Charles-Alban Deledalle

Loic Denis

Giampaolo Ferraioli

Florence Tupin

COMBINING PATCH-BASED ESTIMATION AND TOTAL VARIATION REGULARIZATION FOR 3D INSAR RECONSTRUCTION

Keywords: SAR interferometry, multi-channel In-SAR, Non-local means, TV regularization

In this paper we propose a new approach for height retrieval using multi-channel SAR interferometry. It combines patchbased estimation and total variation regularization to provide a regularized height estimate. The non-local likelihood term adaptation relies on NL-SAR method, and the global optimization is realized through graph-cut minimization. The method is evaluated both with synthetic and real experiments.

INTRODUCTION

High accuracy Digital Elevation Model of the observed ground scene can be generated using Interferometric Synthetic Aperture Radar systems in a multi-channel configuration [START_REF] Bamler | Syntetic aperture radar interferometry[END_REF]2]. An effective way to combine the available multi-channel interferometric data is to exploit statistical estimation methods [START_REF] Eineder | A maximum-likelihood estimator to simultaneously unwrap, geocode, and fuse SAR interferograms from different viewing geometries into one digital elevation model[END_REF][START_REF] Ferraiuolo | Maximum a posteriori estimation of height profiles in InSAR imaging[END_REF]. The height retrieval from InSAR data poses at least two difficulties: (i) the phase information is very noisy, hence it requires some smoothing while preserving at best the spatial resolution; and (ii) the phase is wrapped, so that it may not be uniquely invertible to provide the height.

In this paper we propose to adapt patch-based methods, in particular NL-SAR approach [START_REF] Deledalle | NL-SAR: A Unified Nonlocal Framework for Resolution-Preserving (Pol)(In)SAR Denoising[END_REF], to recover directly an elevation exploiting the statistical distribution of data in the interferometric multi-channel case. Often, for simplicity, the statistical independence approximation of the multi-channel interferometric phases is adopted for describing the statistical distribution of the data. In a recently presented paper [START_REF] Baselice | Selected Topics in Applied Earth Observations and Remote Sensing[END_REF], it has been shown that the height reconstruction can be effectively obtained exploiting the whole complex data acquired in the multi-baselines interferometric configuration, removing the statistical independence assumption. Following this approach, in this paper rather than marginalizing the data distribution with respect to missing parameters, as is usually done in the literature, we exploit the joint distribution as done in [START_REF] Baselice | Selected Topics in Applied Earth Observations and Remote Sensing[END_REF]. The adopted strategy includes two steps: first NL-SAR method can provide non-local (i.e., patch-based) estimates of the covariance matrices at each pixel from the multichannel available images, while preserving at best the resolution. Second, height values can be regularized using an edge-preserving regularization such as total variation [START_REF] Shabou | Urban digital elevation model reconstruction using very high resolution multichannel InSAR data[END_REF]. Following the approach proposed in [START_REF] Sutour | Adaptive Regularization of the NL-Means: Application to Image and Video Denoising[END_REF] the problem can be formulated as maximum a posteriori estimation with a modified likelihood term. The modified likelihood enforces that the solution at pixel i is close to the observed value at that pixel but also to the observed values at pixels j that are similar (i.e., whose surrounding patches are in good match). Spatial regularity is enforced through the total variation term.

THE MODEL

Let us consider a pixel i of the whole image and let us suppose that D different channels are available. The measured values can be collected in a vector g i of D complex values. This vector is generally called the scattering vector. Under the classical hypothesis of fully developed speckle (Goodman's model), the observations g i at pixel i are distributed according to a circular complex Gaussian:

p(g i |Σ i ) = 1 π D det(Σ i ) exp -g † i Σ -1 i g i (1)
with g † i the Hermitian transpose of column vector g i . This distribution relies on the complex covariance matrix Σ i at pixel i which depends on the radiometry R, the inter-channel coherence γ a,b and the interferometric phases ψ a,b :

Σ = R      1 s 1,2 • • • s 1,D s 1,2 1 s 2,D . . . . . . . . . s 1,D s 2,D 1
     . ( 2
)
where the generic element of the matrix is defined as s a,b = γ a,b exp(jψ a,b ). The interferometric phases ψ a,b are related to the height h through a function f a,b that accounts for the interferometric baseline, eventual atmospheric distortions and other calibration parameters: ψ a,b = f a,b (h) [2]. In Eq. ( 2) the radiometry R is considered the same among the available channels.

In order to estimate the height of the pixels, a Maximum a Posteriori (MAP) approach is implemented. The likelihood term of the a posteriori distribution is derived from the distribution of Eq. ( 1) using a non-local approach: the data that can help in the estimation of the height ĥi at pixel i, are not only the observed value at that pixel but also the observed values at pixels j that have similar surroundings. This leads to a weighted maximum likelihood estimation [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF]. Concerning the a priori term the Total Variation (TV) model is adopted.

According to Bayesian approach and taking the logarithm of the non-local likelihood and the a priori term, the estimation problem becomes:

ĥ(NL) = arg min h - i j ω i,j log p(g j | h i ) + TV(h) .
(3) where h is the vector of unknown heights to be estimated (one height h i per pixel), ω i,j are the non-local coefficients that balance the weight of observations g j at pixel j according to their relevance for the estimation h i at pixel i and TV(h) is the total variation energy defined as TV(h) = (i,j) |h i -h j | where (i, j) span all neighbor pixels. The function of Eq. ( 3) can be simplified into an expression with a separable data-term. Let us consider only the first part (non-local likelihood term). After dropping the constant D log π which is irrelevant for the optimization problem, the non-local negative log-likelihood can be written as:

- j ω i,j log p(g j | Σ i ) ∝ j ω i,j g † j Σ -1 i g j + log det(Σ i ) . (4)
By introducing the coefficients λ (NL) i = j ω i,j and the non-

local empirical covariance matrix C (NL) i = 1
λi j ω i,j g j g † j , the non-local negative log-likelihood becomes:

- j ω i,j log p(g j | Σ i ) ∝ λ (NL) i log det(Σ i ) + λ (NL) i tr(Σ -1 i C (NL) i
) .

(

) 5
Finally, since log det(Σ i ) is independent from h i [START_REF] Baselice | Selected Topics in Applied Earth Observations and Remote Sensing[END_REF], and by adding the a priori term, the MAP solution for the height estimation is given by: ĥ

(NL) = arg min h - i λ (NL) i tr(Σ -1 i C (NL) i ) + TV(h) (6)
Thus, weighting the likelihood term with non local weights is equivalent of computing a non local estimation of the observations and injecting it in the energy. The non-local empirical covariance matrix C (NL) i can be computed using NL-SAR method [START_REF] Deledalle | NL-SAR: A Unified Nonlocal Framework for Resolution-Preserving (Pol)(In)SAR Denoising[END_REF]. NL-SAR is a patchbased approach adapted to multi-channel complex SAR data. Patch similarity is derived from a generalized likelihood ratio test taking the circular complex Gaussian distribution. A set of parameters (size of the patch, size of the search window, strength of pre-filtering) is tested, and the results are combined after a debiasing step to provide the "best" estimate (the quality being given by the equivalent number of looks). The sum of non-local weights λ (NL) i = j ω i,j could be set to any positive values (the weighted mean being invariant up to a multiplication factor). However, it should differ from 1 in order to give more importance to observed values g j when many locations j are similar to the reference location i compared to the case of a pixel i with no similar pixel within the search window. Following the development of [START_REF] Sutour | Adaptive Regularization of the NL-Means: Application to Image and Video Denoising[END_REF], we may define λ (NL) i to be the inverse of the estimated residual standard deviation: λ i = LNLRB i , with LNLRB i defined as the estimated equivalent number of looks at pixel i also provided by NL-SAR method [START_REF] Deledalle | NL-SAR: A Unified Nonlocal Framework for Resolution-Preserving (Pol)(In)SAR Denoising[END_REF]. Concerning the optimization step, due to the non-convexity of the data fidelity term involved in ( 6), a graph-cut based minimization method has been adopted. The minimization problem involves a non-convex but separable data-term and a convex pairwise term. It is solved exactly (up to the chosen height quantization) by graph-cuts using Ishikawa's construction [START_REF] Ishikawa | Exact optimization for markov random fields with convex priors[END_REF].

