fills the eerie trees".) 3 "you will see such things/ as are not easily believed from speech alone". 4 "why do you break me?" 5 Inf. 13, 35: "ricominciò a dir: "Perché mi scerpi?" ("it cried again: 'Why do you tear me?") explains to the tree why he made his companion injure his branches 6 . The pagan poet invites the shrub to reveal his identity, so that his companion can make up for his act of violence by restoring the reputation of the person that seems to be inside the plant (Inf. 13,(52)(53)(54). The speaking thorn-bush appears to be the soul of Pier delle Vigne, chancellor and minister of Frederick II, who killed himself after having been accused of treachery. In the following verses the suicide tells about his death, his entrance in Hell and the way he was transformed into a thorn-bush. All of a sudden the conversation between Virgil, Dante and Pier is interrupted by a new sound: they hear the barking of the black hounds ("nere cagne", Inf. 13, 125) that chase the wastrels, the sinners who, during their lives, have intentionally thrown away their possessions 7 . Canto 13 ends with the account of an anonymous Florentine suicide who asks the two visitors to gather the leaves of "his tree" which have been torn during the chase.

The conversation with Pier delle Vigne, as mentioned in the introduction, is without doubt a reminiscence of classical texts. What strikes us, when examining critical contributions on this issue, is the lack of agreement in the identification of -what Genette would have calledthese hypotexts 8 . Let us consider some recent articles on the matter. According to Peterson, the Pier delle Vigne episode recalls "two Ovidian episodes of human metamorphosis into a tree: that of Daphne changed into a laurel and that of Phaeton"s daughters turned into poplar trees" (Peterson 2007, p. 206). He adds: "The text is marked in this way, such that one can only think of Ovid". Racci"s opinion is similar to that of Peterson: although she does not mention Ovid"s Daphne myth, she stresses the connection between canto 13 and the story of Phaeton (Racci 1994, p. 217-218). Guthmüller agrees with Peterson and Racci in recognizing the decisive impact of Ovid"s Metamorphoses, but he indicates another tale, that of Dryope, (Met. IX), as the main source of inspiration for Dante"s selva dei suicidi (Guthmüller 2000, p. 22). In his text Guthmüller also refers to the story of the Heliads (Met. IV) and that of Erysicthon (Met. VIII). Heuzé, on the other hand, considers the intertextual link between Canto 13 and the Metamorphoses as rather superficial (Heuzé 2009, p. 40). For him the most important source is the episode in the Aeneid (III, where Aeneas damages the grave of Polydorus, son of Priam, who had been murdered by Polymnestor, king of Thracia. Confalonieri, author of an essay dedicated to the theme of the "uomo-pianta" in Italian literature, also connects Canto 13 to the third book of the Aeneid. He links one particular passagewhere the suicide talks about his changed body (Inf. 13, 73-75)to the Ovidian account of Dryope 9 .

Unfortunately none of these critics care to verify the correctness of their statements by simply consulting the classical sources. For this reason we shall now take a closer look at these texts. We do not merely want to verify which classical text(s) Dante chose to rewrite, we also intend to find out what exactly caused confusion among scholars.

Daphne or the Heliades, Dryope or Polydorus?

6 Inf. 13, 50-51: "ma la cosa incredibile mi fece/ indurlo ad ovra ch"a me stesso pesa". ("But your plight, being incredible, made me/ goad him to this deed that weighs on me".) 7 As for the episode of the "scialacquatori" (and its relationship to the myth of Actaeon), cf. Vanacker 2009, pp. 107-113. 8 Cf. Genette 1982 9 Confalonieri 2008, p. 452: "Piero giura di fatto sul proprio corpo, naturalmente cogliendolo nella sua dimensione vegetale; qualcosa di simile accade nelle Metamorfosi di Ovido, nell"episodio di Driope (...). È un passaggio in cui l"influenza di Ovidio sull"elaborazione dantesca del motivo dell"uomo-pianta (...) sembra avvertirsi distintamente".

