Keeyoon Sung
email: ksung@jpl.nasa.gov

Edward H Wishnow

Brian J Drouin

Laurent Manceron

Marine Verseils

D Chris Benner

Conor A Nixon

The rotational spectrum of HD broadened by H2 at temperatures between 100 -296 K

Laboratory measurements of the R(0) -R(3) pure rotational transitions of hydrogen deuteride (HD) have been performed at low pressures (< 1 bar) and temperatures between 98 and 296 K. The measurements were conducted using a Fourier transform spectrometer coupled to the Soleil synchrotron far-infrared source to obtain pure HD and HD-H2 mixture spectra. The observed spectra have been fitted using a non-linear least-squares multispectral fitting program. For each transition the line position, intensity, pressure broadening, pressure-induced frequency shift, and the temperature dependencies of these quantities have been determined simultaneously. These spectroscopic line parameters are compared to previous measurements made at higher gas pressures. Notably the present, and previous, measurements of the self-and H2-broadened linewidths are smaller by a factor of five compared with those listed in the HITRAN and GEISA databases. This work is applicable to the low pressure, low temperature regimes found in the atmospheres of the giant gaseous planets.

Introduction

. Accurate determination of HD abundances from observations requires precise knowledge of spectroscopic line parameters, such as positions, intensities, and shape parameters (e.g., collisional broadening, frequency shift coefficients, collisional line narrowing), and their temperature dependences. For example, when HD R(0)-R(2) transition parameters from Feuchtgruber (2013) were used in modelling Cassini/CIRS data of Saturn, the D/H ratio was found to be about 30% lower than on Jupiter [Pie17]; a surprising result that contradicts predictions of a higher value on Saturn, and requires confirmation. The current HITRAN 2020 HD line intensities are calculated values based on a theoretical dipole moment function [Pac08] with uncertainty estimates of 10 -20 % [Gor22]. Collisional broadening coefficients are generally molecular specific [See Var90], and the HITRAN linewidths for HD broadened by H2 differ substantially (by about a factor of five) from published measurements [Ess84; Dra87a; Dra87b; McK84; McK86; Uli89; Lu93]. There is significant scatter among these measurements, and disagreement with theoretical calculations [SM92]. The HD measured, theoretical and HITRAN transition frequencies, however, all agree to within 0.0001 cm -1 [Pac10; Sch87].

Graphical Highlight:

Figure HD and HD-H2 measured and fitted spectra. The lower part of each panel shows observed (dots) and calculated (solid) spectra. The upper portion shows the fitted residuals (obs-calc). All observed spectra, for each transition, are fit simultaneously such that the residuals are comparable to the measurement noise level.

Early laboratory measurements were performed at high densities, up to 123 amagat, where collision-induced absorption and collisional interference effects become significant [Tre68; Nel82, Nel83; McK84; Uli89; Uli91; Wis92; Lu93]. Consequently, the measured HD dipole moment showed a variation with density, and these effects have been examined by Poll and co-workers particularly [Pol76; Tip78; Ma85; Pol85; also Tab85]. The permanent dipole moment, exclusive of interference effects, is however, independent of density, and in the vibrational ground state it is theoretically expected to vary only slightly with rotational state [START_REF] Pachucki | Electric dipole rovibrational transitions in the HD molecule[END_REF][START_REF] Józwiak | Positions and intensities of hyperfine components of all rovibrational dipole lines in the HD molecule[END_REF]. The present study is an effort to measure the HD spectrum using experimental conditions close to those of planetary atmospheres. Spectra have been obtained over the 50 -360 cm -1 range, at very high spectral resolution, and the data analyzed using a multispectrum fitting program to determine spectroscopic line parameters for the R(0) -R(3) transitions. A collisional (Dicke) narrowing effect was observed in laboratory spectra [START_REF] Essenwanger | Rotational spectrum of HD at low pressures[END_REF], so a non-Voigt line shape profile has been used in the fitting. 2 Experimental details 2.1 Interferometer and gas cells HD rotational transitions weakly absorb radiation, and measurements of low pressure samples require fairly long absorption paths. Furthermore, the Doppler width at low temperature in the farinfrared is very small, and pure HD measurements at low pressures require operating the spectrometer at its highest resolution. The use of the synchrotron radiation source permitted measurements of the R(0)-R(3) rotational transitions at high spectral resolution (~0.0006 cm -1 ), with good signal-to-noise, over a reasonable experimental time period. Measurements were conducted on the AILES beamline at the Synchrotron Soleil, France, during two sessions: 2018 Nov 10-17, and 2019 Sep 23-27. The far-infrared source was coupled to a Bruker 125HR Fourier transform spectrometer, and the radiation then passed through a Chernintype low-temperature multipass absorption cell to a bolometer detector, as described in Tchana et al [START_REF] Tchana | A new, low temperature long-pass cell for mid-infrared to terahertz spectroscopy and synchrotron radiation use[END_REF]. The entire beam path, exclusive of the absorption cell, was evacuated. The spectral resolution of the measurements was tailored to the density of the gas sample, and the highest resolution employed was 0.00056 cm -1 (0.5/L, where L is the maximum optical path difference, Bruker res. = 0.00102 cm -1 ). The temperature of the gas sample was determined from an average of selected platinum resistors placed at different locations inside the cell or attached to the inner cell wall surface. The cell was cooled with liquid N2, where the temperature was controlled by changing the pressure of a helium exchange gas in a chamber surrounding the cell, and by electrical heaters attached to the cell. Once a stable condition was established, the average temperature varied only by about ±1.5 K over a week. This spectrometer system was previously used in a study of NH3 with the same multipass cell at room temperature [START_REF] Yu | Submillimeter-wave and far-infrared spectroscopy of high-J transitions of the ground and v2=1 states of ammonia[END_REF][START_REF] Sung | Far-infrared 14 NH3 line positions and intensities measured with a FT-IR and AILES beamline, Synchrotron SOLEIL[END_REF]. Measurements were made using three different absorption pathlengths chosen to achieve measurable peak absorptions and to avoid saturation.

A second straight-through cell, 5.1 cm long, was used for pure HD measurements at higher pressures. The short cell was also completely enclosed by the vacuum system. This cell was used at cold and room temperatures, and it was cooled by flowing cold N2 gas through coils attached to its exterior. The experimental conditions are listed in Table 1 below. Platinum resistance thermometers, various cell locations Frequency calibration standards H2O in the 200 cm -1 region b a 1 atm = 760 Torr = 1013 mb.; b Features from residual water in the FT-IR chamber (i.e., not from the sample cell).

Sample Conditions and Experimental Procedures

The gas sample pressures were monitored by a set of capacitance gauges during the entire data collection period. The high purity HD was purchased from Cambridge Isotope, Inc. (Euristop). The certified purity was HD (98.73%), H2 (0.76%), and D2 (0.51%). The H2 broadening gas was research grade purity (99.99%) and the extra HD impurity in the H2 sample was taken into account using the natural abundance values listed in HITRAN 2020 [START_REF] Gordon | The HITRAN2020 Molecular Spectroscopic Database[END_REF] (e.g., H2 0.999668 and HD 0.000311432). The partial pressures of HD and H2 in a mixture are computed from the pressure readings of HD (PHD) and H2 (PH2), by: Total HD = 0.9873 × PHD + 0.0003114×PH2 (Eq.1a) Total H2 = 0.0076 × PHD + 0.999688×PH2 (Eq.1b) The data acquisition procedure began by cooling the multipass cell. Once a stable cell temperature was achieved, an initial sample of pure HD was admitted to the cell and very high resolution spectra were obtained. Nearly 24 hours of interferometer scans were collected to achieve adequate signal-to-noise for these highest resolution measurements. H2 broadening gas was then added to the HD sample to obtain a mixture spectrum which, due to the higher pressure, can be resolved at lower spectral resolution. The process of adding H2 to the mixture continued, and spectra of various mixing ratios were obtained. Sets of corresponding background spectra were obtained at the lower resolution with an empty cell or H2 at a comparable pressure to the sample gas (at these low pressures the collision-induced absorption of H2 is unmeasurable). For the case of short cell measurements at room temperature, N2 gas was used for the background. In many cases the empty cell spectra had a continuum level that was more consistent with the sample spectra. In total, three pure HD spectra and 14 HD+H2 mixture spectra were acquired between 98 and 297 K, and the experimental conditions are summarized in Table 2. *A 1 mb of CO was added to test the instrumental line shape and the spectral line resolving power for the given spectral resolutions. The presence of the CO did not impact the HD line parameter retrieval. # Fitted HD transitions for which parameters are retrieved.

Transmission spectra are formed by dividing sample spectra by the best consistent set among the background spectra. For example, transmission spectra are selected from those that produce the least prominent 'channel' spectra (unavoidable ripples that arise from subtle differences between sample and background spectra). The signal-to-noise of the transmission spectra formed is ~100, depending on the spectral region and resolution. An example of a HD-H2 transmission spectrum at 192 K is shown in Fig 1, where all four HD lines have measurable intensity, and the R(0) -R(3) transitions are seen near 89.23, 177.84, 265.24, and 350.85 cm -1 , respectively. Fig. 1 The R(0) -R(3) transitions of the HD-H2 transmission spectrum at 192 K over an optical path of 21.14 m. The HD pressure is 20.2 mb and the total sample pressure is 151.5 mb. 3 Data analysis 3.1 Frequency calibration All the HD spectra have been frequency calibrated using a few well-isolated H2O lines. These features arise from residual water vapor in the evacuated FTS chamber, which is at room temperature. Since the pressure of the FTS chamber is very low, the water lines are quite narrow with no significant pressure shift. H2O is not present in the cold gas samples as it condenses in the cell fill tube or on the walls. The spectra at room temperature exhibit, however, pressure broadened H2O contaminant features with the superposed sharp lines from the FTS chamber. The frequencies of the sharp components of the H2O lines are compared to those listed in HITRAN 2020 [START_REF] Gordon | The HITRAN2020 Molecular Spectroscopic Database[END_REF] to obtain a calibration factor. The calibrated spectra have a frequency accuracy of better than 0.0001 cm -1 .

