for review only - university of toronto t-spacefor review only 3 strow et al. [8] who reported line...

For Review Only

Analysis of Fourier transform spectra of N2O in the v3 band

for atmospheric composition retrievals

Journal: Canadian Journal of Physics

Manuscript ID cjp-2017-0303.R2

Manuscript Type: Article

Date Submitted by the Author: 09-Dec-2017

Complete List of Authors: Predoi-Cross, Adriana; Home, 512 Silkstone Crescent West; University of Lethbridge, Physics and Astronomy Hashemi, Robab; University of lethbridge, Physics and Astronomy; Harvard-Smithsonian Center for Astrophysics, Atomic and Molecular Physics Division Devi, V. Malathy; The College of William and Mary

Naseri, Hossein; University of Lethbridge Faculty of Arts and Science, Physics and Astronomy; Farmers Edge Smith, Mary Ann; Science Directorate, NASA Langley Research Center, Science Directorate

Keyword: N2O, air-broadening, intensities, pressure induced shift, line mixing coefficients

Is the invited manuscript for consideration in a Special

Issue? : Ursula Franklin commemorative Festschrift

https://mc06.manuscriptcentral.com/cjp-pubs

Canadian Journal of Physics

For Review Only

1

Analysis of Fourier transform spectra of N2O in the νννν3 band for atmospheric composition retrievals

Adriana Predoi-Cross, Robab Hashemi, V. Malathy Devi, Hossein Naseri,

and Mary Ann H. Smith

Adriana Predoi-Cross.1 Dept. of Physics & Astronomy, University of Lethbridge, Alberta T1K 3M4,

Canada. Present address: 512 Silkstone Crescent West, Lethbridge, Alberta T1J 4C1, Canada.

Robab Hashemi. Dept. of Physics & Astronomy, University of Lethbridge, Alberta T1K 3M4, Canada.

Present address: Harvard-Smithsonian Center for Astrophysics, Atomic and Molecular Physics Division,

Cambridge, Massachusetts 02138, USA

V. Malathy Devi. Dept. of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA.

Hossein Naseri. Dept. of Physics & Astronomy, University of Lethbridge, Alberta T1K 3M4, Canada.

Present address: Farmers Edge, 4309 8 Ave N, Lethbridge, Alberta, Canada

Mary Ann H. Smith. Science Directorate, NASA Langley Research Center, Hampton, Virginia 23681,

USA.

1Corresponding author: E-mail: [email protected].

Abstract

We report measurement results for line positions, intensities, half-width and pressure induced shift

coefficients and line mixing coefficients for N2O broadened by air in the ν3 band. The high signal-to-

noise ratio spectra have been recorded at high resolution using the McMath-Pierce Fourier Transform

Spectrometer (FTS) formerly located at the National Solar Observatory on Kitt Peak, AZ, USA. The

spectra were analyzed using a multispectrum nonlinear least squares curve fitting technique employing the

speed-dependent Voigt profile with a Rosenkranz (weak) line mixing component. The speed dependence

parameters were calculated as suggested in the study of Kochanov (2017). Several comparisons have been

performed between the retrieved parameters and previously published results. For |m| ≤ 40, our results for

line positions, broadening and line mixing coefficients agree best with the results of Loos et al. (2015).

Also, we compared the obtained line positions and intensities with the corresponding values in HITRAN

2016 and GEISA 2015 databases. No significant or systematic differences were noticed. The precision of

our line positions was estimated to be 3×10-5

cm-1

. The reported line positions, intensities and air-

broadening coefficients are accurate to better than 2%. The accuracy of air-pressure induced line shifts

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and line mixing coefficients is better than 5%. The line mixing coefficients and air-broadening

coefficients were also calculated using the Exponential Power Gap (EPG) scaling law, and these

calculated values were found to be in good agreement with the experimental results.

Key words: N2O, air-broadening, positions, intensities, pressure induced shift, line mixing coefficients,

multispectrum nonlinear fit.

1. Introduction

It is well documented that gases included in the NxOy family (NO, NO2, N2O2, N2O, etc.) play a

crucial role in terrestrial atmospheric chemistry. For example, these gases are produced during lightning,

as a result of reaction of nitrogen and oxygen in air. In highly inhabited areas with heavy traffic, the

production of nitrogen oxides is higher, leading to occurrences of acid rain and smog. As one of the

greenhouse gases, nitrous oxide (N2O) is important in radiative transfer [1]. Accurate laboratory

spectroscopic studies of molecular line shapes in different spectral ranges are needed to enable satellite-

based, ground-based and air-borne remote sensing measurements of N2O concentrations. To meet this

demand, we present spectroscopic results of measured line intensities and line shape parameters to

validate and update the existing knowledge and information on line parameters for the mixture of N2O

with air, stored in databases such as HITRAN2016 [2].

Previous studies of nitrous oxide broadened by N2, O2, and N2O include the one by Lacome et al. [3]

who had analyzed the Fourier transform spectra to obtain self-, N2- and O2-broadened line parameters of

N2O and the temperature dependences for the corresponding line-width coefficients in the 4- and 8-µm

spectral regions. Toth [4] published N2- and air-broadened line-widths and frequency-shifts for spectral

lines in the 1800 to 4800 cm-1

range. In a separate study, the author reported the self-broadened line-

widths and pressure-induced line shifts of N2O in the 1800-2630 cm-1

region [5]. Nemtchinov et al. [6]

have studied N2- and O2-broadened half-widths and their temperature dependences between 216 and 296

K for spectral lines in the 4.5 µm region corresponding to the ν3 fundamental band of N2O, but they did

not determine the pressure-induced line shifts.