The first tale is the well-know myth of Apollo and Daphne narrated in the first book of the Metamorphoses (Met. 1,. Daphne was a beautiful chaste nymph who devoted herself to the goddess Diana and who refused to answer the love of Phoebus. She asked her father Peneus for help while being pursued by the god and only just before he could seize her, the nymph was transformed into a laurel 10 . When the metamorphosis was complete, Apollo unsuccessfully tried to kiss the trunk of the tree:

Hanc quoque Phoebus amat positaque in stipite dextra sentit adhuc trepidare novo sub cortice pectus conplexusque suis ramos ut membra lacertis oscula dat ligno; refugit tamen oscula lignum. (Met. 1,(553)(554)(555)(556) But even now in this new form Apollo loved her; and placing his hand upon the trunk, he felt the heart still fluttering beneath the bark. He embraced the branches as if human limbs, and pressed his lips upon the wood. But even the wood shrank from his kisses.

As he was unable to love the nymph, the god decided to make the laurel "his" tree ("Since thou canst not be my bride, thou shalt at least be my tree. My hair, my lyre, my quiver shall always be entwined with thee, O laurel" 11 ). In describing the reaction of the plant, the narrator suggests an almost human conduct: "The laurel waved her new-made branches, and seemed to move hear head-like top in full consent" 12 . In the Metamorphoses this tale is the first of four stories (Io,Met. 1,Syrinx,Met.1,Callisto,Met. 2, where the love of a god for a reluctant young girl is presented as a hunt 13 . Considering the importance of the selva in Canto 13 we should add that the pursuit of these virgins takes place in a wood. The Ovidian wood seems a peaceful and idyllic place, but in reality it harbours dangerous, violent forces 14 . In the case of Daphne it is the transformation into a tree which helps to escape from Apollo"s sexual aggression. Metamorphosis, in her case, means salvation: it is a way to avoid the choice between life and death. By becoming a laurel, in other words, Daphne only puts an end to her life as a human being. For this reason her transformation is not represented as a negative experience. Rather, by turning the laurel into an eternal "symbol of military and artistic triumph" 15 , Apollo seems to consider metamorphosis as a reward.

Let us pass on to the Heliads, Phaeton"s sistersand not his daughters as Peterson wrongly believes -who have very often been seen as a model for Dante"s suicides. In the second book of the Metamorphoses, Ovid describes their grief at the death of their brother who had been killed by Jupiter"s lightning bolt while driving Phoebus" chariot. The girls" sadness was endless and after they had spent four months mourning near Phaeton"s grave, each one of 10 Met. 1, 548-556: "vix prece finita torpor gravis occupat artus,/ mollia cinguntur tenui praecordia libro,/ in frondem crines, in ramos bracchia crescunt,/ pes modo tam velox pigris radicibus haeret,/ ora cacumen habet: remanet nitor unus in illa". (Scarce had she thus prayed when a down-dragging numbness seized her limbs, and her soft sides were begirt with thin bark. Her hair was changed to leaves, her arms to branches. Her feet, but now so swift, grew fast in sluggish roots, and her head was now but a tree"s top. Her gleaming beauty alone remained). 11 Met. 1, 557-559: "(...) at, quoniam coniunx mea non potes esse,/ arbor eris certe" dixit "mea! semper habebunt/ te coma, te ciharae, te nostrae, laure, pharetrae". 12 Met. 1, 566-567: "(…) factis modo laurea ramis/ adnuit utque caput visa est agitasse cacumen". 13 On this subject see Vanacker 2009, pp. 46-51; Fabre-Serris 1995, pp. 276-289; Heath 1992, pp. 53-99. 14 Cf. [START_REF] Segal | Landscape in Ovid's Metamorphoses. A study in the transformations of a literary symbol[END_REF]Newlands 2004, 137: "These landscapes are beautiful but also dangerous. They inevitably fail to protect the innocent the innocent outsiders who come to them seeking shelter and comfort. They always have a deceptive elements, making them collusive with the violence that takes place there and with their gods. Their victims, (…), find their trust in the protection of the landscape misplaced as they are pursued, raped, or transformed by gods". 15 Brown 2005, p. 45. them was transformed into a poplar tree 16 . In the final stage of metamorphosiswhich corresponds to a hybrid condition between plant and human beingthe sisters were still capable of speaking. They called upon their mother who desperately tried to put a stop to the transformation. Despite her efforts Clymene seriously wounded her daughters instead of saving them. The girls, turned into talking trees, begged their mother to stop because their changing bodies could still feel pain:

(…) truncis avellere corpora temptat et teneros manibus ramos abrumpit, at inde sanguineae manant tamquam de vulnere guttae. "parce, precor, mater," quaecumque est saucia, clamat, "parce, precor: nostrum laceratur in arbore corpus iamque vale"cortex in verba novissima venit. (Met. 2,(358)(359)(360)(361)(362)(363) she tries to tear away the bark from their bodies and breaks off slender twigs with her hands. But as she does this bloody drops trickle forth as from a wound. And each one, as she is wounded, cries out: "Oh, spare me, mother; spare, I beg you. "Tis my body that you are tearing in the tree. And now farewell"the bark closed.

In this episode metamorphosis is clearly the consequence of emotional sufferance. The reader does not have the impression that becoming a tree is a way to survive, as in the case of Daphne. Rather he has the feeling that the girls, as human beings, gradually disappear because of excessive grief. In this story the loss of the human body is a way to express some kind of alienation caused by the loss of a loved one.

Compared to the previous episode, one can also establish a difference in the relationship between the character that does not change (Phoebus/ Clymene) and the character that undergoes transmutation (Daphne/ the Heliads). The first myth is a story of impossible lovea god falls in love with a reluctant nymphwhereas the second episode is about a mother trying to rescue her daughters. In the first tale metamorphosis is wanted by the transforming person: Daphne explicitly asks her father to change her human body so as to save her from being raped. The character that does not change, Apollo, is the cause of the transformation of the other person. In the second episode, the transformation into a tree is not asked by the sisters. The character that does not change, their mother, is also not the reason why they experience metamorphosis. Clymene, in contrast, is the person who tries to stop this irreversible process.

The next tale which critics consider a source of inspiration for canto 13 can be found in book 9 of the Metamorphoses where Iole narrates the story of her half-sister, Dryope (Met. 9, 324-393). One day this Oechalian girl took her infant son Amphissos on her arm and went out to gather some garlands for the nymphs. She was standing near a lake when she saw a blooming lotus tree. She picked some of its blossoms in order to give them to her son as toys. Iole, who was with her sister, saw how the flowers began to bleed: 16 Met. 2, 346-355: "(…) e quis Phaethusa, sororum/ maxima, cum vellet terra procumbere, questa est/ deriguisse pedes; ad quam conata venire/ candida Lampetie subita radice retenta est;/ tertia, cum crinem manibus laniare pararet,/ avellit frondes; haec stipite crura teneri,/ illa dolet fieri longos sua bracchia ramos,/ dumque ea mirantur, conplectitur inguina cortex/ perque gradus uterum pectusque umerosque manusque/ ambit, et exstabant tantum ora vocantia matrem". ("Then one day the eldest, Phaëthusa, when she would trow herself upon the grave, complained that her feet had grown cold and stark; and when the fair Lampetja tried to come to her, she was held fast as by sudden roots. A third, making to tear her hair, found her hands plucking at foliage. One complained that her ankles were encased in wood, another that her arms were changing to long branches. And while they look on those things in amazement bark closes round their loins, and, by degrees, their waists, breasts, shoulders, hands; and all that was free were their lips calling upon their mother"). carpserat hinc Dryope, quos oblectamina nato porrigeret, flores, et idem factura videbarnamque aderamvidi guttas e flore cruentas decidere et tremulo ramos horrore moveri. (Met. 9, To please her little son the mother plucked some these blossoms, and I was in the act to do the same (for I was with her), when I saw drops of blood falling from the flowers and the branches shivering with horror.