Retrievals through multispectrum fitting analysis

For each HD transition, all the pure HD and HD-H2 mixture spectra with measureable absorption were fitted simultaneously; spectra included in the fit are indicated in the last column in Table 1. The spectroscopic parameters shown in Table 4 were thereby obtained using the Labfit multispectrum fitting software package [Ben95; Let07; Dro17], which is based on an iterative nonlinear least squares curve fitting algorithm. The package uses a non-Voigt spectral line shape. This analysis technique has produced high quality results for various molecules [Dev10; Dev16a; Dev16b; Sun20].

Mathematical details of the multispectrum fitting package have been presented previously [START_REF] Sung | H2pressure broadening and frequency shifts of methane in the v2+v3 band measured in the temperature range between 80 and 370 K[END_REF], and a brief summary of it is presented below. For a transition centered at v0, the cross section k(v -v0) can be written as

0 = • 0 (Eq. 2)
where S is the line intensity and κ is the molecular line shape profile. A non-Voigt profile, ψ(x, y, ), is used which is defined in terms of the complementary complex probability function, W(z), [START_REF] Humlicek | Optimized computation of the Voigt and Complex probability functions[END_REF] and unitless parameters, z= x + i(y + ), = ln 2 0 ⁄ , = ln 2 ⁄ , = ln 2

, where v0 is the line center frequency in vacuum, γD is the Doppler half-width, γL is the pressure-broadened half-width, and is the collisional narrowing parameter, respectively. The present analysis uses the hard-collision model with the Rautian line profile [Rau67; Pin92; Ben95]. Thus, Eq.( 2) can be expanded to: = ∫ exp (Eq. 3a)

κ 0 = , , = -√ ]
(Eq. 3b) where =

. The Lorentz half-width, , and the line position, v0, as a function of pressure (P) and temperature (T), are based on an empirical model with the line position in vacuum, ν00, and the coefficients, γ o , δ0, and δ′ described in Table 3

[Ben16; Dev16a; Dev16b]: , = × [ 0 0 × ] (Eq. 4) 0 , = 00 × [ 0 0 × 0 ].
(Eq. 5) Table 3 Spectroscopic line parameters for each transition symbols full description Units Short names ν0 zero pressure line center position cm -1 position S line intensity at 296 K cm -1 / (molecule•cm -2 ) intensity 0 (HD or H2) pressure-broadened half-width coefficient at 296 K at 1 atm (See Eq. 4) cm -1 /atm self-width; H2-width temperature dependence exponent of the half-width coefficient (See Eq. 4) unitless width T-dep.

0

(HD or H2) pressure-induced line shift coefficient at 296 K at 1 atm (See Eq. 5) cm -1 /atm self-shift; H2-shift

′ temperature dependence parameter of the pressure-shift coefficient (See Eq. 5) cm -1 /(atm•K) shift T-dep.
β Collisional narrowing parameter (See Eq. 3b) cm -1 /atm narrowing

The lowest pressure and temperature far-infrared spectral linewidths are Doppler limited and the pure HD spectra were just resolved (excepting R(0)) using the highest spectral resolution possible with the FTS. The synchrotron radiation source is understood to have a frequency dependent effective beam diameter [Jaq10], with an effective value, deff, modeled by Eq. (6) [Man19]; this divergence apodization effect on the spectral resolution is included in the fitting process.

≈ 5 √
, where ν is wavenumber in cm -1 . (Eq. 6) Each HD transition was treated separately, but applicable spectra at various temperature and pressure conditions were fitted simultaneously (see Table 2). The transitions were treated independently since, for instance R(0) and R(3) lines were too weak at either room temperature or low temperature, respectively. Since the number of pure HD spectra is limited, the temperature dependence of the self-broadening coefficient, n, has been constrained to that of the HD-H2 broadening. The multispectrum fitting procedure adjusts the spectroscopic line parameters until the differences between the observed and synthetic spectra converge to a minimum, typically at the measurement noise level. A set of continuum oscillations that accounts for 'channel spectra' is also included in the fitting process. The fitted spectra, and residuals, of the four transitions are shown in Fig. 2, and the number of spectra used in the fits is shown above each panel.

) c δ H2-shift (cm -1 /atm/K) -0.000007(2) -0.000010(1) -0.000006(1) -0.000011(2) δ self-shift (cm -1 /atm/K) -0.000007(2) c 0.000015(4) 0.000022(5) -0.000011(2) c β, narrowing (cm -1 /atm)
n/a 0.017(10) 0.033(15) n/a Notes: 1 Position, intensity, half-widths, shifts, narrowing parameters are the values at T0 = 296 K. 2 Line intensity includes the natural abundance following the HITRAN convention. 3 Self-parameters flagged with 'c' are constrained to their corresponding H2-parameters due to a limited number of pure sample spectra.

The uncertainties shown in Table 4 are the errors that result from the multispectrum fitting process. As shown in Fig. 2, all the four HD transitions are very well modelled down to their spectral noise levels. Their peak-to-peak signal-to-noise (S/N) values are 73, 188, 159, 180, respectively, and the retrieval errors are due to these limitations. The systematic errors of the experiment, which exceed the fitting errors, are discussed in Sec. 5. 5 and compared to previous measurements and theoretical predictions in Fig. 3. Figure 3 shows transition frequency differences compared to the HITRAN 2020 values after sorting them by publication year along the x-axis. The HITRAN values and the present work are denoted by square and circle symbols, respectively, throughout this paper. For the R(0) transition, the present value agrees well with the high resolution value measured at 18 K reported by Drouin et al. [START_REF] Drouin | Terahertz Spectroscopy for Space Applications, 2.5-2.7: THz Spectra of HD, H2O and NH3[END_REF], and it also corresponds to the latest theoretical calculations which have been adopted by HITRAN [START_REF] Józwiak | Positions and intensities of hyperfine components of all rovibrational dipole lines in the HD molecule[END_REF]. In general, all the R(0) values are comparable to HITRAN. The R(1) transition is reasonably absorptive for all temperatures studied in the present work. Its position was retrieved with the lowest uncertainty and it agrees with HITRAN to within 0.0001 cm -1 , i.e. the accuracy of the frequency calibration of this work. The R(1) measurement by Ulivi et al. [START_REF] Ulivi | Pure rotational spectrum of hydrogen deuteride by far-infrared Fourier transform spectroscopy[END_REF] and the calculation by Wolniewicz [START_REF] Wolniewicz | The X 1 Σ + g state vibration-rotational energies of the H2 , HD, and D2 molecules[END_REF] are within 0.0003 cm -1 , although their studies are more than three decades old. The R(2) transition also has adequate optical density at all measured temperatures, and it has a low uncertainty similar to that for R(1). The R(2) value determined herein is 0.0005 cm -1 higher than HITRAN, but it is lower than the Ulivi et al. [START_REF] Ulivi | Pure rotational spectrum of hydrogen deuteride by far-infrared Fourier transform spectroscopy[END_REF] measurements by ~0.0005 cm -1 . The population of the J = 3 state is low at cold temperatures, and only seven spectra were used in the fitting; thus, the uncertainly of the R(3) position is larger than that of R(1) and R(2). The R(3) result is larger than the HITRAN value by 0.0010 cm -1 , and larger than that of Ulivi et al. [START_REF] Ulivi | Pure rotational spectrum of hydrogen deuteride by far-infrared Fourier transform spectroscopy[END_REF] by a similar amount. There is a correspondence, however, within probable errors with a previous diode laser measurement of Essenwanger and Gush [E&G84].

Transition frequencies

HD line intensities and dipole moments

A goal of the present work is to determine HD and HD-H2 spectroscopic line parameters in a form that will be useful to modelers of planetary atmospheres. The line intensity S, which is temperature and rotational state dependent, has been obtained through the multispectrum fitting process in the HITRAN formulation at the reference temperature 296 K [Rot98]. The physical property of the molecular dipole moment is, however, temperature independent and its determination has been an objective of previous experimental and theoretical studies Figure 4 shows that the present results are slightly smaller than the HITRAN values for all transitions. For the transitions R(0), R(2), and R(3) the present results are comparable to an average of previous experimental results; for R(1) the present value is a little higher than an average of the experiments and rather closer to the theoretical value. Figure 5a shows a comparison between the newly derived line intensities, S, and previous measurements at various temperatures. For HITRAN and the newly retrieved line intensities at 296 K, the intensity values at all other temperatures are computed using Eq. A11 of Rothman et al. [Rot98]; these extrapolations are shown as continuous lines. Previous experimental dipole moment values at particular temperatures are likewise converted to a line intensity, S, using Eq. 7 above, and these data are shown as individual points. The lower panels of Fig. 5b show percentage differences between the extrapolated HITRAN and other measurements in order to accentuate the variations. Here the present measurements are depicted by open circles at three specific temperatures. The HITRAN values are adopted from theoretical calculations, which have an uncertainty of 10 -20% [START_REF] Pachucki | Electric dipole rovibrational transitions in the HD molecule[END_REF], and this is shown by the dashed lines in red in the figure. The present results fall within ~5% of these theoretical values for all transitions and temperatures. [Uli89, Uli91, Lu93] were also fitted with Fano line shapes although the asymmetries are quite small and the density dependent interference parameters are of order 10 -3 /amagat. The molecular dipole moment in these previous experiments is obtained by extrapolating the integrated line intensity to zero density. The present experiments were conducted using temperatures and densities closer to those of giant planet atmospheres [Nix09; Nix20]. Gas densities used were below 2.0 amagat and collisional effects contribute less than a fraction of 1% to the line intensity. Using low gas densities permitted the fitting of the spectra with a symmetric line shape and a density-independent intensity parameter (see Table 3). The fits shown in Fig. 2 show no residual asymmetry above the experimental noise level. The measured dipole moment is nearly constant as a function of rotational state, and within experimental error this corresponds to theoretical predictions for the pure rotational band [START_REF] Józwiak | Positions and intensities of hyperfine components of all rovibrational dipole lines in the HD molecule[END_REF]. Collisional narrowing is considered as part of the fitted line shape and it is discussed below.