Vitcu et al. [7] have investigated 0310←0110 parallel Q-branch of N2O at 297 K and over the pressure

range of 11 to 30 Torr to measure self- broadening, pressure-induced shifts, and line mixing coefficients.

The line mixing effects for N2O have also been the focus of other line-shape studies such as the one by

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Strow et al. [8] who reported line mixing in the ν2 + ν3 Q-branch of N2O. Margottin-Maclou et al. [9]

observed line mixing effects in N2O absorption spectra recorded at room temperature using a Fourier

transform spectrometer (FTS). Loos et al. [10] have reported highly accurate room temperature

measurements of air-broadening, pressure-shift, speed dependence and Rosenkranz line mixing parameters

for transitions in the ν3 fundamental band of N2O. Hartmann et al. [11] also have examined line mixing

in N2O Q-branches, broadened by N2, O2, and air, both in the laboratory environment and in atmospheric

spectra.

In this study, we investigate the deviations of air-broadened spectral line shapes in the ν3 band of N2O

from the Voigt profile (VP) [12] using the quadratic Speed Dependent Voigt line profile (qSDV) [13] and

taking Rosenkranz line mixing into account. We also performed EPG calculations to estimate the weak

line mixing effects in the Rosenkranz approximation [7,8].

2. Experimental Details

The N2O spectra were all recorded in November 2002, covering the 600-2850 cm-1

spectral range

using the McMath-Pierce FTS located at the National Solar Observatory on Kitt Peak, and the “Langley”

50-cm coolable sample cell. We have used the same experimental setup as the one used in Ref [15] and for

further details in the measurement of temperature and pressure, we refer to the experimental section in Ref

[15]. The spectral resolution was 0.006 cm−1. A globar source, KCl beamsplitter, liquid-helium-cooled

arsenic-doped silicon detectors, and InAs and cooled CaF2 filters were used in the experiment. The

experimental conditions of spectra analyzed are presented in Table 1. Four spectra were recorded using

mixtures of the N2O and air at room temperature, and a low pressure spectrum of pure N2O was recorded

at 294 K. In Figure 1, an example of an experimental spectrum recorded at low pressure is shown.

The sample pressures for all spectra were monitored continually using periodically calibrated

Baratron gauges of appropriate pressure range. A commercially purchased natural sample of N2O with a

stated purity of 99.0 % (minimum purity) was used to obtain the spectra. For air-broadened spectra the high-

purity N2O samples were mixed with known amounts of a commercially-obtained air sample to obtain the

volume mixing ratios of N2O listed in Table 1.

The interferograms were properly oversampled at the experimental resolution (0.006 cm-1

) and the

spectra were appropriately pressure broadened. For wavenumber calibration purposes, the positions of

residual water vapor transitions of the ν2 band appearing within the filter band pass of 1200-2800 cm−1

were used [2]. Any residual water (less than 1%) in the cell could have come from either the N2O or air

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samples (or both). The main components of the water spectral features arising from outside the sample

cell would be the strong narrow lines from residual gas in the evacuated FTS tank, and the broad features

from the atmospheric-pressure optical path (mainly between the globar source and the cell) purged with

dry nitrogen. There might also be a very small component from the short (few cm) paths between the

windows of the 50-cm cell and its evacuated enclosure. We did not observe any contribution attributable

to water inside the sample cell or the cell enclosure, and the positions of the strong narrow water vapor

lines from the FTS tank were used for the calibration of the wavenumber scales of the N2O spectra. This

calibration has been further fine-tuned using self-calibration with respect to the positions of N2O

transitions in HITRAN2016 [2]. Note that the background spectra were not used to ratio the pressure-

broadened spectra, but only to identify the residual H2O features.

3. Spectroscopic analysis

We performed the analysis of spectra in the spectral interval of 2120-2260 cm−1

of the ν3 band.

The multispectrum fitting program “Labfit” [16] was used to retrieve the spectroscopic parameters by

fitting short spectral intervals (4 or 5 cm−1

) to cover the entire band. The line parameters were derived

using the quadratic speed dependent Voigt line shape model. The instrumental line shape was modeled

considering the finite size of the aperture, the sinc function and the apodization used. The user-interactive

“Labfit” program fits the baseline to a polynomial, in this case a 9th

order polynomial, for each fitted

interval. More details of the fitting software are in the Appendix of Ref. [16]. Deviations from the 100%

level of transmittance of the spectra (i.e. baseline), due the detector non-linearity and the source’s stability,

are taken into account because the accuracy of the line parameters depends on the knowledge of the 100%

transmittance level, zero level, and the background of the spectra. The software accounts for the zero level

offsets by considering them as fitted parameters.

For every fitted spectral line, the multispectrum fitting technique is able to retrieve the following

line parameters from the 5 spectra: line position, intensity, air-broadened line-width, air-induced pressure

shift coefficient, and the speed dependence parameter. The apodization was applied because at low

pressures, the widths of the N2O lines were smaller than or comparable with that of the instrumental line

shape, and the side lobes of the sinc functions were visible in the spectra. The software uses a modified

Levenberg-Marquardt [17, 18] algorithm for minimizing the sum of the squares of the residuals between

the simulated and the observed spectra; full details are described in Ref. [16] and its Appendix.