Dryope had wounded Lotis, a nymph who was hiding in the tree after having been pursued by Priapus. Though she had not been aware of injuring a transformed nymph, Dryope was punished at once and changed into a lotus tree 17 . Her fate reminds of the Heliads episode for two reasons. The first parallel is the fact that her loved ones desperately tried to rescue her (Met. 9, 359-366). For a moment Dryope "had only her face remaining, while all the rest was tree" 18 . Similar to the Phaeton"s sisters, she had one last chance to speak. The girl did not beg her relatives to stop wounding her new body. Instead she stresses her innocence ("I have not merited this dreadful thing" 19 ) and asks her family to let her child play beside her tree:

(…) nostraque sub arbore saepe lac facitote bibat, nostraque sub arbore ludat. cumque loqui poterit, matrem facitote salutet, et tristis dicat "latet hoc in stipite mater." stagna tamen timeat, nec carpat ab arbore flores, et frutices omnes corpus putet esse dearum. care vale coniunx, et tu, germana, paterque!" (Met. 9, 376-382) Beneath my tree let him often come and take his milk; beneath my tree let him play. And when he learns to talk, have him greet his mother and sadly say: "Here in this tree-trunk is my mother hid." Still let him fear the pool, pluck no blossoms from the trees, and think all flowers are goddesses in disguise! Farewell, dear husband, and you, sister, and my father! A laurel, poplar trees and a lotus tree… The next tree which, according to Ovid, is also the new body of a human being is an oak. In book 8 one can read the tale of Erysichthon (Met. 8, 738-878) who insulted Ceres by destroying a sacred wood. Inside this wood there was a "mighty oak with strength matured by centuries of growth, itself a grove" 20 . Erysichthon commanded his servants to cut it down, but when he noticed their hesitationthey all knew the oak was sacred to Cereshe took an axe and felled the tree himself. At this point the bleeding tree began to speak and declared that the man would be punished for his blasphemous act. 17 Met. 9, 349-355: "(…) quae cum perterrita retro/ ire et adoratis vellet discedere nymphis,/ haeserunt radice pedes. convellere pugnat,/ nec quicquam, nisi summa movet. subcrescit ab imo,/ totaque paulatim lentus premit inguina cortex./ ut vidit, conata manu laniare capillos,/ fronde manum implevit: frondes caput omne tenebant". ("And when she started back in terror and, with prayers to the nymphs, strove to leave the place, her feet clung, root-like, to the ground; she struggled to tear herself away, but nothing moved except the upper part of her body; the slow-creeping bark climbed upward from her feet and covered all her loins. When she saw this, she strove to tear her hair with her hands, but only filled her hands with leaves; for leaves now covered all her head". 18 Met. 9, 367: "nil nisi iam faciem, quod non foret arbor, habebat". 19 Met. 9, 372: "non meruisse nefas". 20 Met. 8, 743-744: "(…) ingens annoso robore quercus,/ una nemus (...)".