(b)

4.4 HD line shape parameters -width, shifts, and narrowing 4.4.1 Pressure-broadening of the HD transitions The HD self-broadening and H2-broadening coefficients, γ 0 (cm -1 /atm) at 296 K, are retrieved simultaneously and independently through the multispectrum fitting process. Despite a limited number of pure HD spectra, the fitting process also retrieves self-broadening parameters by using the HD partial pressures in the multiple sets of the HD-H2 mixtures. The temperature dependence parameter (n in Eq. 4) for H2-broadening is also retrieved for each transition. The self-broadening temperature dependence, however, is constrained to that of H2-broadening due to the limited number of pure HD spectra. Comparisons of the present broadening parameters and their variations with temperature to previous work are shown for the self-broadened half-widths in Fig. 6a, and for the H2-broadened half-widths in Fig. 6b. In these figures measurements of full width at half maximum (FWHM), B0 in cm -1 /amagat, reported by earlier work [START_REF] Essenwanger | Rotational spectrum of HD at low pressures[END_REF][START_REF] Mckellar | Interference effects in the spectrum of HD: III. The pure rotational band at 77 K for HD and HD-Ne mixtures[END_REF][START_REF] Mckellar | Interference effects in the spectrum of HD: IV: the pure rotational band at room temperature[END_REF]Dra87;[START_REF] Ulivi | Temperature dependence of the collisional interference in the pure rotational far-infrared spectrum of HD[END_REF][START_REF] Lu | Temperature dependence of the pure rotational band of HD: Interference, widths, and shifts[END_REF] have been converted to HITRAN units, cm -1 /atm, HWHM to facilitate comparisons. Note that the temperature dependence for the half-width, γ (cm -1 /atm), in Eq. 4 can also be applied to the full width, B0 (cm -1 /amagat), as long as their units are kept consistent with those of Eq. 4. HITRAN [START_REF] Gordon | The HITRAN2020 Molecular Spectroscopic Database[END_REF] and Feuchtgruber et al. [START_REF] Feuchtgruber | The D/H ratio in the atmospheres of Uranus and Neptune from Herschel-PACS observations[END_REF] provide temperature dependence parameters based on Eq. 4 referenced to T0 = 296K, and Lu et al. [START_REF] Lu | Temperature dependence of the pure rotational band of HD: Interference, widths, and shifts[END_REF] provides parameters referenced to T0 = 77 K. These results are plotted continuously over the temperature range in Fig. 6. Feuchtgruber et al. [START_REF] Feuchtgruber | The D/H ratio in the atmospheres of Uranus and Neptune from Herschel-PACS observations[END_REF] is not an experimental result, but a critical compilation of existing measurements (based on [Evn88; Uli91; Lu93]) for a perturbing gas composed of a H2: He [85:15] mixture. The most prominent finding is that the collisional broadening values listed in HITRAN 2020 are larger than the experimental measurements by about a factor of 5; to place the HITRAN values on the comparison figure they have been multiplied by 0.2. The HITRAN temperature dependent exponent also does not fit the low temperature measurements. The plot of H2 broadening of the R(0) line includes theoretical values of Schaefer and Monchick [START_REF] Schaefer | Line broadening of HD immersed in He and H2 gas[END_REF]; these data are generated using their Table 6 and their Eq. 18, after including the implicit parameter, L0, Loschmidt's number (2.689×10 19 /cm 3 ). Inspection of Figs. 6a and6b shows that our new measurements (in open red circles) are generally consistent with previous experimental results, particularly at the lowest temperatures. The new results differ substantially from the rescaled HITRAN values. The H2-broadening (Fig. 6b) shows somewhat a closer correspondence to previous measurements than the self-broadening (Fig. 6a). The major discrepancy is that current measurements of the self-broadening of the R(2) transition differ substantially from previous measurements. Theoretical calculations by Shaefer and Monchick [START_REF] Schaefer | Line broadening of HD immersed in He and H2 gas[END_REF] show that H2-broadening of the R(0) transition has a minimum near 80 K, where there is fairly good agreement with our measurements. Their calculations differ, however, from the present and previous measurements at temperatures higher than 140 K [START_REF] Lu | Temperature dependence of the pure rotational band of HD: Interference, widths, and shifts[END_REF]. In these figures it is apparent that the HITRAN temperature exponents do not match well the experimental values. The present results are a closer match, but some discrepancies remain due perhaps to adopting a simple model for the temperature dependence of the linewidth (See Eq. 4). Since the new results have been derived from simultaneously fitting spectra over all temperatures and pressures, they are expected to have good consistency among the retrieved parameters. ▷), Dra87(x), Uli89( ☆), Lu93(◊), SM92 (hexagram), and this work (○).The series of symbols, Lu93 (*) and Lu93 (•), presented across the temperature ranges are extrapolations using the empirical model, Eq. 4, based on measurements at 77, 195 and 296 K, respectively, with Tref = 77 K. The present data series are calculated using Eq.4 and the fitted parameters of Table 4. Note that the HITRAN 2020 widths are reduced by a factor of 5.

(a) (b) 4.4.2 Pressure-induced frequency shifts Pressure-induced frequency shifts and temperature dependencies, δ 0 (cm -1 /atm), for the R(0)-R(3) transitions have been retrieved from the fit. There was adequate data to obtain both HD self-shifts and H2 induced shifts for R(1) and R(2), but the self-shifts and temperature dependent exponents of R(0) and R(3) have been constrained to the values of the H2-induced shifts for these two lines. The self-shift values have not previously been listed in the HITRAN [START_REF] Gordon | The HITRAN2020 Molecular Spectroscopic Database[END_REF] or GEISA [START_REF] Jacquinet | The 2015 edition of the GEISA spectroscopic database[END_REF] databases. The self and H2 frequency shift results, extrapolated over the temperature range 77 -300 K, are shown in Figs. 7a and7b, respectively. The present work is shown as the continuous string of open circles. Previous measurements at discrete temperatures, again converted to HITRAN units, are also plotted for comparison. The shift values for all transitions over all temperatures are quite small. The agreement between the current work and previous measurements is better for the H2 frequency shifts than those for the self-shift cases, and the current work matches reasonably well the previous R(0) -R(2) H2 values. The situation for R(0) is particularly interesting as the present results show a positive frequency shift with pressure at for all measured temperatures, but previous precise measurements by Drouin et al. [Dro11] at 18 K show a clear negative shift. Schafer and Monchick [START_REF] Schaefer | Line broadening of HD immersed in He and H2 gas[END_REF] conducted a theoretical study of H2-shifts for R(0), which indeed shows a change in the sign of the frequency shift with temperature. Their Fig. 7, however, shows a positive shift at low temperature and a negative shift above ~ 60K. The values plotted in this graph are reproduced from their Eq. 19 and the parameters listed in their Table 6, but it appears that a negative sign in their equation was omitted (a factor of Loschmidt's number is also needed in their Eqs. 18 and 19 to obtain the reported values in their Fig 7 andTable 7). When these issues are taken into consideration, the present shift values and the Drouin et al. results, confirm this picture of a change in the pressure shift direction at temperatures near 60 K.

Collisional narrowing

The collisional (Dicke) narrowing effect has been studied in various molecules [Dic53; Gal61; Rau67; DeC84; Var84; Bra03; Weh06; refs. therein], and it was observed in pure HD spectra for the R(3) and R(6) transitions [START_REF] Essenwanger | Rotational spectrum of HD at low pressures[END_REF]. These previous room temperature experiments at low pressures showed minimum linewidths at pressures where the magnitudes of the Doppler broadening and pressure broadening are comparable. The collisional narrowing effect is small and more pronounced for R(6) than R(3) as the Doppler broadening increases with the transition frequency. In the present work, narrowing parameters β (defined by Eq. 3b) have been retrieved for the R(1) and R(2) transitions to be 0.017(10) and 0.033(15) cm -1 /atm, respectively, without considering their temperature dependence. The narrowing parameter for the R(0) line was not well constrained. For the R(3) transition, a small value was retrieved, comparable to the error in the fit. It is interesting that the narrowing parameters are greater than the broadening parameters by a factor of 1.5 to 3. A similar situation was found for line narrowing by Nazemi et al. [START_REF] Nazemi | Collisional effects on the rovibrational transitions of the HD fundamental band[END_REF] in the HD fundamental band and by WcisƗo et al. [START_REF] Wcislo | The implementation of non-Voigt line profiles in the HITRAN database: H2 case study[END_REF] in the H2 fundamental bands. A comparison of the present line narrowing can be made to a value of the 'optical' diffusion constant proposed by Pine [START_REF] Pine | N2, O2, H2, Ar, and He broadening in the v3 band Q branch of CH4[END_REF], Dopt [cm 2 /s] = kBT/[2πmc×(P×β)], where kB is the Boltzmann constant, m is the mass of HD, c is speed of light, P is pressure in atm, and β is the narrowing parameter in cm -1 /atm at 296 K. Using a mass diffusion coefficient value of 1.40 cm 2 /sec, for a HD+H2 mixture [START_REF] Weissman | Determination of Gaseous-Diffusion Coefficients from Viscosity Measurements[END_REF], the line narrowing parameter is computed to be ~0.031. Hence, the new measurements are close to, or smaller than, the derived value by a factor of ~1.0 -1.8. Note, however, that the mass diffusion constant is an aggregate property of the system, while narrowing parameters are transition specific.