NUMERICAL EXPERIMENTS

In order to validate the presented approach a simulated test case has been considered. The dataset is made of three complex images acquired with different baselines. Two of the three available interferograms are shown in the first row of Figure 1, together with the mean coherence map and the true profile. The estimation of the true profile is not an easy task due to the presence of noise and of high phase jumps. The second row shows (from left to right) the results obtained using the Maximum Likelihood (ML) approach proposed in [START_REF] Baselice | Selected Topics in Applied Earth Observations and Remote Sensing[END_REF], using the ML-NL approach (using only the likelihood term of Eq. ( 6)), the MAP-NL approach (using Eq. ( 6) and a sub-optimal minimization procedure based on Iterated Conditional Modes (ICM)) and the MAP-NL approach (using Eq. ( 6) and an optimal minimization procedure based on graphcuts [START_REF] Ishikawa | Exact optimization for markov random fields with convex priors[END_REF].) MAP-NL achieves a strong reduction of the variance of height estimation while preserving edges (no blurring phenomenon).

The presented approach has also been tested on a real dataset. This dataset is composed of three COSMO-SkyMed Stripmap images acquired close to Naples train station. Two Second row: the results using the ML corrlelated approach, the ML-NL correlated approach, the MAP-NL approach based on ICM and the MAP-NL approach based on graph cuts of the three available interferograms are shown in the first row of Figure 2, together with the logarithm of the mean amplitude and the mean coherence map. The second row shows (from left to right) the results obtained using the Maximum Likelihood (ML) approach proposed in [START_REF] Baselice | Selected Topics in Applied Earth Observations and Remote Sensing[END_REF], using the ML-NL approach (using only the likelihood term of Eq. ( 6)), the MAP-NL approach (using Eq. ( 6) and a sub-optimal minimization procedure based on ICM) and the MAP-NL approach (using Eq. ( 6) and an optimal minimization procedure based on graph-cuts [START_REF] Ishikawa | Exact optimization for markov random fields with convex priors[END_REF]). Independent estimation of the height at each pixel leads to a very noisy result (i.e., strong variance of the heights). The regularization reduces these fluctuations without noticeable resolution loss.

CONCLUSIONS

In this paper, a non-local regularized method of height computation for multi-channel InSAR interferometry has been proposed. First results are promising and further work includes the following points. First, other experiments have to be led, specially on the influence of the coherence values on the results. Besides, the impact of channel number vs. the coherence values will be studied. On the methodological part, the influence of reflectivity and coherence values (which are pre-estimated in the presented approach) has to be analyzed and a joint estimation scheme should be studied.

Fig. 1 .

 1 Fig. 1. Simulated Dataset. First row: Two of the three available interferograms, mean coherence map and the true profile.Second row: the results using the ML corrlelated approach, the ML-NL correlated approach, the MAP-NL approach based on ICM and the MAP-NL approach based on graph cuts


P Nixon

Irwin

A Jolly
email: jolly@lisa.u-pec.fr

V Cottini

A Fayt

L Manceron

F Kwabia-Tchana

Y Benilan

J-C Guillemin

C Nixon

P Irwin

Gas phase dicyanoacetylene (C 4 N 2 ) on Titan: new experimental and theoretical spectroscopy results applied to Cassini CIRS data

Gas phase dicyanoacetylene (C4N2) on Titan: New experimental and theoretical spectroscopy results

applied to Cassini CIRS data

Introduction

 Khanna et al. (1987)have measured the infrared spectrum of solid C 4 N 2 and found a strong absorption band at 478 cm -1 matching an unassigned feature in the thermal emission spectrum of Titan, observed by the Voyager IRIS spectrometer. Using radiative transfer modeling, Samuelson et al. (1997) and later Coustenis et al. (1999) have confirmed the agreement in position between the observed spectral feature at 478 cm -1 and the laboratory spectrum of solid C 4 N 2 . Since then, C 4 N 2 has been systematically listed among the detected molecules on Titan. But concerning its presence in the gas phase, only upper limits have been determined

by Samuelson et al. (1997), de Kok et al. (2008) and Khlifi et al. (1997). Samuelson et al. (1997) computed an upper limit that is two orders of magnitude lower than the inferred concentration of C 4 N 2 ice. This is, of course, not expected under thermal equilibrium conditions, leaving the large abundance of the solid phase unexplained. Samuelson and coauthors thus proposed to explain the disequilibrium between the two C 4 N 2 phases as due to the rapidly changing conditions in Titan's atmosphere after equinox. The proposed scenario is that a strong enhancement of C 4 N 2 in both phases takes place during the dark polar winter.

After equinox, the gas is rapidly destroyed by sunlight but, because of a delayed response to the changing seasons, Titan's polar atmosphere appears to be still cooling down and thus enhancing the icy component. This scenario has been tested by de Kok et al. (2008), using Cassini CIRS data from 2007 at the end of the winter season, when significantly more C 4 N 2 gas is expected. An upper limit of gaseous C 4 N 2 was deduced, which was not in agreement with the scenario of a large buildup of C 4 N 2 during the polar winter. A detection of C 4 N 2 gas or improved new upper limit is thus still desirable to constrain the debated solid phase abundance in Titan's atmosphere.

ϯ

The Composite Infrared Spectrometer (CIRS, Flasar et al. 2004) carried on-board the Cassini spacecraft in Saturn orbit has been able to observe features of many gases in Titan's atmosphere since its first flyby in 2004. It is capable of recording spectra at a relatively high spectral resolution of 0.5 cm -1 in the mid-and far-infrared regions, where it is sensitive to vibrational emissions of gases and condensates. Besides detecting Titan's most abundant or intense species with CIRS spectra (CH 4 , HCN, CO, CO 2 , C 4 H 2 , C 2 N 2 , C 3 H 4 , HC 3 N, C 2 H 2 , C 2 H 4 , C 2 H 6 ), it recently became possible to observe features not quantitatively measurable in the first years of the mission -such as water (Cottini et al., 2012a) -to succeed in the first detection of different isotopologues with 13 C (Jennings et al., 2008, Jolly et al., 2010) and also to detect for the first time gaseous propene (Nixon et al., 2013). Improved calibration of CIRS data, accumulation of spectral data over time leading to improvements in signal-to noise (S/N) and newly available laboratory spectroscopic studies in the spectral regions explored by CIRS, including the study described in this paper, have enhanced the chance for detection of new species and/or for improvements in the computed abundance upper limits.

In this work, gaseous C 4 N 2 samples have been synthesized and purified in order to measure precise band intensities. Previous experimental results by Samuelson et al. (1997) andKhlifi et al. (1997) have been revised and the intensity of the ν 9 band at 107 cm -1 has been determined for the first time. In addition, we have developed the first line list of C 4 N 2 for both bending modes ν 8 and ν 9, based on the improvement of a detailed rotational analysis by Fayt et al. (2004).