(…) et obliquos dum telum librat in ictus, contremuit gemitumque dedit Deoia quercus, et pariter frondes, pariter pallescere glandes coepere ac longi pallorem ducere rami. cuius ut in trunco fecit manus inpia vulnus, haud aliter fluxit discusso cortice sanguis, quam solet, ante aras ingens ubi victima taurus concidit, abrupta cruor e cervice profundi. (...) repetitaque robora caedit, redditus et medio sonus est de robore talis: "nympha sub hoc ego sum Cereri gratissima ligno, quae tibi factorum poenas instare tuorum vaticinor moriens, nostril solacia leti". (Met. 8,(757)(758)(759)(760)(761)(762)(763)(764)(765)(766)(767)(768)(769)(770)(771)(772)(773) and while he poised his axe for the slanting stroke, the oak of Deo trembled and gave forth a groan ; at the same time its leaves and its acorns grew pale, its long branches took on a pallid hue. But when that impious stroke cut into the trunk, blood came streaming forth from the severed bark, even as when a huge sacrificial bull has fallen at the altar, and from his smitten neck the blood pours forth. (…) Then, as he struck the oak blow after blow, from within the tree a voice was heard: "I, a nymph most dear to Ceres, dwell within this wood, and I prophesy with my dying breath, and find my death"s solace in it, that punishment is at hand for what you do".

The severe punishment announced by the oak reflected Erysichthon"s extreme act of aggression. The insulted goddess, Ceres, asked Famine for help and affected the man with an insatiable hunger. His constant craving for food and water made him sell his daughter and consume his worldly possessions. At the end Erysichthon even "began to tear his own flesh with his greedy teeth and, by consuming his own body, fed himself"21 .

There is an interesting connection between this case and the previous story: Erysichthon, like Iole"s half-sister, is punished for wounding a nymph hiding in a tree. Unlike Dryope, though, he intentionally chopped down the sacred oak. In this story, the person who is punished and transformed into a tree is guilty.

For the last episode, we must look at the beginning of the third book of the Aeneid where Aeneas describes how an unusual event convinced him not to found a city in Trace. After he and his family went ashore in this part of Greece, the hero decided to offer a sacrifice to the gods. On the top of a small hill he saw cornel bushes and myrtles: as he plucked some branches of a tree, he saw black blood coming out of it ("For from the first tree which is torn from the ground with broken roots trickle drops of black blood and stain the earth with gore" 22 ). Although this strange phenomenon scared him, Aeneas repeated his act when, suddenly, he heard a voice coming out of the earth: tertia sed postquam maiore hastilia nisu adgreditor genibusque adversae obluctor harenae (eloquar, an sileam?), gemitus lacrimabilis imo auditor tumulo, et vox reddita fertur ad auris: "quid miserum, Aenea, laceras? iam parce sepulto, parce pias scelerare manus. non me tibi Troia externum tulit, aut cruor hic de stipite manat. heu! fuge crudelis terras, fuge litus avarum. nam Polydorus ego. hic confixum ferrea texit telorum seges et iaculis increvit acutis". (Aen. 3,(37)(38)(39)(40)(41)(42)(43)(44)(45)(46) But when with greater effort I assail the third shafts, and with my knees wrestle against the resisting sands -should I speak or be silent?a piteous groan is heard from the depth of the mound, and an answering voice comes to my ears. "Woe is me! why, Aeneas, do you tear me? Spare me in the tomb at last; spare the pollution of your pure hands! I, born of Troy, am no stranger to you; not from a lifeless stock oozes this blood. Ah! Flee the cruel land, flee the greedy shore! For I am Polydorus. Here an iron harvest of spears covered my pierced body and grew up into sharp javelins".

The voice appeared to be that of Polydorus, the son of Priam"s, who had been murdered by Polymnestor. The king of Trace, who was supposed to raise Polydorus, killed him in an attempt to steal the treasure of Troy. Several elements in this episode recall Dante"s encounter with Pier delle Vigne. Every reader will already have noticed that Polydorus" exclamation ("Quid miserum, Aenea, laceras?", Aen. III, v. 41) is almost identical to the words shouted by Pier. In the next section we will find out if there are more of these parallels by confronting Canto 13 with the Aeneid and the Ovidian myths discussed above.