Measurement errors for line strengths and line shape parameters

As discussed in Sec. 4.1, the retrieval errors presented in Table 4 are the errors that result from the fitting process alone. Further analysis has been conducted to assess the systematic uncertainty of each parameter due to the uncertainties of the experimental conditions and spectral measurements. The uncertainty of the line intensity measurements is a combination of two categories of uncertainties given by Eqs. 8a and 8b, i.e. the uncertainty of the sample temperature, and the combined uncertainties of the transmission, mixing ratio, pressure, and pathlength. Since the line intensity S expressed by Eq. A1 is an implicit function of the temperature T, the total partition function Q, and the transition-specific lower state energy E", etc., the impact on the line intensity retrieval is estimated from temperature measurement errors of ±1 K as presented in Table 2. The fractional uncertainties in the intensity due to temperature offsets are given by Eq. 8a. and shown in Fig 8a as a solid line within the measured temperature range and as a dashed line for extrapolated temperatures. The uncertainties range from 1 -3.5 % depending on the HD transition and the measurement temperature. [V&C89]. The observed transmission τ at the line center can be written as = -⋅ ⋅ ⋅ ⋅ , where S is the line strength, ξ and p are the mixing ratio and pressure of the sample, l is the path length, and c0 is a normalization constant of the line shape profile. After taking the logarithm on both sides and rearranging, the measurement uncertainty for the line strength can be related to the spectral signal-to-noise (SNR) and the experimental conditions expressed in Eq. 8b for a single spectrum case. The value of δτ in Eq. 8b is estimated from the reciprocal of the SNR of the HD spectra listed in Table 6. The uncertainties of the HD mixing ratios, the pressure readings, and the pathlength determination are less than 0.2% each. By substituting these values into Eq. 8b, the intensity uncertainty is 4% or less for HD transitions with transmissions in the range 10 to 70%, as in the presently analyzed spectra. Finally, these estimates are for the case of a single spectrum. Since line parameters are obtained by fitting multiple spectra simultaneously, the statistical uncertainties are further reduced by the square root of the number of spectra acquired for each transition. The resultant line intensity uncertainties are presented in Table 6, and they are assumed to be accurate for the measured temperatures in the range 98-298 K. The net combined intensity uncertainties from Eq. 8a&b weighted by square root of the number of spectra, which correspond to 1.5, 0.5, 1.0, 1.0% for the R(0) -R(3) transitions, respectively. Line width and frequency shift errors are assessed as described in Benner et al. [START_REF] Benner | Line parameters including temperature dependences of air-and self-broadened line shapes of 12 C 16 O2: 2.06-µm region[END_REF]. Since these parameters define the molecular line shape profile, and are retrieved simultaneously, they are intrinsically coupled. In addition, their temperature dependence parameters are also retrieved simultaneously based on the empirical model (See Eqs. 4 and 5). The correlation coefficients reported by the multispectrum fitting package, Labfit [Ben95, Let07, Dro17], accounts for these couplings as part of the fitting solutions. Benner et al. [START_REF] Benner | Line parameters including temperature dependences of air-and self-broadened line shapes of 12 C 16 O2: 2.06-µm region[END_REF] gives the measurement uncertainties for the line widths in Eq. 9a, and the shift uncertainties in Eq. 9b.

= 0 0 × { ln 2 , × } (Eq. 9a) = 0 0 0 2 , 0
(Eq. 9b), where the ϵ's are the retrieval errors presented in Table 4, and ρ's are the correlation coefficients determined from the line parameter retrievals listed in Table 7. It should be noted that these correlation coefficients reflect constraints on parameters assuming the line shape model adopted in this work. Table 7. The correlation coefficients between the line width (γ 0 ) and pressure shifts (δ 0 ) and their corresponding temperature dependence parameters, n and δ' . 8a, which shows values varying between 1 -8% for self-widths, and 1 -4 % for H2-widths, depending on transitions and temperatures. Fig. 8b shows that shift uncertainties increase as temperatures decrease, amounting to ~50% at the lowest temperatures. Figure 10 shows the line shift as a function of temperature overlaid with the measurement uncertainties. Recall that line shape parameters and retrieval errors presented in Table 4 are the values at the reference temperature at 296 K. Their uncertainties are expected to vary with the temperature, as given in Eqs. 9a and 9b, and it is these uncertainties which are the realistic values for the line shape parameters. (a) (b)

Conclusion

New measurements of the pure rotational spectra of HD and HD-H2 mixtures have been obtained at temperatures between 98 and 296 K, at pressures below 1 atm. Multispectral fitting analysis of the data using a non-Voigt line shape yields spectroscopic parameters for the R(0) -R(3) transitions of HD. These parameters are in general agreement with previous work, however notably, the pressure-broadened linewidths reported here, and previously, are a factor of 5 less than those listed in the HITRAN and GEISA databases. Note that the databases also have the value 0.05 cm -1 /atm for the H2 rotational linewidths, and these also need correction [START_REF] Cosmo | The S0(1) quadrupole line of H2[END_REF][START_REF] Reuter | Line strength and self-broadening coefficient of the pure rotational S(1) quadrupole line in H2[END_REF]. The low temperature and low pressure experimental conditions used here are closer to the conditions found in the atmospheres of the giant gaseous planets than have been used previously. As such, the present results are particularly relevant to the interpretation of planetary spectra and should be valuable to planetary science.

Fig. 2

 2 Fig.2HD and HD-H2 mixture spectra, measured and fitted. The lower part of each panel shows observed (dots) and calculated (solid) spectra. The upper portion shows their fitted residuals (Obs-Calc). For each transition, all spectra are fit simultaneously such that the residuals are comparable to the measurement noise level.

Fig. 3

 3 Fig. 3 Line position differences (in cm -1 ) compared to HITRAN for previous measurements and theory. The reference indices and symbols are: 1: HITRAN 2020(□), 2: Wol83(◊), 3: EG84(◁ ), 4: McK86(▽ ), 5: Evn88(☆), 6: Uli91(△), 7: Pac10(Hexagram), 8: Dro11(▷ ), 9: Cza18(Hexagram), 10: Joz20(x), 11: JPL Catalog(*), 12: This work(○). Note that the y-axis range for R(0) and R(1) are smaller than the other two. The deviations of E&G84(◁ ) and Mc86(▽ ) have been divided by factors of 10 and 20, respectively.

  [Wol76, Nel83, Ess84; McK84; McK86; Dra87a; Dra87b; Uli91; Wis92; Lu93; Pac08; Joc20]. The relationship between the line intensity S and the molecular dipole moment μ is given by: where the details of this equation are given in the Appendix. The new dipole moment results are compared to previous work and the HITRAN values in Fig. 4. The four transitions are shown in separate panels with HITRAN values denoted as open squares and the present results as open circles throughout this manuscript, with both having solid horizontal lines color-coded for comparison purposes. The previous values are sorted by their references.

Fig. 4 .

 4 Fig. 4. Comparison of HD molecular dipole moment measurements and theory. The reference indices and symbols are 1: HITRAN(□), 2: Wol76(▷ ), 3: For77(+), 4: Nel83(◁ ), 5: Ess84(△), 6: McK84(▽ ), 7: Tho85(•), 8: McK86(▽ ), 9: Dra87(x), 10: Uli89(☆), 11: Uli91(☆), 12: Lu93(◊), 13: Pac08(hexagram), 14: Joz20(*), 15: This work(○). Multiple data points for the same source indicates that measurements were made at more than one temperature. Missing symbols for some references indicates that their values are outside the plotted regions.Figure5ashows a comparison between the newly derived line intensities, S, and previous measurements at various temperatures. For HITRAN and the newly retrieved line intensities at 296 K, the intensity values at all other temperatures are computed using Eq. A11 ofRothman et al. [Rot98]; these extrapolations are shown as continuous lines. Previous experimental dipole moment values at particular temperatures are likewise converted to a line intensity, S, using Eq. 7 above, and these data are shown as individual points. The lower panels of Fig.5bshow percentage differences between the extrapolated HITRAN and other measurements in order to accentuate the variations. Here the present measurements are depicted by open circles at three specific temperatures. The HITRAN values are adopted from theoretical calculations, which have an uncertainty of 10 -20%[START_REF] Pachucki | Electric dipole rovibrational transitions in the HD molecule[END_REF], and this is shown by the dashed lines in red in the figure. The present results fall within ~5% of these theoretical values for all transitions and temperatures.

  Fig. 5(a) (a) Line intensities (solid lines) computed using Eq. 7 and HITRAN parameters, and fitted parameters in Table 4, are compared with previous measurements (symbols) (b) The differences between line intensities of HITRAN 2020 and previous experiments at various temperatures: Ess84(△), McK84(▽ ), McK86 (▽ ), Dra87(x), Uli89(☆), Uli91(☆), Lu93(◊), Joz20(*), and this work (○). Intensities derived from the present work are shown at the discrete temperatures of previous experiments. Since the HD dipole moment is quite small, collision-induced absorption, and collisional interference effects can be pronounced compared to the allowed dipole moment transitions [Pol85]. Measurements of the fundamental band show large line asymmetries with increasing gas densities, and these lines are well fitted by a Fano line shape (e.g. Rich & McKellar [Ric83]). The line asymmetries are significantly less prominent in the rotational band even at relatively large gas densities. The rotational band experiments of McKellar et al. [McK84, McK86], and Tabisz et al. [Uli89,[START_REF] Ulivi | Pure rotational spectrum of hydrogen deuteride by far-infrared Fourier transform spectroscopy[END_REF][START_REF] Lu | Temperature dependence of the pure rotational band of HD: Interference, widths, and shifts[END_REF] were also fitted with Fano line shapes although the asymmetries are quite small and the density dependent interference parameters are of order 10 -3 /amagat. The molecular dipole moment in these previous experiments is obtained by extrapolating the integrated line intensity to zero density. The present experiments were conducted using temperatures and densities closer to those of giant planet atmospheres [Nix09; Nix20]. Gas densities used were below 2.0 amagat and collisional effects contribute less than a fraction of 1% to the line intensity. Using low gas densities permitted the fitting of the spectra with a symmetric line shape and a density-independent intensity parameter (see Table3). The fits shown in Fig.2show no residual asymmetry above the experimental noise level. The measured dipole moment is nearly constant as a function of rotational state, and within experimental error this corresponds to theoretical predictions for the pure rotational band[START_REF] Józwiak | Positions and intensities of hyperfine components of all rovibrational dipole lines in the HD molecule[END_REF]. Collisional narrowing is considered as part of the fitted line shape and it is discussed below.