This new set of precise spectroscopic parameters has given us the chance to search for gaseous C 4 N 2 through the unexplored ν 9 band at 107 cm -1 . This was done by comparing CIRS data with the results of a radiative transfer model, including the new ν 9 line list, in the far infrared region where the sensitivity of the detector is much better than in the spectral region of the ν 8 mode (472 cm -1 ).

Experimental

Dicyanoacetylene (2-Butynedinitrile) was prepared by a method previously reported by Coll et al. (1999). The purity of the sample was checked using mass spectrometry just before injection in the cell. No impurity, other than water and nitrogen could be detected within the ϰ sensitivity limit of our setup (about 0.5% of the C 4 N 2 peaks), thus 98 % represents a conservative estimate of the sample purity. As can be seen in figure 1, only main peak mass 76 and fragment masses 50, 37, 26, 24, 12 were observed, in agreement with the NIST standard ionization mass spectra of C 4 N 2 . Note that mass 62 fragment was not observed in our spectrum (even though the same, 70 eV ionization energy was used), but given its assignment (C 4 N + ), it is likely that it did not originate from the C 4 N 2 precursor in the NIST spectrum. Dicyanoacetylene spectra were recorded between 50 and 650 cm -1 , using the Fourier Transform spectrometer (Bruker IFS125HR) located at the AILES beam line at Synchrotron SOLEIL, in France. It was equipped with a 6 µm Si/mylar multilayer beam splitter and a 4 Kliquid helium cooled Si composite bolometer detector. All spectra were recorded with the internal Globar source, an aperture diameter of 3.15 mm, and taken at room temperature (296.5 K) using a multipass cell of 20 cm base length for a total optical path of 84.9 cm. The sample pressure was monitored using 10 and 100 mbar range thermostatic capacitive gauges (Pfeiffer vacuum, Germany) with 0.1 % stated accuracy. ϱ

Far infrared intensity measurements

Spectra in the far infrared were recorded at 0.1 and 0.5 cm -1 resolution for various pressures between 0.5 and 59 mbar. Adding a broadening gas is commonly used to avoid saturation effects, as observed in our previous studies with HC 3 N (Jolly et al., 2007) or C 2 N 2 (Fayt et al., 2012b). In the case of C 4 N 2 , adding 800 mbar of nitrogen to the sample did not show any effect on the absorption spectra, even for strong Q branches, so that only pure samples were used in the present study. We already observed this phenomenon when studying other "heavy" molecules like HC 5 N (Benilan et al., 2007) or C 6 H 2 (Shindo et al., 2003) and believe that small rotational constants implying very closely lying rotational lines are able to avoid saturation effects in the same way as line broadening in lighter molecules.

Figure 2 shows the C 4 N 2 spectrum from 50 to 650 cm -1 , as recorded at 0.1 cm -1 resolution with a pressure of 4 mbar. The two fundamental perpendicular bands ν 9 and ν 8 dominate this spectrum with their strong and sharp Q-branches at 107.6 cm -1 and 471.6 cm -1 , respectively. A parallel combination band (ν 6 +ν 9 ) is observed at 610.9 cm -1 , as well as two weaker parallel difference bands (ν 6 -ν 9 ) at 398.0 cm -1 and (ν 8 -ν 7 ) at 209.6 cm -1 . Intensities in the 50 -450 cm -1 range (with ν 9 ) are reported here for the first time, while the region above 450 cm -1 (with ν 8 ) was previously reported by Khlifi et al. (1997).

In Winther's report (ASP Conference Series 1995), ν 8 was believed to be the strongest band by about a factor of two compared to ν 9 , but Jensen (2004), on the contrary, predicted that ν 9 was 10 to 40 % stronger than ν 8 , depending on the calculation methods. The present work shows that ν 9 is significantly stronger than ν 8, in agreement with Jensen's prediction.

In this study, integrated absorption coefficients for all five bands have been derived from all recorded spectra, regardless of the resolution. Results reported in Table 1 have been obtained by averaging integrated absorption coefficients using spectra up to 4 mbar for the strong bending modes, only from 4 to 60 mbar for the two weakest combination bands and using all spectra from 0.5 to 60 mbar for the strongest combination bands. The goal of this selection is to eliminate small absorption values, as well as transmission values close to zero. As can be seen in figure 3, the dispersion of the individual values is very small representing a maximum of 3 % deviation from the average. This dispersion has been used to evaluate the uncertainty ϲ on the results given in Table 1. The measured coefficients are very consistent over a large range of pressure and for two different resolutions, thus excluding any saturation effect. The present results (Table 1) can be compared with those of Khlifi et al. (1997) for ν 6 +ν 9 and ν 8 . We first found a strong disagreement by more than a factor of two. But, by reading carefully Khlifi et al. 's paper (1997), it was found that all published integrated absorption coefficients were multiplied by a factor ln(10). While it is common to multiply experimentally determined absorbance (log I/I 0 ) by ln(10) to obtain integrated absorption coefficients in cm - 2 atm -1 (base e), we suppose that, in this case, experimental absorbance were already determined in base e as confirmed by Khlifi et al.'s caption of figure 2, so that it became a mistake to multiply by ln(10). We therefore report in table 1, Khlifi et al.'s results divided by this factor and, finally, find a perfect agreement for the combination band and a 10 % difference for the integrated absorption coefficient of ν 8 . This slight discrepancy can be due to a different resolution (0.1-0.5 in our study compared to 4 cm -1 ), causing a significant effect for such a sharp band. As mentioned in the introduction, Samuelson et al. (1997) determined an upper limit of the vapor mole fraction of C 4 N 2 in Titan's atmosphere, using their own laboratory data on the ν 8 band. The values published by Samuelson et al., a mean absorption ϳ cross section of 1.94 10 -19 cm 2 mol -1 and a band width of 8 cm -1 , can be converted to an integrated absorption coefficient at 296 K: 38.5 cm -2 atm -1 . It is thus 25 % lower than the presently determined coefficient. Very few details about the experimental protocol are given in Samuelson et al.'s publication so that we cannot try to find any explanation but an eventual impurity in the sample could easily explain this discrepancy. 10) (see explanation in the text).

ϴ

Rotational analysis and band spectra simulations

The ν 9 band system of C 4 N 2 has been studied for the first time at high resolution by Winther et al. (1994). A very large number of hot bands were found to overlap, leading to unresolved Qbranches and serious difficulties in the rotational analysis. Nevertheless, the twelve strongest hot bands could be analysed. The very large number of hot bands is due to a high value of the vibrational partition function (Q v ), as a consequence of very low lying vibrational states.

Using the list of all nine vibrational modes given by Winther et al. ( 2005) and the formula given by Herzberg (1945), a Q v value of 18.4 can be calculated at 296 K, which means that 95 % of the molecules are in an excited vibrational state at room temperature. Even at 150 K, the average temperature of Titan's atmosphere, hot bands are very relevant, since they still account for 67 % of the total band system intensity.

In 2004, the global rovibrational analysis of linear molecules developed in Louvain-la-Neuve, initially applied to pentatomic molecules (Vigouroux et al., 2000), has been adapted for hexatomic molecules and applied to C 4 N 2 (Fayt et al., 2004). Furthermore, general procedures In 2005, the ν 7 +ν 9 (368 cm -1 ) and 2ν 7 -ν 9 (403 cm -1 ) band complexes have been analysed by the same group (Winther et al., 2005). On the basis of higher combinations of ν 7 and ν 9 modes, they have established the basic model for the anharmonic and Coriolis interactions between the four bending modes (ν 6 to ν 9 ) and the ν 3 stretching mode. This interaction scheme is illustrated in their figure 3 for the (4ν 9 ) polyad to which we can associate a polyad quantum number N = 4, with N ≡ 14v 1 +14v 2 +4v 3 +15v 4 +7v 5 +4v 6 +2v 7 +3v 8 +v 9 , by analogy with From that time, on the basis of the excellent complementary spectra recorded in Oulu, the global analysis has been extended to vibrational states up to more than 2000 cm -1 , including the modes 3, 5, 6, 7, 8, and 9 and their combinations (the modes 1, 2, and 4 are above 2100 cm -1 ). From the fit applied to 10650 selected lines in 427 bands, we have determined a set of 266 molecular parameters, and the agreement with the high resolution spectra is currently within 0.0001 to 0.001 cm -1 .