"We once were men and now are turned to thorns"

The first reason why the connection between Dante"s selva dei suicidi and the third book of the Aeneid may seem quite obvious is the fact that, in Canto 13, Virgil refers to his own text when he explains to Pier why he let Dante injure his tree: "S" elli avesse potuto creder prima", rispuose "l savio mio, "anima lesa, ciò c"ha veduto pur con la mia rima, non averebbe in te la man distesa; ma la cosa incredibile mi fece indurlo ad ovra ch"a me stesso pesa (...)". (Inf. 13,(46)(47)(48)(49)(50)(51) "Could he have believed it otherwise, O wounded soul," my sage spoke up, "what he had seen only in my verses, he would not have raised his hand against you. But your plight, being incredible, made me goad him to this deed that weighs on me (…)".

If we want to find a parallel between Aeneas" adventure in Trace and Dante"s encounter with the human thorn-bushes, we must first examine the relationship between the character who wounds a tree and the person who is wounded. Similar to Virgil"s hero Dante explores an unfamiliar region where, as a visitor, he has a conversation with a person he has only just injured. This relationship cannot be found in the Ovidian myths: considering the stories of Daphne, the Heliads, Dryope or Erysichthon, one immediately understands that none of these tales are about travellers meeting somebody in a new land.

Wherein lays the difference between Dante-pilgrim and Aeneas? Both characters hurt a tree which loses dark blood (cf. Inf. 13, 34: "sangue bruno"; Aen. III, 28: "atro […] sanguine"), but the latter, in fact, wounds vegetation growing on top of a grave. Dante, similar to Dryope or Erysichthon, injures a person that has become a tree. If we want to be precise, we have to mention that Aeneas plucks twigs from several trees standing on the hill 23 , whereas Dante plucks a branch from only one tree 24 . In this sense the pilgrim"s act reminds more of Dryope or Erysichthon, who both damage one plant. An attentive reader will also have noticed that Aeneas hears a voice coming out of the grave 25 , whereas Dante hears a voice coming out the thorn-bush 26 . So the idea of a person being locked up inside a tree must have been taken from the Metamorphoses. This equivalence becomes clear when we compare the following three citations. The first passage is one of the questions Virgil addresses to Pier.

Perciò ricominciò: "se l"om ti faccia liberamente ciò che "l tuo dir priega, spirito incarcerato, ancor ti piaccia di dirne come l'anima si lega in questi nocchi (...)" 27 . (Inf. 13, 85-89) Thus he began again: "So that this man may, with ready will, do as your words entreat, may it please you, imprisoned spirit, to tell us further how the souls are bound inside such gnarled wood (…)".

The next two citations have been taken from Ovid"s account of Dryope (Met. 9) and Erysichthon (Met. 8): scilicet, ut referent tardi nunc denique agrestes, Lotis in hanc nymphe, fugiens obscena Priapi, contulerat versos, servato nomine, vultus. (Met. 9,(346)(347)(348) For, so you must know, as the slow rustics still relate, Lotis, a nymph, while fleeing from Priapus" vile pursuit, had taken refuge in this shape, changed as to features but keeping still her name. 23 Cf. Aen. III, 27-40: "nam quae prima solo ruptis radicibus arbos/ vellitur, huic atro liquuntur sanguine guttae/ et terram tabo maculant (...). rursus et alterius lentum convellere vimen/ insequor et causas penitus temptare latentis (...) tertia sed postquam maiore hastilia nisu/ adgredior genibusque adversae obluctor harenae/ (...) gemitus lacrimabilis imo/ auditur tumulo (...)". ("For from the first tree which is torn from the ground with broken roots trickle drops of black blood and stain the earth with gore. (…) Once more, from a second also I go on to pluck a tough shoot and probe deep the hidden cause (…). But when with greater effort I assail the third shafts, and with my knees wrestle against the resisting sands (…) a piteous groan is heard from the depth of the mound (…)" 24 24 Cf. Inf. 13, 32: "e colsi un ramicel da un gran pruno". ("and plucked a twig from a tall thorn-bush") 25 Cf. Aen. III, 39-40: "(…) gemitus lacrimabilis imo/ auditur tumulo (…)". ("a piteous groan is heard from the depth of the mound"). 26 Cf. Inf. 13, 33: "e "l tronco suo gridò (…)". ("and its stem cried out"). 27 emphasis mine.