Fig. 6

 6 Fig. 6 Comparison of (a) Self-and (b) H2-pressure-broadened line widths, HWHM (in cm - 1 /atm). The symbols are for HITRAN 2020 (□), Feu13(◁), Ess84 (△), McK84 (▽ ), McK86(

Fig. 7

 7 Fig. 7 Comparison of (upper) Self-and (lower) H2-frequency shifts with pressure (cm -1 /atm). The symbols are for HITRAN 2020 (□), Feu13(◁), McK84 (▽ ), McK86(▷), Dra87(x), Uli89(☆), Lu93(◊), SM92 (hexagram), and this work (○). Note that HITRAN 2020 values are not available.

  Fig.8(a) Line intensity uncertainties propagated from temperature errors of ±1 K at temperatures within (solid line) and outside (dashed line) the measured range. (b) The net combined intensity uncertainties from Eq. 8a&b weighted by square root of the number of spectra, which correspond to 1.5, 0.5, 1.0, 1.0% for the R(0) -R(3) transitions, respectively. Line width and frequency shift errors are assessed as described in Benner et al.[START_REF] Benner | Line parameters including temperature dependences of air-and self-broadened line shapes of 12 C 16 O2: 2.06-µm region[END_REF]. Since these parameters define the molecular line shape profile, and are retrieved simultaneously, they are intrinsically coupled. In addition, their temperature dependence parameters are also retrieved simultaneously based on the empirical model (See Eqs. 4 and 5). The correlation coefficients reported by the multispectrum fitting package, Labfit[START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF][START_REF] Letchworth | Rapid and accurate calculation of the Voigt function[END_REF][START_REF] Drouin | Multispectrum analysis of the oxygen A-band[END_REF], accounts for these couplings as part of the fitting solutions. Benner et al.[START_REF] Benner | Line parameters including temperature dependences of air-and self-broadened line shapes of 12 C 16 O2: 2.06-µm region[END_REF] gives the measurement uncertainties for the line widths in Eq. 9a, and the shift uncertainties in Eq. 9b.

Fig. 9 .

 9 Fig. 9. (a) Measurement uncertainties (in %) for the Self-and H2-widths (top and bottom, respectively) as a function of temperature, (b) Measurement uncertainties for the for the Selfand H2-frequency shifts (top and bottom) in 10 -3 cm -1 /atm as a function of temperature.

Fig. 10 .

 10 Fig.10. Self-shifts and H2-shifts (left and right) as a function of temperature with overlaid uncertainty estimates (Also see Fig.7).

Fig. 1

 1 Fig. 1

(

  Fig.2

  Fig.6a

  Fig.7a

  Fig.7b

R

  Fig.8a

  Fig.9a

Table 1

 1

	. Experimental Parameters and Conditions
	Spectral Region	50 -360 cm -1
	IR source	AILES beamline, Synchrotron Soleil
	Beam Splitter	6 µm Ge on Mylar
	Scan rate (HeNe fringes)	60 KHz
	Detector	4 K Bolometer + 400 cm -1 lowpass filter
	Spectral resolutions	up to 0.00056 cm -1 (unapodized) [Bruker res. 0.00102 cm -1 ]
	Gas samples	HD (98.73%) and H2 ( ≥ 99.99 )
	Absorption path lengths (m)	0.051, 3.14, 9.14, 21.14
	Gas cell windows	Diamond, 0.4 mm thick
	Sample temperatures	98 -296 K
	Sample pressures (mb)

a 20 -1002 for HD; 100 -1002 for HD+H2 mixtures Temp. sensors (accuracy 0.1 K)

Table 2 .

 2 Measurement conditions for HD & HD-H2 spectra

	Spec No. Ps (mb)	Pt (mb)	L (m)	T (K)	Res(B) (cm -1 ) &	R0123 #
	3 spectra of Pure HD spectra
	1	1002.3	1002.3	0.051	298.0(1)	0.01	-1 2 3
	2	988.0	988.0	0.051	176.0(10) 0.01	-1 2 -
	3	35.2	35.2	3.14	95.4(10) 0.00102	0 1 2 -
	14 spectra of HD + H2 mixture
	4	46.5	151.8	9.14	295.8(8)	0.002	0 1 2 3
	5	46.5	300.8	21.14	296.0(8)	0.004	0 1 2 3
	6	46.5	624.8	21.14	295.7(8)	0.009	0 1 2 3
	7	20.2	601.0*	21.14	193.3(1)	0.009	0 1 2 3
	8	20.2	300.0*	21.14	193.1(7)	0.002	0 1 2 3
	9	20.2	151.5*	21.14	192.4(4)	0.002	0 1 2 3
	10	35.2	910.3	9.14	129.7(9)	0.01	0 1 2 -
	11	35.6	921.9	9.14	128.6(13) 0.02	0 1 2 -
	12	35.2	415.5	9.14	123.5(16) 0.005	0 1 2 -
	13	34.2	206.0	9.14	118.5(4)	0.005	0 1 2 -
	14	35.2	201.0	3.14	101.2(6)	0.003	0 1 2 -
	15	35.2	300.0	3.14	100.3(5)	0.003	0 1 2 -
	16	35.2	400.0	3.14	100.1(3)	0.005	0 1 2 -
	17	35.1	106.5	3.14	98.1(9)	0.0017	0 1 2 -
	Notes: Pt = Total pressure (i.e. HD + H2); Ps = HD sample pressure
	& Res(B) = Bruker FTS resolution parameter.

Table 4

 4 HD line parameters and uncertainties retrieved from fitted spectra.

	Transitions Parameters@296K	R(0)	R(1)	R(2)	R(3)
	ν0, Position (cm -1 )	89.22792(3)	177.84141(3)	265.24055(3) 350.85401(4)
	S intensity (cm/molecule)	5.561(36)×10 -28 2.402(5)×10 -27 2.886(9)×10 -27 1.522(7)×10 -27
	γ 0 H2-width (cm -1 /atm)	0.0120(4)	0.0114(1)	0.0104(1)	0.0097(2)
	γ 0 self-width (cm -1 /atm)	0.0114(7)	0.0125(2)	0.0131(5)	0.0081(7)
	n H2-width expon. (no unit) -0.027(37)	0.127(10)	0.174(13)	0.141(40)
	n self-width expon. (no unit) -0.027(37) c	0.127(10) c	0.174(13) c	0.165(40) c
	δ 0 H2-shift (cm -1 /atm)	0.00017(35)	0.00141(22)	0.00106(13)	-0.00108(17)
	δ 0 self-shift (cm -1 /atm)	0.00017(35) c	0.00518(68)	0.00633(89)	-0.00108(17

Table 5

 5

	. Comparison of line center positions of HD
	Position (cm -1 )	R(0)	R(1)	R(2)	R(3)
	HITRAN 2020	89.2279(1)	177.8413(1)	265.2401(1)	350.8530(1)
	Measurements &
	This work	89.2279(1)	177.8414(1)	265.2406(1)	350.8540(1)
	JPL Catalog	89.22793(0)	177.84127(2)
	Drouin 2011	89.2279316(8)
	Ulivi 1991		177.84172(16)	265.24116(17) 350.85295(12)
	Evenson 1988	89.227950(5)
	McKellar 1986		177.828(2)	265.207(2)	350.844(2)
	E&G 1984				350.852(2)
	Theoretical calculations
	Wolniewicz 1983*	89.228	177.841	265.239	350.852
	Ulivi 1991	89.227950(5) 177.841790(17) 265.241119(55) 350.85295(11)
	P&K 2010	89.227933(8)
	Jozwiak 2020 #	89.2279(2)	177.84127	265.24009	350.85301
	Czachorowski 2018*	89.226758	177.83894	265.23666	350.84854
	& References for the measurements are JPL Catalog [Pic91; http://spec.jpl.nasa.gov],
	Drouin2011 [Dro11], Ulivi 1991 [Uli91], Evenson 1988 [Evn88], McKellar 1986 [McK86],
	E&G [Ess84], Wolniewicz 1983[Wol83], P&K 2010[Pac10], Jozwiak 2020 [Joz20],
	Czachorowski 2018 [Cza18].

# Calculated with H2Spectre code of Czachorowski et al.

[START_REF] Czachorowski | Nonadiabatic relativistic correction in H2, D2, and HD[END_REF]

and

[START_REF] Komasa | Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory[END_REF]

. * Obtained from differences in the dissociation energy table. Retrieved spectral transition frequencies are listed in Table

Table 6 .

 6 The uncertainties of the line intensity S from Eqns 9a and 9b The uncertainty resulting from the rest of the experimental conditions is estimated using the approach of Sung et al. [Sun09] and Varanasi and Chudamani

	Transition	in %	SNR	τ range	in % No of Spec Meas. unc.
	R(0)	1.2	73	0.1 -0.7	~ 4	15	1.5
	R(1)	0.5	188	0.1 -0.7	~1.5	17	0.5
	R(2)	3.1	159	0.2 -0.7	~ 2	17	1.0
	R(3)	1.5	184	0.4 -0.7	~ 1.5	7	1.0

  The measurement uncertainties for the line widths are presented in Fig.

					For Self-shifts
	R(0)	-0.7019	←	0.7693	←
	R(1)	-0.6916	←	0.9339	0.1363
	R(2)	-0.5191	←	0.7150	0.2391
	R(3)	-0.5380	←	0.0666	←

Transitions

, for H2-widths , for Self-widths , For H2-shifts ,

Acknowledgments:

Part of the research described in this manuscript was performed at the Jet Propulsion Laboratory, California Institute of Technology, and was supported by PDART program under the National Aeronautics and Space Administration. Data acquisition on the AILES beamline at the Synchrotron Soleil was granted under Projects (20180459 and 20190213). C. Nixon acknowledges support from the Fundamental Laboratory Research (FLaRe) program within the NASA Internal Scientist Funding Model (ISFM). We dedicate this paper to the memory of Irving Ozier (1938-2022), with appreciation for his contributions to molecular spectroscopy, and to members of this research collaboration.