Due to the high density of transitions in the spectral region of present study, the spectra were fitted

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in short spectral intervals (4 to 5 cm−1

) beginning with the lowest-pressure spectrum, and adding higher-

pressure spectra one at a time. In Figure 2, in the top panel, the overlaid experimental spectra are plotted.

The bottom panel presents the weighted fit residuals (Observed-Calculated). The fit residuals were

minimized by using the qSDV model and a weak line mixing component. After the initial fit the spectra

were given weights calculated as the ratios between the overall standard deviation and the standard

deviations of individual fitted spectra. The software was displaying both the overall standard deviations

and the ones for individual spectra.

The following formulae were used to retrieve the broadening and pressure shift coefficients:

��, �� = � ��1 − �� + ��

�� (1) ∆!"=Ptot[δo(air)(1-χ)+δo(self)χ] (2) #�� = #�� + #%�� − �&� (3)

where ��, �� is the Lorentz half-width at pressure P and temperature T, Ptot is the total sample pressure, χ is the volume mixing ratio of N2O, and δ

o represents the pressure-shift coefficient (in

cm−1

atm−1

). �� is the Lorentz half-width of the line at the reference pressure Po (1 atm) and reference temperature To (296 K). n1 and n2 represent the temperature dependence exponents of air broadening and

self-broadening, respectively, the observed shift of the line in cm-1

is ∆ν, and the temperature dependence

of pressure induced shift coefficient is denoted by #%. The list of initial values for the line parameters was taken from the HITRAN2016 database [2], with initial values for parameters such as δ' not included in

HITRAN set to zero. By minimizing the statistical errors using the multispectrum fit method, precise line

parameters consistent with all measured spectra can be retrieved.

When we use the qSDV profile [13], the Lorentz width can be described as a function of velocity

as presented in Ref. [19]:

�� = ��'(� )1 + * +, --./0 − 123 (4)

where the speed of the molecular collision is v, vm is the mean speed of the molecular collision, the most

probable speed of the collision is presented by vp, and S is the parameter representing speed dependence in

the equation. The value of 1.5 is taken for constant c [14].

In our study we were not able to retrieve accurate values for the speed dependence parameter for

each transition (the resolution and the S/N of the spectra were not sufficiently high to retrieve individual

values of speed dependence). Hence, we used the calculated speed dependence parameters as described by

Kochanov [20]. The expressions in that paper allow users to compute the speed-dependence parameters

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for different gas mixtures and different values for the exponent q in the effective inter-molecular potential.

We have assumed a value of q = 6 in the expression of effective potential V~r-q

for the N2O-air mixture.

In all fits with the speed dependent Voigt profile we have assumed a value of 0.0895 for the speed

dependence parameter S in Eq. (4). According to Ref. [20] there is no rotational quantum number

dependence for the speed-dependence parameter, even though recent experimental studies such as that of

Loos et al. [10] suggest that there is a rotational quantum number dependence. A constant value of S =

0.0895 has been fixed for all N2O transitions in our fits. We note that this value of the speed dependence

parameter is nearly 10 times larger than the average values obtained by Loos et al. [10].

The asymmetric component that accounts for weak line mixing effects was added to the modelled

line profile. Because the line mixing parameters could not be unambiguously determined for all transitions

from our spectral fits, we chose to use the Exponential Power Gap (EPG) scaling law to calculate the line

mixing coefficients. Considering the collisional transfer of energy that occurs between two energy levels

labelled j and k, in this semi-empirical method we can write that the weak line mixing coefficient, Y o

(T )

is:

45�� = 2 ∑ 898:;":?>"9 (5)

In the equation above @;5 are the off-diagonal elements of the relaxation matrix. The components of the dipole moment are presented by dk and dj , !A5 and !A; are line positions in cm−1. The dipole moment components were calculated from the intensities in HITRAN 2016 [2].

The real parts of the diagonal elements of the relaxation matrix present the air broadening

coefficients in the relaxation matrix formalism, and the off-diagonal elements are related to the

collisional transfer rates κjk, as Wjk = βκjk, where β = 0.418. The value of β was determined such that

the best agreement between the observed and calculated line mixing coefficients, is achieved. By

using the detailed balance relationship, the rate of transfer from state k to j can be connected as follows

to the rate of transfer from j to k:

B5C;5 = B;C5; (6) where ρk is the population of the rotational level k and the expression for ρk can be found in Ref. [21] as

B5 =�2D + 1��EF�?G:HI�� where, KB is the Boltzmann constant in units of cm-1/K. The energy value for each level, Ek, is reported in the HITRAN database [2]. Also, from the sum rule we have:

∑ J;@;5 = 0�L�MN; (7) In the EPG formalism, the collisional transfer rates from the lower rotational level k to a higher

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rotational level j can be written as:

C;5 = �� OPQG9:PR� S?T �EF �?UPQG9:PHI� �. (8)

where ∆Ejk is the energy gap between the two rotational levels in cm−1

, Bo is the rotational constant in

the lower energy level, and KB is Boltzmann’s constant. Using the nonlinear least squares technique and

the Matlab software, the parameters a, b, and c were optimized. Assuming that the collisional rates are the

same between the upper and lower two vibrational levels, the diagonal elements of the relaxation matrix

can be presented as:

@55 = W0 XY∑ C;5; Z[\\M] + Y∑ C;5; Z�^M]_. (9) We have retrieved the parameters a, b, and c that would best reproduce both the measured air-broadening

and the measured line mixing parameters. They are 0.02757(4), 0.36385(3) and 1.00765(9), respectively.