Nympha sub hoc ego sum Cereri gratissima ligno (Met. 8, v. 771) I, a nymph most dear to Ceres, dwell within this wood.

Wounding a tree is without doubt an essential element in Dante"s text. We have seen in the previous section that, apart from the Aeneid, the stories of the Heliads, Dryope and Erysichthon also develop the motif of the bleeding plant. This is not so in Ovid"s Daphne myth and this is one of the main reasons why the link with the wood of the suicides indicated by Peterson does not seem very convincing.

Other parallels between Canto 13 and the Aeneid can be drawn when one examines the reaction of the person who damages a tree (Aeneas/ Dante) and the behaviour of the person who is wounded (Polydorus/ Pier). Dante"s reaction to the tree"s exclamation is very similar to that of Aeneas: both men are very frightened by what they hear and they do not immediately understand what is happening:

(…) ond"io lasciai la cima cadere, e stetti come l"uom che teme (Inf. 13,(43)(44) (…) and I let drop the twig and stood like one afraid.

(…) mihi frigidus horror membra quatit, gelidusque coit formidine sanguis. (Aen. 3,(29)(30) A cold shudder shakes my limbs, and my chilled blood freezes with terror.

Obvious parallels can also be found in the reactions of Polydorus and Pier delle Vigne. In addition to the almost identical answer shouted at the person responsible for their injuries (cf. Aen. 3, 41: "quid miserum, Aenea, laceras? (…)"; Inf. 13, v. 33 "e "l tronco suo gridò: Perché mi schiante?"; v. 35: "ricominciò a dir: "Perché mi scerpi?"), one can notice that being wounded by a stranger is an opportunity to reveal their identities and to convey what has happened to them during their lives. We already know from the previous section that Polydorus had been murdered by Polymnestor28 . In Inferno 13 it is Virgil who interrogates the thorn-bush because Dante does not feel capable of asking questions. The pagan poet first asks the tree to reveal his identity and to tell his companion why his soul ended up in this horrendous place. Then he asks Pier to explain how the suicides had found their place in the wood and how they had been metamorphosed into trees. In this passage the visitor (Dante)and the readerreceives a lot of information about the life and death of the character that did not even seem human at the beginning of the text. In this way Canto 13 is very similar to the Polydorus episode in the Aeneid. One aspect, however, reminds more of an Ovidian myth. In his answer to the first question, Pier delle Vigne swears on his new body: Per le nove radici d"esto legno vi giuro che già mai non ruppi fede al mio segnor, che fu d"onor sí degno. (Inf. 13,(73)(74)(75) "By this tree"s new-sprung roots I give my oath: not once did I break faith with my true lord, a man so worthy of honor. (…)" As Confalonieri has correctly suggested, "qualcosa di simile accade nelle Metamorfosi di Ovidio, nell"episodio di Driope (...)". Like Pier, the girl attests her innocence by taking an oath in which she refers to "her tree": (...) si mentior, arida perdam quas habeo frondes, et caesa securibus urar. (Met. 3,(373)(374) If I say not the truth, parched with the drought may I lose my foliage and may I be cut down by the axe and burned.

It is likely that Ovid"s Dryope myth was not only a source of inspiration for the words spoken by Pier delle Vigne. The anonymous suicide Dante and his guide meet at the end of Canto 13 does not swear on his body, but the way he calls attention to his thorn-bush clearly evokes the oaths taken by Pier and Dryope.

Ed elli a noi: "O anime che giunte siete a veder lo strazio disonesto c"ha le mie fronde sí da me disgiunte, raccoglietele al piè del tresto cesto. (…)" (Inf. 13,(139)(140)(141)(142) And he to us: "O souls who have arrived to see the shameless carnage that has torn from me my leaves, gather them here at the foot of this wretched bush".