= , (-) ] × ℝ (A.1) where c2 = hc/k = 1.4388 cm•K, Ia is the isotopomeric abundance, EJ is the lower state energy, is the transition frequency, T is the temperature, h is Planck's constant, k is Boltzmann's constant, and c is the speed of light. The total internal partition function, Q(T) is expressed by

2) In practice, we have used the total internal partition computed by the TIPS program [START_REF] Gamache | Total internal partition sums for 166 isotopologues of 51 molecules important in planetary atmospheres: Application to HITRAN 2016 and beyond[END_REF]. The statistical weighting factor,

for HD. ℝ is the weighted square of the transition moment, which is independent of temperature, but dependent on J. Note the summation over the states , , as defined by

.

(A.3) Townes and Schawlow (Pgs. 22-23) [START_REF] Towns | Microwave Spectroscopy[END_REF] show that the probability of absorption of randomly polarized radiation by randomly oriented molecules is a sum over the dipole moment matrix elements for a transition from states JM to J'M'

and the sum for all J,M equals × + + , for absorbing transitions in the R-branch, i.e.

J+1←J, where is the square of the molecular dipole moment and it is independent of J. Thus, is related to the HITRAN quantities above by

1 / 2 1 . (A.5) Finally the relation between the line intensity and the dipole moment squared as shown in Eq 7 is:

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Conflict of Interest


Christian Iasio
email: c.iasio@brgm.fr

Ingrid Canovas
email: icanovas@tutatnota.com

Elie Chevillot-Miot
email: elie.chevillot@gmail.com

Tendry Randriamalala
email: brgmt.randriamalala@brgm.fr

A new approach to structured processing of feedback for discovering and investigating interconnections, cascading events and disaster chains

Keywords: Knowledge management, multiperspectivity, lessons learning, crisis management

A new approach to structured processing of feedback for discovering and investigating interconnections, cascading events and disaster chains

INTRODUCTION

Subject matter and study goals

After an emergency, each entity involved in crisis management may provide hot and cold feedback. Major crises may produce incidents and emergencies involving scenarios not always foreseen in crisis management plans. When this sort of "unframed" crisis management [START_REF] Lagadec | Risques et crises : questions sur nos ancrages[END_REF] occurs, post-crisis review and feedback are particularly valuable for optimising crisis management plans and procedures. Recounting and investigating the organisational scenario and the most influential events of a natural disaster as complex as that generated by the sequence of three hurricanes that hit the French West Indies between 5 and 19 September 2017 is a major challenge. It involves processing dense and closely interconnected information. A common flaw of feedback is the lack of integration of different perspectives on the same event. While a comprehensive post-disaster review requires narratives and witness statements alongside quantitative and geospatial data, the integration and analysis of all these data sources can be complex. New approaches [START_REF] Harris | An Extension of the Human Factors Analysis and Classification System (HFACS) for use in Open Systems[END_REF] and tools, as well as new uses of available tools [START_REF] Brian Thoroman | An Integrated Approach to Near Miss Analysis Combining AcciMap and Network Analysis[END_REF] This work draws on an example of the ANR APRIL 1 project's results to present the specifications and use of a method under development at BRGM, 2 the "queryable category-based feedback knowledge graph" (ExG), which aims to improve the capitalisation of experiences. This used individual feedback sources to build an overall representation of occurrences, i.e. a model of real observed or lived events, when hurricanes Irma, José and Maria hit the French West Indies in 2017. Using the prototypal implementation of this method, the project established a comprehensive, multiperspective post-disaster review of the crisis, by pooling individual feedback sources into an overall frameset.

Literature review and theoretical framework

Covering the full workflow from the collection to the capitalisation of experience feedback on a practical and conceptual level requires a stack of tools for data production, processing, analysis and visualisation. The ExG method implemented by means of a set of prototypal tools within the scope of APRIL project was designed to produce and manage this workflow.

Existing tools implement different techniques for extracting structured text from narratives or unstructured text fragments. MAXQDA. 3 , MonkeyLearn 4 and Atlas.ti, 5 are some example of solutions embedding AI to help tag, analyse and visualise results, including analysis of feelings. Another approach rely on adapting and customising pre-trained language models to the specific corpus at hand. CorText 6 is an advanced solution of this type usually used for bibliometrics applications. Even if these tools may boost and shorten the effort and time needed to construct the ExG database, they do not allow the semantic data processing and knowledge engineering required for our case study.

The knowledge management of experience feedback archives is currently performed by very different approaches, depending on the context, domain and objective(s) of the feedback collection. The ontology-based knowledge base may help deal with this issue [START_REF] De Nicola | Knowledge Fusion for Distributed Situational Awareness driven by the WAx Conceptual Framework[END_REF]. Looking for a solution rooted in this approach introduces the question of how to define the ontology of reference [START_REF] Liu | Ontologies for Crisis Management: A Review of State of the Art in Ontology Design and Usability[END_REF][START_REF] Osman | Ontology Integration: Approaches and Challenging Issues[END_REF]. To put this simply, the question is how to systematically adapt or transform the heterogeneous amount of information from retrospective experiences, consisting of narratives and other types of data, into structured datasets that are searchable and exploitable by computer aided methods, including machine learning technologies. Building a "crisis metamodel" may represent the first step in creating a dedicated "crisis ontology" able to support reasoning mechanisms (Bénaben et al., 2008). These form the basis for the deduction of collaborative processes [START_REF] Benaben | An AI Framework and a Metamodel for Collaborative Situations: Application to Crisis Management Contexts[END_REF]). The objective is to provide an appropriate approach for context-agnostic crisis modelling, embedding reasoning mechanisms able to infer the relevant collaborative process among crucial actors and the critical paths of events and decisions involved in crisis management [START_REF] Chehade | Handling effective communication to support awareness in rescue operations[END_REF]. The ultimate goal is improving and adapting operational plans to typical "emergent behaviours" and groups [START_REF] Quarantelli | Emergent Behavior and Groups In The Crisis Time Of Disasters, Disaster Research Center[END_REF].

Other well-known tools for retrospective analysis and modelling of accidents occurring in complex sociotechnical systems are the AcciMap [START_REF] Lintern | Jens Rasmussen's risk management framework[END_REF], the HFACS [START_REF] Shappell | Human Factors Analysis and Classification System-HFACS[END_REF], the STAMP (Levenson, 2004) or the FRAM [START_REF] Hollnagel | FRAM: The Functional Resonance Analysis Method: Modelling Complex Socio-Technical Systems[END_REF], and subsequent versions (e.g. [START_REF] Kaptan | The Evolution of the HFACS Method Used in Analysis of Marine Accidents: a Review[END_REF]). These can be also used for feedback review and the retrospective analysis of natural and natural hazard triggered technological (Na-Tech) disasters [START_REF] Hollnagel | The Fukushima Disaster-systemic Failures as the Lack of Resilience[END_REF] to formulate recommendations on safety improvements.

The ExG data collection and management method is complementary to these tools. In particular, its most innovative element is the approach to define a reference ontology for the conceptualisation and analysis of experiences.

Research objectives and design

The ExG aims to be a theoretical and operational framework for enabling the retrospective modelling of complex sociotechnical systems, to improve resilience. This work in progress describes the theoretical underpinnings and development of the ExG, and its prototypal application to accomplish the ambitious objectives of the ANR APRIL project: the analysis of the emergency response feedback collected two years after the hurricane season that struck the French West Indies in 2017. Different retrospective interviews of actors and decision-makers, about the two weeks of crisis and its aftermath, were aggregated. As they occupied different roles and hierarchical positions in 1 Optimize anticipation and decision-making in extreme crisis situations to maintain the resilience of society.

2 The French Geological Survey The application of the method and implementation of the ExG prototype for this case study relied on a synergy of skills in human and social sciences, disaster management, and information and communication technology. The research design consisted of the steps shown in Figure 1.

THEORETICAL METHOD AND PROTOTYPAL IMPLEMENTATION

We provide a theoretical description of the ExG method and prototypal implementation as part of the APRIL project. We focus mainly on the technical specifications of steps 3, 5, 6 and 7.

Structure of a graph-inspired syntax for individual feedback aggregation

Once the relevant information contained in the unstructured feedback corpus is identified, it must be translated into data, so that it can be manipulated and analysed in a reproducible way. The ExG method extracts simple sentences from the storytelling for easy processing and visualisation. For sentence segmentation, basic level expressions [START_REF] Rosch | Principles of Categorization[END_REF] are preferred and the word order in sentences must be linear, with no embedding or distance relationships. The subject and object terms of a sentence represent nodes connected by a verb (edge), or relation (edge), with which they constitute a triple (Figure 2), as in the sentence "The EDF staff (subject) secures (verb) the electricity grid (object)".

This preliminary data structuring, based on the definition of a common syntax, has proven to be fundamental for the reconstruction of the overall experience, because it makes it possible to connect:

• heterogeneous data (qualitative, quantitative, geospatial, etc.); and

• identical pieces of information formulated using different terms, depending on the stakeholder.

It also facilitates the integration of further data (reports, official records, etc.) to complete the feedback review.

The term graph from each feedback source (the interviews in our case study) shows only the connections explicitly stated by the witness. We define these types of relations as "topological", since they are the direct links, or "edges", recognised by the observer among actors, emotions and events as being relevant to them. The individual topological term graph (or "topological graph") is assumed to capture at least part of the mind map that the witness developed experiencing the crisis, necessarily biased by their role and position, as well as other factors "external" to the events, such as their background and past experiences.

Because of the common syntax, some nodes (e.g. "prévision intensité ouragan") can refer to facts narrated by several sources, possibly in relation to different subjects, objects or attributes. Different individual topological graphs can be merged into a comprehensive multiperspective network [START_REF] Liu | Multi-perspective Network Representation Based on Human Curation[END_REF] of the overall disaster.