Since the broadening coefficients do not have a vibrational dependence, we have added to our input files

estimated line mixing coefficients for transitions of N2O belonging to other bands. Since the majority of

these transitions with estimated coefficients had intensities lower by at least one order of magnitude than

the transitions with measured coefficients, it is possible that the influence of implementing calculated

values for line mixing coefficients for weak and very weak transitions is very small, but we believe it

contributed to our low fit residuals.

In addition to the lane shape parameters we also report the experimentally-determined line intensities

and positions for the N2O transitions studied here. As mentioned earlier, the spectra were first calibrated

with respect to line positions belonging to the ν2 band of H2O [2]. The calibration was then improved by

using self-calibration of N2O transitions relative to the N2O line positions in the HITRAN 2016 database

[2]. The retrieved N2O line positions were compared with corresponding values listed in the HITRAN

2016 [2] and the GEISA 2015 database [22], as well as the positions reported in Refs. [6,10], and the

position differences are plotted in Figure 3 as a function of the rotational quantum index m (m = −J in the

P branch and J+1 in the R branch, where J is the lower-state rotational quantum number). Our line

positions agree very well with the values in the HITRAN 2016 and GEISA 2015 databases, as quantified

by the low RMS difference values 1.357×10-6

cm-1

and 1.351×10-6

cm-1

, respectively. The range of values

for the index m is narrower for the study of Loos et al. [10] (i.e. |m| ≤ 40) than the range for m in our study

(|m| ≤ 55) and in the HITRAN and GEISA databases. The line positions from Ref. [10] (which are

actually the HITRAN2012 values [23]) agree best with our retrieved line positions, as shown by Figure 3.

The scatter in these differences is also very low (RMS of 6.228 × 10-7

cm-1

). The retrieved line positions

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are from the present work are listed in Table 2.

As stated earlier, we also retrieved the line intensities for ν3 N2O transitions with |m| ≤ 55. In

Figure 4 we present our results and how they compare with the line intensities from the HITRAN 2016

and GEISA 2015 databases and from the intensities reported by Nemtchinov et al. [6]. We compare the

line intensities by plotting the percentage differences between the results of present study for the qSDV

profile and the values from the other sources ((Other Value − PS)×100/PS). There is more scatter in the

difference values obtained for the P-branch due to the overlap between transitions of the ν3 band and

transitions from other N2O bands (see Figure 1). Panel (B) of Figure 4 compares the line intensities results

through ratios between database or Nemtchinov et al. values and our corresponding retrieved line

intensities. The RMS values for the ratios of our line intensities to HITRAN and GEISA database values

are 8.32×10-3

and 7.98×10-3

, respectively. The lack of a clear m-dependent pattern in the ratio values

plotted in panel (B) suggests that there is no systematic difference between the sets of intensity results

compared, other than our retrieved intensities being (on average) about 1.2% smaller than HITRAN and

GEISA values and 2% smaller than the Nemtchinov et al. values.

The present results for air-broadening and air-shift coefficients are listed in Table 2, and they are

plotted in Figures 5 and 6 along with previous measurements [3,4,6,10], database values [2,22], and

values from the EPG calculation. The present results plotted in Figure 5 also include a set of air-

broadening coefficients retrieved using the Voigt profile (VP) with a line mixing component. Figure 5

shows that the measured results for air-broadening coefficients obtained from our spectra using the qSDV

profile are slightly larger (about 1 %) than the air-broadening values obtained from the same spectra using

VP. An examination of Figure 5 (B) shows that our PS(SDV) measured air-broadening coefficients are

larger than those obtained by Lacome et al. [3], Toth [4], , and Nemtchinov et al. [6] that were all

retrieved using the Voigt profile. As expected, the best agreement (within ± 0.5% or better) is with the

values published by Loos et al. [10], also obtained using the SDV profile and accounting for line mixing.

We note that our measurements cover a slightly larger range of |m| values than Ref. [10]. At high |m|

values (above 40-45) our experimental values are significantly different than the values listed in the

current databases [2,22]. We note that the HITRAN2016 [2] N2O air-broadened widths are the same as in

HITRAN2012 [23]. These air-broadened widths were carried forward from HITRAN2004 [24], where a

polynomial in |m| was fit to the measurements of Refs. [3,4,6]. The agreement between our measured air-

broadening coefficients and corresponding calculated values obtained using the EPG scaling law is within

±4% for most m values as can be seen in Table 3 and Figure 5 (B).

The air-shift coefficients are plotted in Figure 6 (A) as a function of m. Comparing these values

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with the published measurements by Loos et al. [10], and values from the HITRAN2016 [2] database, we

found that they are in agreement, and the differences are plotted vs. m in Figure 6 (B). We note that the

HITRAN2016 air-induced shift values for |m| ≤ 40 in the ν3 band are from Loos et al. [10], while the

shifts for higher |m| values are empirical estimates (based on the work of Toth [4]) carried forward from

HITRAN2012 [23] and earlier versions of that database. Figure 6(B) shows that the differences between

the present results and those of Loos et al. [10] are generally less than ±0.0005 cm-1

atm-1

, while the

disagreement between our values and the HITRAN2016 values is larger for |m| > 40. Similarly to the

widths, the shifts retrieved from our spectra using VP are only slightly different from those retrieved using

SDV. The error bars in Figure 6(A) indicate that the precision of our measured SDV pressure shift

coefficients is less for the weaker lines in both P - and R- branches.