By diagonalisation of the energy matrices based on those parameters we determine the eigenvalues (rovibrational energies) and eigenvectors of any N polyad of interest. For the time being we limit our calculations to N = 16 because the rank of the matrices rapidly increases with N (rank = 918, 1266, and 1762 for N = 14, 15, and 16 respectively). For a given vibrational transition with the corresponding transition dipole moment, a program calculates the wavenumber and the intensity of all lines of all subbands of all pairs of polyads (N = 1 ← 0 to 16 ← 15 for the ν 9 band, and N = 3 ← 0 to 16 ← 13 for the ν 8 band because the ν 8 state belongs to the N = 3 polyad).

ϭϭ

In addition to the large number of hot bands, the small rotational constant of C 4 N 2 spreads the population at room temperature into more than 200 different rotational states resulting in more than 600 rovibrational transitions for the cold band alone (N = 1 ← 0). Due to the degeneracy of the vibrational bending mode ν 9 , the number of rovibrational transitions belonging to the first hot band system (N = 1 ← 0) is three times higher. In addition, this hot band system is much more intense than the cold band due partly to the vibrational factor which has been described in details by Fayt et al. (2004). As can be seen in figure 4, this is also true at 150 K where the first hot band is the most contributing hot band system. At room temperature, the contributions of the hot band systems continue to increase up to N = 7 ← 6. While the contribution of this hot band system is still important at room temperature, the intensity is already spread into 130 000 lines. The integrated intensity which is also represented in figure 4 shows that at 150 K, the band system intensity stagnates with the addition of the N = 10 ← 9 hot band system which accounts for only 0.4 % of the total intensity. On the contrary, at room temperature, the contribution of the last calculated hot band system still accounts for more than 2 % of the total intensity and the integrated intensity has not reached the total band system intensity given by the stagnation level of the intensity calculated at 150 K.

ϭϮ Calculations presented in figure 4 ensure that 100 % of the intensity of the band system is included in our calculated line list of the ν 9 band at 150 K, which is not the case at room temperature. This is an important result in the context of an application to Titan's low temperature atmosphere. ϭϯ

In figure 5 we compare a calculated with an experimental transmission spectrum taken at room temperature, since no low temperature spectra were recorded in the laboratory. The comparison is very satisfying concerning the shape of the band and many small structures which are very well reproduced in the modelled spectrum. As expected, about 10 % of the band intensity is missing in the calculated spectrum compared to the experimental spectra because of the incomplete line list. Figure 5 also shows a calculated spectrum at 150 K which is shifted down by 0.2 for the clarity of the figure. The shape of the spectrum at 150 K changes strongly, showing much stronger and sharper peaks than at room temperature and also a much narrower profile. Those variations are particularly spectacular at the resolution of 0.1 cm -1 that was chosen in figure 5, but even at 0.5 cm -1 , the best CIRS resolution, the central peak of the ν 9 band of C 4 N 2 should benefit from a large intensity enhancement at 150 K compared to the observed peak at room temperature. Such a sharp peak at low temperature is clearly increasing the detection chances of C 4 N 2 in Titan's atmosphere.

C 4 N 2 upper limits from CIRS data

We proceeded to search for the signature of gaseous C 4 N 2 in Titan's CIRS spectra using the new line list of C 4 N 2 mentioned above; in particular looking for the most intense band centered around 107 cm -1 (the ν 9 ). Since no emissions of C 4 N 2 were observed, we instead retrieve a value for the abundance upper limit in Titan's lower stratosphere.

We use two different types of CIRS spectra corresponding to nadir observations of Titan's disk and of its limb. These spectra were acquired by the far-infrared focal plane (FP1) of CIRS, which consists of a circular field-of-view (FOV) with a 3.9 mrad angular diameter at full width half maximum, spanning wavenumbers 10-600 cm -1 (Flasar et al., 2004).

We consider an average of ~1800 high resolution (0.5 cm -1 ) CIRS nadir spectra of Titan during northern (60° -90°) winter (acquired in Dec. 2006-Dec. 2007), where the gas is predicted to increase substantially; we also ϭϰ

We use the strongest band of C 4 N 2 centered at 107 cm -1 (ν 9 ) in preference to the ν 8 band at 471 cm -1 , because it is more intense and also because of the higher sensitivity of the CIRS detector in the far infrared region compared to the 400-500 cm -1 region. The range 100-112 cm -1 , used to test the presence of C 4 N 2 , was chosen because it includes a methane line (at 104.5 cm -1 ) and enough wavenumbers to evaluate the noise but yet avoid the presence of other gas or instrumental issues.

For Titan's atmospheric model and radiative transfer computations we use the same parameters for gas spectral properties, aerosols, collision induced absorption coefficients, and adopt the same code (NEMESIS, (Irwin et al., 2008)) as described in (Cottini et al., 2012a;Cottini et al., 2012b). For this study, we use a temperature profile representative of northern latitudes (74°) constructed using Cassini radio occultations (Schinder et al., 2012). This is the most appropriate available profile to fit both averages that were used in this work, acquired in the same period and latitudes. In Fig. 6 the temperature profile is shown, plus the C 4 2 saturated vapor pressures (SVP) as a function of temperature (Fray and Schmitt, 2009) for five possible values of gas mixing ratios. Their intersection provides the pressure (altitude) at which the gas condensates; these values are used to set the vertical profiles of C 4 N 2 , to zero below the condensation altitude for the various mole fractions. In contrast to temperature profiles at lower latitudes, around 74°N, condensation occurs at higher altitudes since there is a cooling of part of the stratosphere. Therefore, the altitude range in which we have condensation for different C 4 N 2 mixing ratios is also more limited.

ϭϱ Their intersection provides the pressure at which the gas should condense: ~ 114 km for a mixing ratio q of 10 -12 , ~128 km for q = 10 -11 , ~132 km for q = 10 -10 , ~138 km for q = 10 -9 and ~145 km for q = 10 -8 .

We first model the spectrum in the range of interest by fitting the methane band at 104.5 cm -1 and retrieving at the same time a multiplying factor to the input aerosol density profile. Then we fix the retrieved values and compute synthetic spectra introducing C 4 N 2 for different abundances in the forward calculations. For the upper limit computation we adopt the same method applied in Teanby et al. ( 2009) and Nixon et al. ( 2010); we define a measure of agreement between model and dataχ 2 -weighted by an estimate of the random noise in terms of standard deviationσ j -of the residuals in the considered spectral range:

ቀܫ ௗ௧ ሺߥ ሻ െ ܫ ௗ ൫ߥ , ݍ ൯ቁ ଶ ߪ ଶ ெ ୀଵ ϭϲ
I data( ν i) and I model( ν i) are respectively the data and model spectra at wavenumber ν i , while q j is the test mixing ratio of C 4 N 2 . χ 0 2 is the reference case for q j = 0.

We then compute synthetic spectra over a range of q j and each time we calculate the change to the χ 2 , defined as ∆χ 2 = χ j 2χ 0 2 .