Although not to be considered a complete representation of everything that occurred, the resulting network contains distinct perspectives of the same events and should represent what really happened more objectively [START_REF] Fauconnier | The Way We Think[END_REF][START_REF] Smirnov | Knowledge Fusion Patterns: a Survey[END_REF].

It is worth mentioning that at least the individual outputs of this transcription process should be submitted to the feedback author (witness/interviewee/reporter) for validation. They might disagree with some specifications, such as the role of certain players, or clarify certain sequences or actions. The validation of the overall topological graph is more challenging. It should focus on a multiperspective representation of a specific topic or event obtained by filtering and/or exploring the overall topological graph. A focus group of domain experts, who may have been directly involved in the disaster, but not necessarily contributing to the feedback corpus, should discuss and reach a consensus on this new representation. Validation at this stage should also concern the cover the definition of the case-based ontology discussed below.

Under the APRIL project, the ExG prototype tool for the data editing phase (Step 3, Figure 1) used open-source wiki-based "TiddlyWiki" 7 software, considered a valuable personal and collaborative learning tool (Fitzgerald, 2007). Using the plugin TiddlyMap 8 the relevant "elementary facts" were edited at the same time as the individual topological graph, resulting in an interactive network representation of the feedback. The authors also used the search and filtering functions of the software for the analysis of the overall graph (Step 4, Figure 1). They extracted event-or topic-specific graphs by integrating and connecting terms and relations from different individual inquiries, for:

• the validation of the overall interconnections of elementary facts collected in the feedback corpus;

• the definition of the categories inspiring the case-based ontological concepts according to the criteria described below.

Semantic data model criteria and case-based ontology requirements

For a comprehensive understanding and capitalisation of this rich, complex and multiperspective feedback corpus, the overall experience should be represented on a more theoretical level. We should be able to query the elements and relations contained in the overall topological graph of the feedback using more functional and conceptual definitions, and inference processing.

Hence, the pillars of the transformation of facts into conceptual instances, core specification of the ExG method, are:

1. semantic data modelling, for the definition of a case-based hybrid ontology [START_REF] Debruyne | GOSPL: A method and tool for fact-oriented hybrid ontology engineering[END_REF];

2. the ability to translate facts into "universals" [START_REF] Bittner | Normalizing medical ontologies using Basic Formal Ontology[END_REF];

3. the production of the semantic network representing the ontological graph of the experience concerned The semantic data model is strongly interconnected with the ontology definition strategy. Therefore, both have to be treated and resolved at the same time (Step 5, Figure 1).

Concerning the definition of the ontological concepts, we referred again to the general, basic principles proposed by [START_REF] Rosch | Principles of Categorization[END_REF] for the formation of categories:

1. The task of category systems is to provide maximum information with the least cognitive effort.

2. The perceived world comes as structured information rather than as arbitrary or unpredictable attributes.

Our novel approach does not rely on an a-priori ontology, based on a literature review and generic theoretical knowledge of crisis management. In agreement with [START_REF] Furtado | A Knowledge Acquisition Tool for Multi-Perspective Concept Formation[END_REF], our hypothesis is that the definition of ontological concepts should be considered as an objective-oriented, context-dependent process. Here, "concepts" represent perceived regularity among terms recording events or objects, designated by a label [START_REF] Novak | The Theory of Underlying Concept Maps and How to Construct them[END_REF]. Moreover, concepts should be organised to represent the experience from different perspectives.

This domain-specific ontology should consist of coarse granularity concepts that do not necessarily discriminate between relevant classes on their own. Instead, the combination of these concepts for the classification of a certain term (or short text) may define, by their intersection, an inferred class that represents its best semantic definition, or domain-consistent approximation. This will affect both the design of the semantic data model and the way in which the instances are classified.

The concepts are extrapolated and selected from the overall topological graph during the analytical phase (Step 4, Figure 2). Exploratory filtering in the wiki-based tool aims to discern new concepts and relations. The design of the ExG platform involves the integration of automated [START_REF] Furth | Towards the Semantification of Technical Documents[END_REF] and semi-automatic incremental building of ontologies. However, for this case study, the extraction of concepts and vocabulary, as well as the application of the rule set to transform the corpus terms into semantic instances, are performed by recursive wiki and RFD triplestore processing, or via interactive graphical exploration, as in the example discussed below.

Figure 3. Theoretical representation of the semantic data model designed for the ExG method, chosen for the processing of feedback on the crisis management experience

The semantic data model affects the reasoning capability of the knowledge base [START_REF] Keet | An Introduction to Ontology Engineering[END_REF]. The ExG semantic model assumes a structured set of independent concepts and properties capable of describing remarkable processes constituting the experience of actors or "agents", events and attributes, useful for characterising and qualifying their instances for the aspects relevant to the application aim (Figure 3). The reference structure has been described as a "sketch data model" [START_REF] Barr | Category Theory for Computing Science[END_REF] because it is based on the category-theoretical notion of mixed sketch. In this context, a sketch is defined as a graph with imposed commutativity and other conditions; it is a way of expressing structure.

Using the wiki-based graphical tool embedded in the ExG platform, the domain expert defines (Step 5, Figure 1):

• the semantic data model suitable for the scope of the knowledge base, here a disaster management review;

• the ontology concepts, by analysing the information contained in the topological graphs.

The semantic annotation of nodes and edges

The classification process of any term contained in the overall topological graph includes checking which concepts are relevant and choosing the relevant class for each relevant concept (Step 6, Figure 1). To keep the ontology simple and adaptable to the context associated with a certain instance, the ExG semantic data model requires that each element of the topological graph is classified associating different concepts. Each object must be classified with at least one type of concept depending on its typology ("agent" or "process"), while all the types of attributes are optional concepts.

This workflow (Figure 4), from the graphical editing of elementary facts to the annotation of their terms by a dedicated ontological layer based on the aforementioned criteria results in the conceptual representation of occurrences by "universals" [START_REF] Bittner | Normalizing medical ontologies using Basic Formal Ontology[END_REF].

ExG knowledge graph querying and exploitation

This theoretical representation of the experience requires validation. However, beyond checking if the contributors to the feedback corpus are able to recognise and describe the dynamics and general characteristics of their experience, the focus group should be opened to experts from different contexts and similar experiences, to verify if the generalisation is valid for a wider range of circumstances and issues.

We use SPARQL queries to extract specific outputs and to test the consistency of the ontological mapping of input data. At this stage of the workflow, the knowledge management system's inference capabilities can be better exploited to extract original insights less obvious at the case-specific level (Step 7, Figure 2). The goal being to improve disaster management, the conceptual representation of the overall feedback graph for this specific postdisaster review may be analysed considering other hazard types, similar risks and impact scenarios. The outputs may concern critical paths and emergent relationships, alternative scenarios, potential cascade effects, at an abstract level, but still grounded on the facts collected and structured in the topological graphs.

DEMONSTRATION: AN EXAMPLE APPLICATION

Case study data collection

The scope of the APRIL project, the literature on crisis management efficacy and resilience [START_REF] Lagadec | Risques et crises : questions sur nos ancrages[END_REF]Sphere Association, 2018[START_REF] De Nicola | Knowledge Fusion for Distributed Situational Awareness driven by the WAx Conceptual Framework[END_REF] and ontologies for crisis management available in the literature [START_REF] Liu | Ontologies for Crisis Management: A Review of State of the Art in Ontology Design and Usability[END_REF][START_REF] Wienen | Accident Analysis Methods and Models -a Systematic Literature Review[END_REF] fuelled initial discussions about this research (Step 1, Figure 1). The WiP Paper -AI and Intelligent Systems for Crises and Risks Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 291 preliminary mind map of the scope of the inquiry was a term graph including the relevant elements connected by a preliminary selection of expected relations (according to expert judgement) (Figure 5). At this stage, both arguments and interconnections describing the matter of interest are still considered not necessarily comprehensive, meaning it will still be possible to add to them during feedback collection. This early stage of the research workflow does not involve any formal ontologies or data structures.

The research consortium then discussed the design of the retrospective interviews and the selection of witnesses to obtain a comprehensive, reliable feedback corpus. This analysis was carried out by another workgroup, and its details are beyond the scope of this article. However, a list of interviewee roles during the events together with a short summary of the interviews are provided, showing the representativity of the feedback sources.

Forty-six crisis managers operating in different contexts during the 2017 hurricane season are the feedback sources for this major natural disaster. Figure 6 summarises their organisations and roles:

• public (Prefecture, national police force, etc.) and private (DAUPHIN TELECOM, 9 EDF, 10 etc.) services;

• officers at the local (Saint-Martin), departmental (Guadeloupe), zonal (Martinique) and national (CIC 11 ) levels in the national crisis management plan;

• various levels of experience in crisis management, i.e. different levels of knowledge and understanding of events (no experience, training, field experience).

Two years after the events, most people having since changed roles and locations, they accepted a semi-structured individual interview to provide a multiperspective reconstruction. The meetings were between 75 and 180 minutes long and followed an adjustable script with open-ended questions, but still consistent with the mind map in Figure 5. The crisis managers were requested to do the following:

• Introduce themselves -their role, tasks, personal and professional experience,

• Share their own experience, focusing mainly on their own perception, instead of the documentary narrative,

• Detail the crisis highlights, as well as the actions carried out before, during and after the passage of each hurricane,

• Specify the sources and types of reference information for their actions and decisions.

• Describe the main difficulties they faced (i.e. domino effects, actions or decisions at different levels).

9 Telecommunications facility manager for the French West Indies

292

• Describe their organisational framework for facing that crisis (partners, collaborators and direct contacts),

• Describe their perception of preparedness.

• Give their opinion about a tool for improving major disaster management (i.e. methodological or technical tool, etc.).

As the interviews and the graphical editing of the topological graph progressed, other topics beyond those in the mind map were emphasised by the witnesses, and found to be relevant for this research. These were human factors, such as:

• personal and professional experience, which may have a significant impact on personal crisis management skills, and may affect the decision chain; and

• feelings (i.e. stress, fear, uncertainty and trust), which may explain ineffective decisions or actions, and the biased understanding of positive or negative alternatives.