The results of calculations for air-broadening and line mixing coefficients carried out with the

EPG scaling law are presented in Table 3. The calculation results are plotted in Figures 5(A) and 7. As

can be observed from these two figures, even though the EPG law is semi-empirical the results it provides

are mostly within about ±10% of the measured values, and this law could be considered for extrapolations

of broadening and of line mixing coefficients beyond the range of experimental results. In addition, line

mixing coefficients calculated by this method can be used in applications where experimental line mixing

coefficients are not available for the N2O transitions of interest.

An examination of Figure 7 shows that the calculated line mixing coefficients for P- and R-branch

transitions have similar patterns but of opposite sign and show a smooth m = 55. Where the intensity is the

highest, the sign of line mixing parameter changes due to the fact that intensity is transferred from weak to

strong absorption regions of the spectra. In addition, it is encouraging to note that both the line mixing

coefficients calculated with the EPG law and our retrieved line mixing coefficients agree well with the

experimental values of line mixing coefficients reported in Ref. [10].

4. Conclusions

In this study, we report accurate line-shape parameters of air-broadened N2O obtained from

retrievals using the quadratic SDV profile with an additional component to account for line mixing. Line

positions and intensities, air-broadened half-width coefficients, air-shift coefficients, and line mixing

coefficients using the Rosenkranz method are retrieved. These line shape parameters in the ν3 band are

reported for transitions up to |m| = 55.

Our comparison of line positions with published results and those listed in the HITRAN 2016 and

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GEISA 2015 databases show good agreement between the various sets. When we compared our

measured intensities with results from the HITRAN2016 and GEISA2015 databases, we were unable to find

systematic differences among the results. The observed differences are attributed to the fact that the line

intensity information stored in databases was obtained using the Voigt profile, whereas the present set of

intensities were obtained using the speed-dependent Voigt profile.

The air-broadened half-width coefficients are in good agreement with the values published by

Lacome et al. [3], Toth et al. [4], Nemtchinov et al. [6], and Loos et al. [10]. The air-broadening

coefficients obtained with the SDV model are slightly smaller than earlier published values [3,4,6] (~2%

percent), the majority of which were obtained using the Voigt profile. This observation is consistent with

results published by other groups (for example Ref. [25]). Indeed with very few exceptions, our air-

broadening and shift results agree best with those published by Loos et al. [10] where the authors also

used the SDV line shape model. In fact, we have extended the range of air-broadening and shift

coefficients obtained with the SDV model from the |m|≤40 of Ref. [10] to |m|≤55. At values of |m| above

50, there is more scatter in our results, in particular in the P-branch, that is attributed to the overlap with

transitions from other N2O bands and due to the fact that the transitions are much weaker at higher |m|.

The measured and calculated line mixing coefficients show very good agreement with the values

obtained by Loos et al. [10]. The data recorded for this study do not cover a wide range of temperatures,

and for this reason the temperature dependences of width and shift coefficients could not be determined.

A follow-up study involving several cold spectra of N2O and air mixtures is underway, and in the future

we expect to report our results for temperature dependences of line parameters.

Acknowledgements

The spectra used in this study were recorded with the assistance of Mike Dulick while he was at the the

McMath-Pierce Fourier transform spectrometer facility at the National Solar Observatory on Kitt Peak.

We are grateful to Dr. D. Chris Benner of the Department of Physics, College of William and Mary for

allowing us to use his Labfit software in our multispectrum analysis. The researchers at the University of

Lethbridge were funded by the Natural Sciences and Engineering Research Council of Canada and

Alberta Innovates Technology Futures (AITF) (R. Hashemi). The research at the College of William and

Mary, and NASA Langley Research center was supported by grants and cooperative agreements with the

National Aeronautics and Space Administration.

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24. L S Rothman, D Jacquemart, A Barbe, D C Benner et al. J Quant Spectrosc Radiat Transf.

96, 139 (2005).

25. A Predoi-Cross, F Rohart, J-P Bouanich, D Hurtmans, Can J Phys 87(5), 485 (2009).

List of Tables

Table 1. Experimental conditions of recorded spectra. VMR is the volume mixing ratio, P is the total

sample pressure in Torr and T is the temperature in K. The pathlength is 50 cm for all spectra.

Table 2. Measureda line positions in cm

-1, intensities in cm

-1/(molecule·cm

-2), air-broadened half-width

coefficients and air-shift coefficients of N2O in cm-1

atm-1

obtained using the speed-dependent Voigt

profile. A constant speed dependence value of 0.0895 has been used for each transition. The Einstein A

coefficients in s-1

are also reported.

Table 3. Measured air-broadened half-width coefficients (cm-1

atm-1

at 296 K) and line mixing parameters

(atm-1

) and corresponding calculated values obtained using the EPG scaling law.

List of Figures

Fig. 1. Experimental spectrum of the ν3 band of nitrous oxide recorded at P= 1.012 Torr and T=294.15

K. The path length of the absorption cell is L = 50 cm.

Fig. 2. Example of a fitted spectral interval of the ν3 band of nitrous oxide broadened by air (see Table 1).

Panel (A) shows the observed spectra, and Panel (B) shows the fit residuals obtained using the quadratic

speed dependent Voigt profile with a weak line mixing component.

Fig. 3. Measured line position differences with values in the HITRAN2016 [2] and GEISA2015 [22]

databases and with values reported by Nemtchinov et al. [6] and Loos et al. [10]. Note that the line

positions listed in Table 3 of Ref. [10] are from the 2012 edition of HITRAN [23]. The differences

have been obtained by subtracting our results from the values presented in the other lists. The average

Page 12 of 32



For Review Only

13

values are presented using dashed lines (see legend). Note that m = −J for the P -branch transitions,

m = J + 1 for the R-branch transitions, and J is the lower state rotational quantum number.