In Fig. 7 we show ∆χ 2 as a function of the C N 2 mixing ratio q j . Detection would be made if ∆χ 2 was decreasing to a minimum. In our case ∆χ 2 increases monotonically and when it reaches a level of +1, +4 or +9 respectively we determine an upper limit on the abundance at the 1-σ, 2-σ, and 3-σ level. the measure of agreement between data and model computed for a range of gas abundances from the one without the gas. Vertical dashed lines show the abundances for which ∆χ 2 is +1, +4, +9, corresponding to gas non-detections (upper limits) at the 1-σ, 2-σ and 3-σ significance levels respectively.

Using the method described above we computed the upper limits -see Table 2. We have listed the CIRS observations used to compute both averages and their latitudes. We also indicate the corresponding altitude computed for nadir spectra, based on the sensitivity of the ϭϳ spectrum to the gas abundance using gas profiles that are constant above the level of 100% saturation vapor pressure and zero below. Altitudes of limb spectra are deduced from the geometry of the observations. The 1-σ Noise Equivalent Spectral Radiance (NESR) is estimated as the standard deviation of the residuals computed for the spectral range. At the 1σ level we obtain an upper limit of 7x10 -10 for the nadir average and of 5.3x10 -10 for the limb average, with errors as standard deviation of the residuals equal to respectively 0.42 and 4.37 nW cm -2 sr -1 /cm -1 .

Our results improve upon the previous upper limit for C 4 N 2 determined from CIRS data by de By comparison of Table 2 with Fig. 6, we see that our upper limits (applicable around 130 km of altitude for nadir measurements and 130-160 for the limb ones) are similar to the upper limits from saturation mixing around the same altitude, therefore allowing ice to be potentially present around and below 130 km. The ice feature was possibly observed by Anderson et al. (2010) at 130-160 km, where our limb measurements restrict the gas abundance to less than 1.5x10 -9 (3-sigma limit). Condensation at this level would occur for similar or higher gas abundances; therefore the detection of the ice feature is in principle possible, especially considering that the CIRS FP1 field of view covers a wide range of altitudes. Limb average of T35 70°N 133-161 4.37 5.3x10 -10 1.04x10 -9 1.52x10 -9 a part per billion ϭϴ

Conclusions

New experimental measurements of the infrared spectrum of C 4 N 2 reaching to the far infrared enabled us to determine the strength of the ν 9 band at 107 cm -1 . This vibrational band system is composed of a very large number of lines belonging to many hot bands which have been thoroughly analyzed by a global analysis method. As a result of our rovibrational analysis together with the intensity measurements, we determined the first line list of the ν 9 band of C 4 N 2 . Considering the sharpness and the strength of the band and the good sensitivity of the CIRS detector in ν 9 band region, the detection condition of C 4 N 2 in the gas phase appeared better than ever. Yet, no signal was observed and only an upper limit could be determined thanks to the inclusion of the new line list in our radiative transfer model of Titan's atmosphere. We obtain an abundance upper limit of C 4 N 2 in the gas phase which does not completely rule out the presence of C 4 N 2 in the solid phase at the observed altitude. However, by confirming the low abundance upper limit, we reconfirm the inconsistency in the gas-tosolid ratio pointed out by Samuelson et al. (1997) • Infrared spectra in far and mid-infrared of dicyanoacetylene with a pure sample.

• First band intensity measurement of the ν 9 band.

• Global rovibrational analysis and first line list calculation for the ν 9 band.

• Abundance upper limit determination of gaseous dicyanoacetylene in Titan's atmosphere using radiative transfer calculation and CASSINI-CIRS far infrared observations.

Figure 1 :

 1 Figure 1: Sample mass spectra (lower panel) compared to NIST standard ionization mass spectra (upper panel) of C 4 N 2 .

Figure 2 :

 2 Figure 2: Far infrared spectrum of pure C 4 N 2 at 0.1 cm -1 resolution and a pressure of 4 mbar.

Figure 3 :

 3 Figure 3: Integrated absorption coefficients for the five observed vibrational bands between 50 and 650 cm -1 determined for various sample pressures and two different resolutions. The dotted line shows the averaged value.

  have been developed for calculation of the relative (and absolute) intensities of all allowed ϭϬ transitions between two vibrational polyads of linear molecules, taking into account the wavefunction mixing due to essential or accidental resonances. Those predictions in frequency and intensity of all expected lines belonging to bands above a certain intensity threshold help to identify new hot bands. Each new identification progressively improves the molecular parameters and the precision of the prediction, until the weakest bands are assigned. The final results obtained by Fayt et al. (2004) were the assignment and analysis of almost 100 different bands belonging to the ν 9 band system and the determination of a basic set of 40 global rotational and vibrational parameters, limited to the ν 9 and ν 7 modes.

  C 2 H 2(Amyay et al., 2009) orICN (Fayt et al., 2012a). A new set of 84 molecular parameters was obtained, of which 26 concern the anharmonic and Coriolis resonances. Details about the global rovibrational analysis of C 4 N 2 and the calculation of any spectrum (wavenumbers and intensities), as well as many examples of intensity calculations, are given inFayt et al. (2004) andWinther et al. (2005).

Figure 4 :

 4 Figure 4: Contribution of the hot band systems to the overall band intensity of ν 9 at 296 K (red circles) and 150 K (blue squares): plain objects show the individual intensities of hot band systems from the N" polyad; open objects give the intensities integrated up to and including the hot band system from the N" polyad.

Figure 5 :

 5 Figure 5: Experimental transmission spectrum of the ν 9 bending mode of C 4 N 2 at room temperature and 0.1 cm -1 resolution compared to calculated transmissions using the new line list described above for 296 and 150 K. The calculated transmission at 150 K has been shifted down by 0.2 for the clarity of the graph.

  use a vertical average (25 spectra centered at the altitude range 133-161 km) from a limb integration of Titan at 70°N acquired during winter (Sept. 2007), the same data in which Anderson et al. (2010) possibly observed the solid C 4 N 2 feature at 478 cm -1 .

Figure 6 :

 6 Figure 6: The temperature profile (in black) for a latitude of 74°N adopted for our atmospheric model is taken from Cassini radio occultation measurements (Schinder et al., 2012). In color are shown saturated vapor pressures (from Fray et al., 2009) of C 4 N 2 for five possible mixing ratios. Their intersection provides the pressure at which the gas

Figure 7 :

 7 Figure 7: Left panels: in black are shown averages of CIRS nadir (above) and limb (below) spectra that we used to compute C 4 N 2 upper limits. In color are computed C 4 N 2 gas spectra for different possible abundance values. Right panel: we plot in black the deviation (∆χ 2 ) of

  Kok et al. (2008) and equal to 9x10 -9 .Samuelson et al. (1997) derived a 1-σ upper limit of 4x10 -10 for the stratosphere based on the absence of emission in the v 8 band at 471 cm -1 from Voyager 1 IRIS spectra acquired during the 1980 flyby.Khlifi et al. (1997) estimated a weaker restriction of 8.5 x10 -9 also from the IRIS dataset, by comparison of the noise level at 471 cm -1 with the observed emission of HC 3 N at 500 cm -1 , and scaling for the respective band intensities.