The significance of these factors and their relationships with other elements influencing the development of the crisis led us to include them in the preliminary mind map. But, even more remarkably, these complementary factors, though missing in the preliminary scope of the research, partly shaped the ontological concepts and influenced the design of the dedicated semantic data model at the analysis stage of the feedback corpus (Steps 4 and 5, Figure 1).

The experience feedback processing and topological graph analysis

To breakdown the information collected by the semi-structured interviews into "elementary facts", the components of the initial mind map in Figure 6 complemented by the arguments pointed out during the interviews, were used to recognise the relevant elements cited in the corpus and label the verbs in the triples. Any term (subjects and objects) added to the individual topological graphs was referred to a noun used in the mind map: resource, message, damage, etc. As the interviews were in French, the terms of the mind map were translated and used in this language, to reduce the risk of distorting the original information during processing. The elements were labelled to respect stakeholder feedback, i.e. something considered as a resource by somebody might be referred to as a need by someone else. All the triple elements were edited manually. During the data entry, the researcher was able to verify if any element was already present in the corpus by previous interviews, and reuse the pre-existing node, in case.

The homogeneous collection of individual topological graphs obtained by each interview generated a network of nodes and links providing a graphical representation of the collective experience of the disaster. However, the visualisation of the huge amount of interconnected "elementary facts" as topologically connected terms is useless. Relevant information and critical paths needed to be obtained by different techniques. To extract topic-specific portions of this multiperspective, integrated, but still raw, data collection, we used filtering criteria and interactive gradual exploration of the overall topological graph. In the first case, the result is a semi-automatic graph focused on specifics terms, whereas the manual selections of nodes allows investigate the possible "multi-hop" paths between two elements not directly connected. Using these two techniques for topological graph exploration, we implemented the analyses required for the follow up of the ExG implementation and those concerning real elements of remarkable facts.

Analysis of a topological graph: the "blackout" issue

To show an example of extraction from the overall topological graph of the 2017 hurricane crisis, we analysed the events of energy blackouts and communication breakdown, their precursors and major consequences.

The filtering consisted in selecting a set of labels for aggregating pertinent key nodes ("réseaux" for networks , "communication HS" for communication breakdown, and "absence" for lack -of communication and energy-) and their direct relations, over a specific period (before, during and after Irma) (Figure 7).

Starting from the aforementioned filtered graph, in the second approach we made a new graph saving only those nodes we retained as pertinent to the blackout and communications breakdown review, concerning the preparation phase before Irma struck (Figure 8). We repeated iteratively the filtering and the selection until refreshing the connected nodes did not upload any new items considered "relevant" to the question.

The resulting topological graph shows a message given by the director of the communication facilities manager (DAUPHIN TELECOM) about the possibility of a communications blackout, which other stakeholders disbelieved ("incrédulité"). This finding highlights a gap in the risk analysis of the entities responsible for the safety plan and disaster management.

This new graph shows an isolated cluster of facts concerning the energy facility manager suggesting the lack of critical communication before the Irma's strike. EDF, who did not attend COD meetings at that time, overlooked a crucial piece of information to the main coordination centre. It concerned a scenario of major disruption to the power service due to the hurricane, and the plan for an early deployment of a rehabilitation taskforce ("prépositionnement renfort" in the Figure 8; the text in these last two figures is in French, as resulting from the transcription in the original language of the information.) for the electricity grid and the global communications networks at St. Barth and St. Martin.

If confirmed, the detection of this lack of information transfer is a critical issue for the effective hurricane preparedness and mitigation. Unfortunately, due to the challenges of the pandemic after February 2020, and the other research priorities of the consortium, the facts emerging from this analysis could not be validated with the contributors of the feedback corpus.

However, we investigated this particular circumstance in the knowledge graph, to verify whether other types of relationships that bridge the gap among notable actors of this crisis, emerged by semantic inference. A detailed description of each concept is beyond the scope of this work in progress. However, the annotations on Figure 9 show the Agent and Process concept classes, the types of concepts for the attributes, and explain that they are separated into "identity specific" and "context specific". According to the semantic data model of Figure 3, the combination of these types of attributes, other than their possible qualification, distinguishes between all the objects defined as agents and all the types of events retained as relevant to the case study.

Analysis of the experience knowledge graph: from facts to theory

To finalise this study case, the ExG prototype will be enriched with different SPARQL queries meeting the APRIL research objectives. For this work, we developed a semantic graph request to render a conceptual representation The graph resulting from this SPARQL request (Figure 10) contains all the entities useful for describing the terms of the topological graph in Figures 7 and8. These are "universals" that generalise the agent and resources, and their conditions, the events and activities, with their attributes. The ontological graph of the experience maintains an evidence-based real-life level that allows decisions to be taken and crisis management issues to be anticipated, even when indirectly linked to each other, such as the crucial importance of communications recovery for issuing warnings about the water supply. Figure 10 also describes the situation detected in the topological graph of Figure 8, of people aware of critical scenarios, but who might not be heard, nor exchange each other, before the disaster occurrence because they are not included in emergency response coordination meetings before the hurricane strike.

DISCUSSION

The analytical processing of the ExG ontological graph highlighted the critical paths of certain events, decisions or phenomena, as well as cascading effects (Figure 10). In this example, they revealed lack of relations, which slowed down or blocked the transfer of information crucial for good crisis management. The multiperspective representation of testimonies may suggest an improved plan for dealing with similar crises.

Finally, we obtained an abstract representation of the crisis, or a "metacrisis", including a model of relationships valid at a more general level than this specific experience, but still able to capitalise what really occurred in the past. The major value of such a dynamic and searchable representation of a post-disaster assessment lies in the capitalisation of a major disaster on more general perspective, improving the preparedness and effectiveness of the global crisis management system and increasing community resilience.

CONCLUSION

The "queryable category-based feedback knowledge graph" (ExG) that BRGM is developing and plans to test in different applications, is a knowledge management system designed to provide insights and learn lessons across the range of organisational management, decision-making and operational activities needed to achieve complex or critical objectives. The different points of view, experiences and contexts, as well as the requirements for improving this type of crisis management were collected by about forty practitioners at different levels of decision-making in public and private safety services within French civil protection institutions. We used the ExG prototype to validate the workflow, the process implementation and the minimal user requirements.

We believe that, together with the new approach to a hybrid ontology definition and the original process of knowledge collection introduced by this article, the sketch data model provides a robust framework for the feedback inductive analysis promoted by the ExG method.

The roadmap of ExG finalisation aims to produce a platform for multiperspective design and continuous improvement of resilient sociotechnical systems. This consists of modules for managing the workflow from data definition to their final manipulation and analysis. The design of the ExG platform shall remain open and able to integrate several existing solutions for specific workflow tasks, if their output results compliant to the linked data engine and the core specifications of the method. Most developmental efforts should be instead invested in optimising the data conceptualisation, the semantically enhanced analysis and the representation of outputs for different applications.

WiP Paper -AI and Intelligent Systems for Crises and Risks Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 297 crises extrêmes pour maintenir la RésILience de la société", which is funded by ANR grant ANR-18-OURA-0001, within the context of ANR call for projects "Ouragans 2017".

3

  https://www.maxqda.com/ 4 https://monkeylearn.com/ 5 https://atlasti.com/ 6 https://www.cortext.net/ WiP Paper -AI and Intelligent Systems for Crises and Risks Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 287 the various sites affected by the hurricanes, the corpus of interviews represented a multiperspective data source for a comprehensive review of the disaster, structured in a queryable graph.

Figure 1 .

 1 Figure 1. Overview of the research design, highlighting the implementation of ExG method and tool (RDF: resource description framework)

Figure 2 .

 2 Figure 2. Syntax and usage of simple expressions representing "elementary facts" in ExG, for the structured transcription of a relevant sentence or piece of useful information contained in feedback

7

  https://tiddlywiki.com/ 8 http://tiddlymap.org/ by the overall feedback.

Figure 4 :

 4 Figure 4: From facts to "theory": the conceptualisation of an experience.

Figure 5 .

 5 Figure 5. Initial term graph of the arguments and explanatory interactions defining the scope of the APRIL project research. These elements inspired the semi-structured interview framework and the feedback breakdown into "elementary facts" (Steps 2 and 3, Figure 1). Each symbol in the graph is tagged by its meaning.

10

  French energy supplier (electricity and natural gas) WiP Paper -AI and Intelligent Systems for Crises and Risks Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022

Figure 6 .

 6 Figure 6. Public and private services represented by the interviewees

Figure 7 .

 7 Figure 7. Topological graph based on specific nodes and their direct relations -automatic selection ("réseaux", "communication H.S" and "absence" before, during and after Irma)

Figure 8 .

 8 Figure 8. Topological graph based on specific nodes and their direct relations -interactive selection ("réseaux", "communication H.S" and "absence" before Irma)

WiP

  Paper -AI and Intelligent Systems for Crises and Risks Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 295 of the facts and information discussed in the analysis of the topological graphs shown above (Figure 4 and 5).

Figure 9 .

 9 Figure 9. Graphical representation of the concepts constituting the ontology implemented by ExG, for the hurricane season post-disaster review. Two types of concept are expanded to show their classes.

Figure 7 .

 7 Figure 7. Ontological graph of the impacts and cascading effects on energy and communication networks affecting the crisis management: conceptual feedback and lessons learned from Irma hurricane at St. Martin

  are thus desirable.

WiP Paper -AI and Intelligent Systems for Crises and Risks Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 286

WiP Paper -AI and Intelligent Systems for Crises and Risks Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022

ACKNOWLEDGMENTS

This work is supported by the project "APRIL--Optimiser l'Anticipation et la Prise de décision en situation de The authors acknowledge the other members of the research consortium for the fruitful and passionate discussions about the development of this original information processing methodology based on ExG, and the reviewers for their thoughtful comments and efforts towards improving this manuscript.