Fig. 4. (A) Measured line intensity percentage difference of present study (PS) compared with

HITRAN2016 and GEISA2015 databases ((Values in database-PS)×100/PS) and with the results of

Nemtchinov et al. (2004). The average values are shown with dashed lines. (B) Ratios between line

intensities in HITRAN2016 and GEISA2015 databases and from the study of Nemtchinov et al. (2004)

and the corresponding line intensities from the present study. The data points corresponding to P45,

P35 and R2 were not included.

Fig. 5. (A) Air- broadening coefficients for N2O transitions overlaid with published results by Toth et

al. [4], Lacome et al. [3], Nemtchinov et al. [6], Loos et al. [10] and parameters stored in the

HITRAN2016 [2] and GEISA2015 [22] databases. Lastly, the values for air-broadening coefficients

calculated using the EPG scaling law are overlaid on the same plot. (B) Percent differences between

our SDV air-broadening coefficients and previous studies, EPG calculations, database values, and

results obtained with the Voigt profile from our spectra ({Other study – PS(SDV)} × 100 / PS(SDV)).

Fig. 6. (A) Retrieved SDV air-induced pressure shift coefficients for N2O transitions of the ν3 band of

N2O overlaid with measurements by Loos et al. [10], values from the HITRAN2016 [2] database, and

results obtained from our spectra with the Voigt profile. (B) Differences (Other work – PS(SDV))

between our SDV air-shift coefficients and the other values shown in panel (A) .

Fig. 7. Line mixing coefficients for transitions in the ν3 band of N2O from the present study (both SDV

and Voigt profiles) plotted overlaid with the results from Ref. [10] and values calculated using the EPG

formalism.

Page 13 of 32



For Review Only

Fig. 1. Experimental spectrum of the ν3 band of nitrous oxide recorded at P= 1.012 Torr and T=294.15 K.

The path length of the absorption cell is L = 50 cm.

240x174mm (96 x 96 DPI)

Page 14 of 32



For Review Only

Fig. 2. Example of a fitted spectral interval of the ν3 band of nitrous oxide broadened by air (see Table 1). Panel (A) shows the observed spectra, and Panel (B) shows the fit residuals obtained using the quadratic

speed dependent Voigt profile with a weak line mixing component.

241x174mm (96 x 96 DPI)

Page 15 of 32



For Review Only

240x174mm (96 x 96 DPI)

Page 16 of 32



For Review Only

Fig. 3. Measured line position differences with values in the HITRAN2016 [2] and GEISA2015 [22] databases and with values reported by Nemtchinov et al. [6] and Loos et al. [10]. Note that the line positions listed in

Table 3 of Ref. [10] are from the 2012 edition of HITRAN [23]. The differences have been obtained by subtracting our results from the values presented in the other lists. The average values are presented using

dashed lines (see legend). Note that m = −J for the P -branch transitions, m = J + 1 for the R-branch transitions, and J is the lower state rotational quantum number.

240x174mm (96 x 96 DPI)

Page 17 of 32



For Review Only

Fig. 4. (A) Measured line intensity percentage difference of present study (PS) compared with HITRAN2016 and GEISA2015 databases ((Values in database-PS)×100/PS) and with the results of Nemtchinov et al.

(2004). The average values are shown with dashed lines. (B) Ratios between line intensities in HITRAN2016 and GEISA2015 databases and from the study of Nemtchinov et al. (2004) and the corresponding line

intensities from the present study. The data points

240x174mm (96 x 96 DPI)

Page 18 of 32



For Review Only

240x174mm (96 x 96 DPI)

Page 19 of 32



For Review Only

Fig. 5. (A) Air- broadening coefficients for N2O transitions overlaid with published results by Toth et al. [4], Lacome et al. [3], Nemtchinov et al. [6], Loos et al. [10] and parameters stored in the HITRAN2016 [2] and

GEISA2015 [22] databases. Lastly, the values for air-broadening coefficients calculated using the EPG

scaling law are overlaid on the same plot. (B) Percent differences between our SDV air-broadening coefficients and previous studies, EPG calculations, database values, and results obtained with the Voigt

profile from our spectra ({Other study – PS(SDV)} × 100 / PS(SDV)).

240x174mm (96 x 96 DPI)

Page 20 of 32



For Review Only

240x174mm (96 x 96 DPI)

Page 21 of 32



For Review Only

Fig. 6. (A) Retrieved SDV air-induced pressure shift coefficients for N2O transitions of the ν3 band of N2O overlaid with measurements by Loos et al. [10], values from the HITRAN2016 [2] database, and results

obtained from our spectra with the Voigt profile. (B) Differences (Other work – PS(SDV)) between our SDV

air-shift coefficients and the other values shown in panel (A).

240x174mm (96 x 96 DPI)

Page 22 of 32



For Review Only

240x174mm (96 x 96 DPI)

Page 23 of 32



For Review Only

Fig. 7. Line mixing coefficients for transitions in the ν3 band of N2O from the present study (both SDV and

Voigt profiles) plotted overlaid with the results from Ref. [10] and values calculated using the EPG formalism.

240x174mm (96 x 96 DPI)

Page 24 of 32



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Table 1. Experimental conditions of recorded spectra. VMR is the volume mixing ratio, P is the

total sample pressure in Torr and T is the temperature in K. The pathlength is 50 cm for all

spectra.