Table 1 :

 1

	ϵ

C 4 N 2 integrated absorption coefficients in the far infrared compared to Khlifi et al.'s results divided by a factor of ln(

Table 2

 2

			: C 4 N 2 abundance upper limits
	Data	Latitude	Altitude (km)	1 σ NESR (nW cm -2 sr -1 /cm -1 )	C 4 N 2 Upper Limits (ppb a ) 1 σ 2 σ 3 σ
	Nadir average of T21, T22, T23, T24, T26, T27, T28, T29, T38, T39	60°-90°N	130 -6 +30	0.42	7x10 -10	1.08x10 -9 1.53x10 -9

phase dicyanoacetylene (C 4 N 2 ) on Titan: new experimental and theoretical spectroscopy results applied to Cassini CIRS data

  and deKok et al. (2008). D͕͘ Ğƚ Ăů͕͘ ϮϬϭϬ͘ WĂƌƚŝĐůĞ ƐŝnjĞ ĂŶĚ ĂďƵŶĚĂŶĐĞ ŽĨ , ϯ E ŝĐĞ ŝŶ dŝƚĂŶΖƐ ůŽǁĞƌ ƐƚƌĂƚŽƐƉŚĞƌĞ Ăƚ ŚŝŐŚ ŶŽƌƚŚĞƌŶ ůĂƚŝƚƵĚĞƐ͘ /ĐĂƌƵƐ͘ ϮϬϳ͕ ϵϭϰͲϵϮϮ͘ ĞŶŝůĂŶ͕ z͕͘ Ğƚ Ăů͕͘ ϮϬϬϳ͘ /ŶĨƌĂƌĞĚ ďĂŶĚ ŝŶƚĞŶƐŝƚŝĞƐ ŽĨ ĐLJĂŶŽďLJƚĂĚLJŝŶĞ ;, ϱ EͿ ďĞƚǁĞĞŶ ϰϬϬ ĂŶĚ ϰϬϬϬ ĐŵͲϭ͘ ͘ :ŽƵƌŶĂů ŽĨ DŽůĞĐƵůĂƌ ^ƉĞĐƚƌŽƐĐŽƉLJ͘ Ϯϰϱ͕ ϭϬϵͲϭϭϰ͘ Žůů͕ W͕͘ Ğƚ Ăů͕͘ ϭϵϵϵ͘ ZĞƉŽƌƚ ĂŶĚ ŝŵƉůŝĐĂƚŝŽŶƐ ŽĨ ƚŚĞ ĨŝƌƐƚ ŽďƐĞƌ|ĂƚŝŽŶ ŽĨ ϰ E Ϯ ŝŶ ůĂďŽƌĂƚŽƌLJ ƐŝŵƵůĂƚŝŽŶƐ ŽĨ dŝƚĂŶΖƐ ĂƚŵŽƐƉŚĞƌĞ͘ WůĂŶĞƚĂƌLJ ĂŶĚ ^ƉĂĐĞ ^ĐŝĞŶĐĞ͘ ϰϳ͕ ϭϰϯϯͲϭϰϰϬ͘ ŽƚƚŝŶŝ͕ s͕͘ Ğƚ Ăů͕͘ ϮϬϭϮĂ͘ tĂƚĞƌ |ĂƉŽƌ ŝŶ dŝƚĂŶΖƐ ƐƚƌĂƚŽƐƉŚĞƌĞ ĨƌŽŵ ĂƐƐŝŶŝ /Z^ ĨĂƌͲŝŶĨƌĂƌĞĚ ƐƉĞĐƚƌĂ͘ /ĐĂƌƵƐ͘ ϮϮϬ͕ ϴϱϱͲϴϲϮ͘ ŽƚƚŝŶŝ͕ s͕͘ Ğƚ Ăů͕͘ ϮϬϭϮď͘ ^ƉĂƚŝĂů ĂŶĚ ƚĞŵƉŽƌĂů |ĂƌŝĂƚŝŽŶƐ ŝŶ dŝƚĂŶΖƐ ƐƵƌĨĂĐĞ ƚĞŵƉĞƌĂƚƵƌĞƐ ĨƌŽŵ ĂƐƐŝŶŝ /Z^ ŽďƐĞƌ|ĂƚŝŽŶƐ͘ WůĂŶĞƚĂƌLJ ĂŶĚ ^ƉĂĐĞ ^ĐŝĞŶĐĞ͘ ϲϬ͕ ϲϮͲϳϭ͘ ŽƵƐƚĞŶŝƐ͕ ͕͘ Ğƚ Ăů͕͘ ϭϵϵϵ͘ WůĂƵƐŝďůĞ ĐŽŶĚĞŶƐĂƚĞƐ ŝŶ dŝƚĂŶΖƐ ƐƚƌĂƚŽƐƉŚĞƌĞ ĨƌŽŵ sŽLJĂŐĞƌ ŝŶĨƌĂƌĞĚ ƐƉĞĐƚƌĂ͘ WůĂŶĞƚĂƌLJ ĂŶĚ ^ƉĂĐĞ ^ĐŝĞŶĐĞ͘ ϰϳ͕ ϭϯϬϱͲϭϯϮϵ͘ ĚĞ <ŽŬ͕ Z͕͘ Ğƚ Ăů͕͘ ϮϬϬϴ͘ ŽŶĚĞŶƐĂƚŝŽŶ ŝŶ dŝƚĂŶΖƐ ƐƚƌĂƚŽƐƉŚĞƌĞ ĚƵƌŝŶŐ ƉŽůĂƌ ǁŝŶƚĞƌ͘ /ĐĂƌƵƐ͘ ϭϵϳ͕ ϱϳϮͲ ϱϳϴ͘ ϭϵ &ĂLJƚ͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϭϮĂ͘ ,ŝŐŚ ƌĞƐŽůƵƚŝŽŶ &d/Z ƐƉĞĐƚƌƵŵ ŽĨ ĐLJĂŶŽŐĞŶ ŝŽĚŝĚĞ ďĞƚǁĞĞŶ ϮϬϬ ĂŶĚ ϱϬϬϬ ĐŵͲ ϭ͘ 'ůŽďĂů ƌŽ|ŝďƌĂƚŝŽŶĂů ĂŶĂůLJƐŝƐ ŽĨ /Z ĂŶĚ Dt ĚĂƚĂ ĨŽƌ /E͘ :ŽƵƌŶĂů ŽĨ YƵĂŶƚŝƚĂƚŝ|Ğ ^ƉĞĐƚƌŽƐĐŽƉLJ Θ ZĂĚŝĂƚŝ|Ğ dƌĂŶƐĨĞƌ͘ ϭϭϯ͕ ϭϭϳϬͲϭϭϵϰ͘ &ĂLJƚ͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϭϮď͘ &ƌĞƋƵĞŶĐLJ ĂŶĚ ŝŶƚĞŶƐŝƚLJ ĂŶĂůLJƐĞƐ ŽĨ ƚŚĞ ĨĂƌ ŝŶĨƌĂƌĞĚ ŶƵ;ϱͿ ďĂŶĚ ƐLJƐƚĞŵ ŽĨ ĐLJĂŶŽŐĞŶ ; Ϯ E Ϯ Ϳ ĂŶĚ ĂƉƉůŝĐĂƚŝŽŶƐ ƚŽ dŝƚĂŶ͘ :ŽƵƌŶĂů ŽĨ YƵĂŶƚŝƚĂƚŝ|Ğ ^ƉĞĐƚƌŽƐĐŽƉLJ Θ ZĂĚŝĂƚŝ|Ğ dƌĂŶƐĨĞƌ͘ ϭϭϯ͕ ϭϭϵϱͲϭϮϭϵ͘ &ĂLJƚ͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϬϰ͘ ŶĂůLJƐŝƐ ŽĨ ƚŚĞ ν ϵ ďĂŶĚ ĐŽŵƉůĞdž ŽĨ ĚŝĐLJĂŶŽĂĐĞƚLJůĞŶĞ ĂŶĚ ĂƉƉůŝĐĂƚŝŽŶ ŽĨ Ă ƚŚĞŽƌLJ ŽĨ ƌĞůĂƚŝ|Ğ ŝŶƚĞŶƐŝƚŝĞƐ ƚŽ Ăůů ƐƵďďĂŶĚƐ͘ :ŽƵƌŶĂů ŽĨ DŽůĞĐƵůĂƌ ^ƉĞĐƚƌŽƐĐŽƉLJ͘ ϮϮϰ͕ ϭϭϰͲϭϯϬ͘ &ůĂƐĂƌ͕ &͘ D͕͘ Ğƚ Ăů͕͘ ϮϬϬϰ͘ džƉůŽƌŝŶŐ ƚŚĞ ^ĂƚƵƌŶ ƐLJƐƚĞŵ ŝŶ ƚŚĞ ƚŚĞƌŵĂů ŝŶĨƌĂƌĞĚ͗ dŚĞ ŽŵƉŽƐŝƚĞ /ŶĨƌĂƌĞĚ ^ƉĞĐƚƌŽŵĞƚĞƌ͘ ^ƉĂĐĞ ^ĐŝĞŶĐĞ ZĞ|ŝĞǁƐ͘ ϭϭϱ͕ ϭϲϵͲϮϵϳ͘ &ƌĂLJ͕ E͕͘ ^ĐŚŵŝƚƚ͕ ͕͘ ϮϬϬϵ͘ ^ƵďůŝŵĂƚŝŽŶ ŽĨ ŝĐĞƐ ŽĨ ĂƐƚƌŽƉŚLJƐŝĐĂů ŝŶƚĞƌĞƐƚ͗ ďŝďůŝŽŐƌĂƉŚŝĐ ƌĞ|ŝĞǁ͘ WůĂŶĞƚĂƌLJ ĂŶĚ ^ƉĂĐĞ ^ĐŝĞŶĐĞ͘ ϱϳ͕ ϮϬϱϯͲϮϬϴϬ͘ ,ĞƌnjďĞƌŐ͕ '͕͘ ϭϵϰϱ͘ DŽůĞĐƵůĂƌ ƐƉĞĐƚƌĂ ĂŶĚ ŵŽůĞĐƵůĂƌ ƐƚƌƵĐƚƵƌĞ͘ //͘ /ŶĨƌĂƌĞĚ ĂŶĚ ZĂŵĂŶ ƐƉĞĐƚƌĂ ŽĨ ƉŽůLJĂƚŽŵŝĐ ŵŽůĞĐƵůĞƐ͘ sĂŶ EŽƐƚƌĂŶĚ ZĞŝŶŚŽůĚ ŽŵƉĂŶLJ͕ EĞǁ zŽƌŬ͘ /ƌǁŝŶ͕ W͘ '͘ :͕͘ Ğƚ Ăů͕͘ ϮϬϬϴ͘ dŚĞ ED^/^ ƉůĂŶĞƚĂƌLJ ĂƚŵŽƐƉŚĞƌĞ ƌĂĚŝĂƚŝ|Ğ ƚƌĂŶƐĨĞƌ ĂŶĚ ƌĞƚƌŝĞ|Ăů ƚŽŽů͘ :ŽƵƌŶĂů ŽĨ YƵĂŶƚŝƚĂƚŝ|Ğ ^ƉĞĐƚƌŽƐĐŽƉLJ Θ ZĂĚŝĂƚŝ|Ğ dƌĂŶƐĨĞƌ͘ ϭϬϵ͕ ϭϭϯϲͲϭϭϱϬ͘ :ĞŶŶŝŶŐƐ͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϬϴ͘ /ƐŽƚŽƉŝĐ ZĂƚŝŽƐ ŝŶ dŝƚĂŶΖƐ ƚŵŽƐƉŚĞƌĞ ĨƌŽŵ ĂƐƐŝŶŝ /Z^ >ŝŵď ^ŽƵŶĚŝŶŐ͗ , ϯ E ŝŶ ƚŚĞ EŽƌƚŚ͘ ƐƚƌŽƉŚLJƐŝĐĂů :ŽƵƌŶĂů͘ ϲϴϭ͕ >ϭϬϵͲ>ϭϭϭ͘ :ĞŶƐĞŶ͕ :͘ K͕͘ ϮϬϬϰ͘ sŝďƌĂƚŝŽŶĂů ĨƌĞƋƵĞŶĐŝĞƐ ĂŶĚ ƐƚƌƵĐƚƵƌĂů ĚĞƚĞƌŵŝŶĂƚŝŽŶ ŽĨ ĚŝĐLJĂŶŽĂĐĞƚLJůĞŶĞ͘ :ŽƵƌŶĂů ŽĨ DŽůĞĐƵůĂƌ ^ƚƌƵĐƚƵƌĞͲdŚĞŽĐŚĞŵ͘ ϲϳϴ͕ ϮϯϯͲϮϯϳ͘ :ŽůůLJ͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϬϳ͘ EĞǁ ŝŶĨƌĂƌĞĚ ŝŶƚĞŐƌĂƚĞĚ ďĂŶĚ ŝŶƚĞŶƐŝƚŝĞƐ ĨŽƌ , ϯ E ĂŶĚ ĞdžƚĞŶƐŝ|Ğ ůŝŶĞ ůŝƐƚ ĨŽƌ ƚŚĞ Ŷ ϱ ĂŶĚ Ŷ ϲ ďĞŶĚŝŶŐ ŵŽĚĞƐ͘ :ŽƵƌŶĂů ŽĨ DŽůĞĐƵůĂƌ ^ƉĞĐƚƌŽƐĐŽƉLJ͘ ϮϰϮ͕ ϰϲͲϱϰ͘ :ŽůůLJ͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϭϬ͘ dŚĞ Ŷϴ ďĞŶĚŝŶŐ ŵŽĚĞ ŽĨ ĚŝĂĐĞƚLJůĞŶĞ͗ ĨƌŽŵ ůĂďŽƌĂƚŽƌLJ ƐƉĞĐƚƌŽƐĐŽƉLJ ƚŽ ƚŚĞ ĚĞƚĞĐƚŝŽŶ ŽĨ Ͳϭϯ ŝƐŽƚŽƉŽůŽŐƵĞƐ ŝŶ dŝƚĂŶΖƐ ĂƚŵŽƐƉŚĞƌĞ͘ ƐƚƌŽƉŚLJƐŝĐĂů :ŽƵƌŶĂů͘ ϳϭϰ͕ ϴϱϮͲϴϱϵ͘ <ŚĂŶŶĂ͕ Z͘ <͕͘ Ğƚ Ăů͕͘ ϭϵϴϳ͘ sŝďƌĂƚŝŽŶĂů /ŶĨƌĂƌĞĚ ĂŶĚ ZĂŵĂŶ ƐƉĞĐƚƌĂ ŽĨ ĚŝĐLJĂŶŽĂĐĞƚLJůĞŶĞ͘ ^ƉĞĐƚƌŽĐŚŝŵ͘ ĐƚĂ͘ ϰϯ ͕ ϰϮϭͲϰϮϱ͘ <ŚůŝĨŝ͕ D͕͘ Ğƚ Ăů͕͘ ϭϵϵϳ͘ 'ĂƐ ŝŶĨƌĂƌĞĚ ƐƉĞĐƚƌĂ͕ ĂƐƐŝŐŶŵĞŶƚƐ͕ ĂŶĚ ĂďƐŽůƵƚĞ /Z ďĂŶĚ ŝŶƚĞŶƐŝƚŝĞƐ ŽĨ ϰ E Ϯ ŝŶ ƚŚĞ ϮϱϬͲϯϱϬϬ Đŵ Ͳϭ ƌĞŐŝŽŶ͗ ŝŵƉůŝĐĂƚŝŽŶƐ ĨŽƌ dŝƚĂŶΖƐ ƐƚƌĂƚŽƐƉŚĞƌĞ͘ ^ƉĞĐƚƌŽĐŚŝŵŝĐĂ ĐƚĂ WĂƌƚ ͘ ϱϯ͕ ϳϬϮͲϳϭϮ͘ EŝdžŽŶ͕ ͘ ͕͘ Ğƚ Ăů͕͘ ϮϬϭϯ͘ ĞƚĞĐƚŝŽŶ ŽĨ ƉƌŽƉĞŶĞ ŝŶ dŝƚĂŶΖƐ ƐƚƌĂƚŽƐƉŚĞƌĞ͘͘ ƐƚƌŽƉŚLJƐŝĐĂů :ŽƵƌŶĂů >ĞƚƚĞƌƐ͘ ϳϳϲ͕ ϲ͘ EŝdžŽŶ͕ ͘ ͕͘ Ğƚ Ăů͕͘ ϮϬϭϬ͘ hƉƉĞƌ ůŝŵŝƚƐ ĨŽƌ ƵŶĚĞƚĞĐƚĞĚ ƚƌĂĐĞ ƐƉĞĐŝĞƐ ŝŶ ƚŚĞ ƐƚƌĂƚŽƐƉŚĞƌĞ ŽĨ dŝƚĂŶ͘ &ĂƌĂĚĂLJ ŝƐĐƵƐƐŝŽŶƐ͘ ϭϰϳ͕ ϲϱͲϴϭ͘ ^ĂŵƵĞůƐŽŶ͕ Z͘ ͕͘ Ğƚ Ăů͕͘ ϭϵϵϳ͘ ϰEϮ ŝĐĞ ŝŶ dŝƚĂŶΖƐ EŽƌƚŚ WŽůĂƌ ^ƚƌĂƚŽƐƉŚĞƌĞ͘ WůĂŶĞƚ͘ ^ƉĂĐĞ ^Đŝ͘ ϰϱ͕ ϵϰϭͲ ϵϰϴ͘ ^ĐŚŝŶĚĞƌ͕ W͘ :͕͘ Ğƚ Ăů͕͘ ϮϬϭϮ͘ dŚĞ ƐƚƌƵĐƚƵƌĞ ŽĨ dŝƚĂŶΖƐ ĂƚŵŽƐƉŚĞƌĞ ĨƌŽŵ ĂƐƐŝŶŝ ƌĂĚŝŽ ŽĐĐƵůƚĂƚŝŽŶƐ͗ KĐĐƵůƚĂƚŝŽŶƐ ĨƌŽŵ ƚŚĞ WƌŝŵĞ ĂŶĚ ƋƵŝŶŽdž ŵŝƐƐŝŽŶƐ͘ /ĐĂƌƵƐ͘ ϮϮϭ͕ ϭϬϮϬͲϭϬϯϭ͘ ^ŚŝŶĚŽ͕ &͕͘ Ğƚ Ăů͕͘ ϮϬϬϯ͘ hůƚƌĂ|ŝŽůĞƚ ĂŶĚ ŝŶĨƌĂƌĞĚ ƐƉĞĐƚƌƵŵ ŽĨ ϲ , Ϯ ƌĞ|ŝƐŝƚĞĚ ĂŶĚ |ĂƉŽƌ ƉƌĞƐƐƵƌĞ ĐƵƌ|Ğ ŝŶ dŝƚĂŶΖƐ ĂƚŵŽƐƉŚĞƌĞ͘ WůĂŶĞƚĂƌLJ ĂŶĚ ^ƉĂĐĞ ^ĐŝĞŶĐĞ͘ ϱϭ͕ ϵͲϭϳ͘ dĞĂŶďLJ͕ E͘ ͕͘ Ğƚ Ăů͕͘ ϮϬϬϵ͘ dŝƚĂŶΖƐ ƐƚƌĂƚŽƐƉŚĞƌŝĐ Ϯ E Ϯ ͕ ϯ , ϰ ͕ ĂŶĚ ϰ , Ϯ ĂďƵŶĚĂŶĐĞƐ ĨƌŽŵ ĂƐƐŝŶŝͬ/Z^ ĨĂƌͲŝŶĨƌĂƌĞĚ ƐƉĞĐƚƌĂ͘ /ĐĂƌƵƐ͘ ϮϬϮ͕ ϲϮϬͲϲϯϭ͘ sŝŐŽƵƌŽƵdž͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϬϬ͘ 'ůŽďĂů ZŽ|ŝďƌĂƚŝŽŶĂů ŶĂůLJƐŝƐ ŽĨ ,E ĂƐĞĚ ŽŶ /ŶĨƌĂƌĞĚ ĂŶĚ DŝůůŝŵĞƚĞƌͲ tĂ|Ğ ^ƉĞĐƚƌĂ͘ :ŽƵƌŶĂů ŽĨ DŽůĞĐƵůĂƌ ^ƉĞĐƚƌŽƐĐŽƉLJ͘ ϮϬϮ͕ ϭͲϭϴ͘ tŝŶƚŚĞƌ͕ &͕͘ Ğƚ Ăů͕͘ ϮϬϬϱ͘ ŶĂůLJƐŝƐ ŽĨ ƚŚĞ |ϳн|ϵ ĂŶĚ Ϯ|;ϳͿͲ|;ϵͿ ďĂŶĚ ĐŽŵƉůĞdžĞƐ ŽĨ ĚŝĐLJĂŶŽĂĐĞƚLJůĞŶĞ ;EͲͲEͿ͘ :ŽƵƌŶĂů ŽĨ DŽůĞĐƵůĂƌ ^ƚƌƵĐƚƵƌĞ͘ ϳϰϮ͕ ϭϯϭͲϭϰϲ͘ tŝŶƚŚĞƌ͕ &͕͘ Ğƚ Ăů͕͘ ϭϵϵϰ͘ dŚĞ ŝŶĨƌĂƌĞĚ ĂŶĚ ZĂŵĂŶ ƐƉĞĐƚƌƵŵ ŽĨ ĚŝĐLJĂŶŽĂĐĞƚLJůĞŶĞ ͗ ƚŚĞ ν ϵ ĨƵŶĚĂŵĞŶƚĂů͘ :ŽƵƌŶĂů ŽĨ DŽůĞĐƵůĂƌ ^ƚƌƵĐƚƵƌĞ͘ ϯϮϬ͕ ϲϱͲϳϯ͘ ϮϬ Highlights for: Gas

	References:
	ŵLJĂLJ͕ ͕͘ Ğƚ Ăů͕͘ ϮϬϬϵ͘ sŝďƌĂƚŝŽŶͲƌŽƚĂƚŝŽŶ ƉĂƚƚĞƌŶ ŝŶ ĂĐĞƚLJůĞŶĞ͘ //͘ /ŶƚƌŽĚƵĐƚŝŽŶ ŽĨ ŽƌŝŽůŝƐ ĐŽƵƉůŝŶŐ ŝŶ
	ƚŚĞ ŐůŽďĂů ŵŽĚĞů ĂŶĚ ĂŶĂůLJƐŝƐ ŽĨ ĞŵŝƐƐŝŽŶ ƐƉĞĐƚƌĂ ŽĨ ŚŽƚ ĂĐĞƚLJůĞŶĞ ĂƌŽƵŶĚ ϯ ŵƵ ŵ͘ :ŽƵƌŶĂů ŽĨ
	ŚĞŵŝĐĂů WŚLJƐŝĐƐ͘ ϭϯϭ͘
	ŶĚĞƌƐŽŶ͕ ͘