The connection between Dryope and Pier delle Vigne helps to understand why critics do not agree about which classical source has been a model for Canto 13. We can explain what may have caused confusion by referring to the character"s life stories and the role of responsibility in these stories. In a place like Hell the question of being guilty or innocent is an important issue. Seen from this perspective, the story of Pier delle Vigne is a strange case because he can be considered innocent and guilty at the same time. On the one hand, Pier declares that he had not committed treachery (cf. Inf. 13, 73-75) when he was alive. Though the reader does not know whether Pier says the truth or not, he realizes that the chancellor, who was blinded and sent to prison, must have suffered a lot. It is this element, the severe punishment of a person who might be innocent, which recalls the story of Dryope29 .

On the other hand, Pier cannot deny that, by committing suicide, he deliberately broke the laws of God. Although he hoped "to escape from scorn" ("fuggir disdegno", Inf. 13, 71) he must have been aware that, by killing himself, he committed a Christian sin. His act was intentional and this element links his case to that of Erysichthon, the man who deliberately damaged a sacred wood. Both Pier and Erysichthon destroyed something (the human body created by God, the oak sacred to Ceres) that was believed to be sacred by the society to which they belonged. Therefore, both men can be held responsible for the events that caused their death. Their conduct was self-destructive and it is interesting to see that this is mirrored in the way they have been punished. Erysichthon faded away because his never-ending desire for food made him eat his own body: vis tamen illa mali postquam consumpserat omnem materiam dederatque gravi nova paluba morbo, ipse suos artus lacero divellere morsu coepit et infelix minuendo corpus alebat. (Met. 8,(875)(876)(877)(878) At last, when the strength of the plague had consumed all these provisions, and but added to his fatal malady, the wretched man began to tear his own flesh with his greedy teeth and, by consuming his own body, fed himself.

As for Pier delle Vigne, God transformed his soul into a thorn-bush and, by doing so, he made the chancellor"s human body disappear.

Quando si parte l"anima feroce dal corpo ond"ella stessa s"è disvelta, Minòs la manda a la settima foce. Cade in la selva, e non l"è parte scelta; ma là dove fortuna la balestra, quivi germoglia come gran di spelta. (Inf. 13,(94)(95)(96)(97)(98)(99) When the ferocious soul deserts the body after it has wrenched up its own roots, Minos condemns it to the seventh gulch. It falls into the forest, in a spot not chosen, but flung by fortune, helter-skelter, it fastens like a seed.

We can conclude by saying that Dante did not rewrite just one classical text when he described the encounter with Pier delle Vigne. He took many structural features (the dialogue, the global story line) and details (dark blood) from the Polydorus episode in the third book of the Aeneid, but for some important elements in the depiction of the wood of the suicides (the human tree, the issue of responsibility) he found his inspiration in Ovidian myths.

We hope to have shown that the relationship between the Divine Comedy and its classical sources is a far more complex issue than one would think at first sight. In fact, by simply mentioning passages in the Aeneid or the Metamorphoses, one denies the fascinating subtlety that distinguishes Dante"s rewriting of classical texts.

Met. 8,[877][878]: "ipse suos artus lacero divellere morsu/ coepit et infelix minuendo corpus alebat".

Aen. 3,[27][28][29]: "nam quae prima solo ruptis radicibus arbos/ vellitur, huic atro liquuntur sanguine guttae/ et terram tabo maculant. (...)".

Aen. 3,[49][50][51][52][53][54][55][56][57]

Cf. Segal 1969, p. 38 : "The story of Dryope is perhaps the most arbitrary of the "innocent" metamorphoses. One can hardly expect Dryope to be held responsible for not knowing which flowers are only flowers and which conceal metamorphosized Nymphs".