Spectra Gas sample VMR P(Torr) T(K)

1 N2O 1.0000 1.012 241.15

2 N2O+air 0.0119 110.95 295.90

3 N2O+air 0.0113 204.90 295.65

4 N2O+air 0.0007 302.05 294.60

5 N2O+air 0.0006 503.55 294.15

Page 25 of 32



For Review Only

Table 2: Measureda line positions in cm

-1, intensities in cm

-1/(molecule·cm

-2), air-broadened half-width

coefficients and air-shift coefficients of N2O in cm-1

atm-1

obtained using the speed-dependent Voigt

profile. A constant speed dependence value of 0.0895 has been used for each transition.The Einstein A

coefficients in s-1

are also reported.

m Line positions

(cm-1

)

Intensities ×××× 1020

(cm-1

/(molecule·cm-2

))

Air

broadening

(cm-1

atm-1

)

Air shift

(cm-1

atm-1

)

Line mixing

(atm-1

)b

Speed

dependencec

A

(s-1

)

-54 2168.74147(4) 1.314(4) 0.07039(24) -0.00358(26) 0.00390(12) 0.0895(F) 102.727

-53 2169.9389(4) 1.598(3) 0.07075(19) -0.00366(23) 0.00477(12) 0.0895(F) 102.326

-52 2171.12972(4) 1.953(3) 0.06980(17) -0.00316(20) 0.00468(12) 0.0895(F) 102.833

-51 2172.31384(3) 2.341(3) 0.07024(17) -0.00356(19) 0.00462(11) 0.0895(F) 101.876

-50 2173.49129(3) 2.858(4) 0.07096(16) -0.00336(17) 0.00553(16) 0.0895(F) 103.273

-49 2174.66204(3) 3.420(4) 0.07006(16) -0.00262(18) 0.00387(17) 0.0895(F) 103.056

-48 2175.82619(4) 4.052(18) 0.07143(41) -0.0028(19) 0.00455(9) 0.0895(F) 102.2

-47 2176.98362(3) 4.784(7) 0.06995(16) -0.00329(17) 0.00498(12) 0.0895(F) 101.56

-46 2178.13426(3) 5.704(8) 0.07061(15) -0.00226(17) 0.0050(13) 0.0895(F) 102.361

-45 2179.27796(4) 8.187(18) 0.07022(17) -0.00120(18) 0.00461(12) 0.0895(F) 124.662

-44 2180.4156(3) 8.060(26) 0.07130(17) -0.00271(23) 0.00507(11) 0.0895(F) 104.695

-43 2181.54621(3) 9.257(12) 0.07099(12) -0.00208(14) 0.00459(10) 0.0895(F) 103.052

-42 2182.67027(3) 11.031(11) 0.07137(9) -0.00237(12) 0.00428(12) 0.0895(F) 105.645

-41 2183.78749(3) 12.586(13) 0.07143(10) -0.00255(12) 0.00449(9) 0.0895(F) 104.237

-40 2184.89802(3) 14.361(18) 0.07078(10) -0.00253(12) 0.00548(9) 0.0895(F) 103.343

-39 2186.00183(3) 16.452(15) 0.07134(8) -0.00242(12) 0.00529(9) 0.0895(F) 103.266

-38 2187.09881(3) 18.838(18) 0.07091(9) -0.00221(11) 0.00490(6) 0.0895(F) 103.745

-37 2188.18919(3) 21.392(18) 0.07104(8) -0.00206(10) 0.00553(7) 0.0895(F) 103.783

-36 2189.27272(3) 24.284(22) 0.07105(8) -0.00185(10) 0.00546(7) 0.0895(F) 104.363

-35 2190.34962(3) 27.347(25) 0.07163(8) -0.00224(9) 0.00488(6) 0.0895(F) 104.488

-34 2191.41987(5) 32.104(150) 0.07125(15) -0.00281(18) 0.00540(5) 0.0895(F) 109.735

-33 2192.48302(3) 34.048(58) 0.07177(10) -0.00227(11) 0.00492(10) 0.0895(F) 104.515

-32 2193.53965(3) 38.100(27) 0.07230(7) -0.00235(8) 0.00485(5) 0.0895(F) 105.573

-31 2194.58947(3) 42.096(30) 0.07266(7) -0.00196(8) 0.00512(6) 0.0895(F) 105.924

-30 2195.63287(3) 46.142(34) 0.07275(8) -0.00259(8) 0.00510(5) 0.0895(F) 105.835

-29 2196.66915(3) 50.243(35) 0.07280(7) -0.00224(8) 0.00468(5) 0.0895(F) 105.673

-28 2197.69871(3) 54.719(39) 0.07277(8) -0.00243(8) 0.00499(5) 0.0895(F) 106.136

-27 2198.72146(3) 58.993(47) 0.07316(9) -0.00250(8) 0.00498(5) 0.0895(F) 106.058

Page 26 of 32



For Review Only

-26 2199.73735(3) 63.187(54) 0.07349(10) -0.00237(9) 0.00393(5) 0.0895(F) 105.881

-25 2200.74653(4) 68.310(83) 0.07360(11) -0.00207(11) 0.00400(4) 0.0895(F) 107.267

-24 2201.74895(5) 73.980(230) 0.07325(22) -0.00255(15) 0.00399(5) 0.0895(F) 109.462

-23 2202.74459(4) 76.255(74) 0.07466(11) -0.00250(10) 0.00402(4) 0.0895(F) 107.000

-22 2203.73337(3) 80.199(74) 0.07533(10) -0.00253(9) 0.00409(5) 0.0895(F) 107.365

-21 2204.71534(3) 83.765(80) 0.07548(10) -0.00231(9) 0.00403(4) 0.0895(F) 107.620

-20 2205.69039(4) 87.045(86) 0.0762(11) -0.00215(10) 0.00399(4) 0.0895(F) 107.945

-19 2206.65883(3) 90.021(90) 0.07672(11) -0.00253(10) 0.00384(5) 0.0895(F) 108.576

-18 2207.62052(4) 92.035(96) 0.07722(12) -0.00284(10) 0.00413(4) 0.0895(F) 108.754

-17 2208.57511(4) 93.155(95) 0.07844(12) -0.00244(10) 0.00185(5) 0.0895(F) 108.561

-16 2209.52314(4) 94.274(100) 0.07903(12) -0.00307(11) -0.00221(5) 0.0895(F) 109.214

-15 2210.46409(4) 94.273(93) 0.07973(11) -0.00228(10) 0.00062(5) 0.0895(F) 109.516

-14 2211.39826(4) 93.620(90) 0.08071(11) -0.00219(10) -0.00076(5) 0.0895(F) 109.915

-13 2212.32567(4) 92.162(87) 0.08111(11) -0.00233(10) -0.00224(5) 0.0895(F) 110.529

-12 2213.24627(4) 89.607(82) 0.08189(11) -0.00202(10) -0.00487(5) 0.0895(F) 110.918

-11 2214.15989(4) 85.999(75) 0.08299(11) -0.00236(10) -0.00200(5) 0.0895(F) 111.087

-10 2215.06667(4) 81.756(73) 0.08398(11) -0.00191(11) -0.00270(5) 0.0895(F) 111.678

-9 2215.96655(8) 76.194(300) 0.08561(21) -0.00211(15) -0.00396(5) 0.0895(F) 111.778

-8 2216.85971(4) 71.076(77) 0.08640(12) -0.00231(12) -0.00509(5) 0.0895(F) 113.969

-7 2217.74596(4) 64.185(50) 0.08767(10) -0.00206(10) -0.00736(5) 0.0895(F) 115.087

-6 2218.62529(3) 56.581(43) 0.08887(9) -0.00211(9) -0.01032(6) 0.0895(F) 116.615

-5 2219.49774(3) 48.309(31) 0.09019(8) -0.00189(9) -0.01145(7) 0.0895(F) 118.894

-4 2220.36329(3) 39.421(27) 0.09113(8) -0.00160(10) -0.01352(6) 0.0895(F) 122.236

-3 2221.22203(3) 30.136(54) 0.09234(11) -0.00127(15) -0.01262(7) 0.0895(F) 128.879

-2 2222.07381(4) 20.494(58) 0.09562(16) -0.00121(20) -0.01738(7) 0.0895(F) 144.417

-1 2222.91871(3) 10.213(12) 0.10026(15) -0.00139(18) -0.01836(9) 0.0895(F) 214.251

1 2224.58788(3) 10.302(11) 0.10053(15) -0.00177(16) 0.01925(11) 0.0895(F) 71.861

2 2225.41215(3) 20.581(18) 0.09544(10) -0.00148(13) 0.01921(7) 0.0895(F) 86.546

3 2226.22968(6) 34.302(170) 0.09259(27) 0.00020(33) 0.01626(7) 0.0895(F) 103.952

4 2227.03986(3) 39.974(36) 0.09157(10) -0.00143(11) 0.01412(6) 0.0895(F) 95.451

5 2227.84333(3) 49.341(34) 0.08975(8) -0.00145(9) 0.01204(6) 0.0895(F) 98.045

6 2228.63983(3) 58.262(48) 0.08936(10) -0.00132(9) 0.01103(6) 0.0895(F) 100.054

7 2229.42949(3) 66.061(55) 0.08800(11) -0.0017(10) 0.01043(5) 0.0895(F) 100.821

8 2230.212(5) 76.312(110) 0.08539(13) -0.00078(15) 0.00878(5) 0.0895(F) 105.773

Page 27 of 32



For Review Only

9 2230.98792(3) 79.555(71) 0.08497(12) -0.00137(10) 0.00647(5) 0.0895(F) 102.06

10 2231.75673(3) 85.537(73) 0.08404(11) -0.00140(9) 0.00558(5) 0.0895(F) 103.051

11 2232.5185(3) 90.633(82) 0.08349(12) -0.00133(10) 0.00429(5) 0.0895(F) 103.887

12 2233.27335(3) 94.523(110) 0.08220(14) -0.00127(11) 0.00394(5) 0.0895(F) 104.285

13 2234.02148(4) 97.398(130) 0.08082(19) -0.00176(16) 0.00346(5) 0.0895(F) 104.574

14 2234.76242(4) 99.054(140) 0.07998(19) -0.00173(12) 0.00192(7) 0.0895(F) 104.489

15 2235.49646(4) 100.49(140) 0.07931(17) -0.00163(12) 0.00126(7) 0.0895(F) 105.023

16 2236.22352(4) 101.8(160) 0.07937(21) -0.00154(12) 0.00055(7) 0.0895(F) 106.363

17 2236.94367(4) 100.66(140) 0.07804(19) -0.00177(11) -0.00184(6) 0.0895(F) 105.905

18 2237.65679(3) 99.412(130) 0.07703(16) -0.00181(10) -0.00116(6) 0.0895(F) 106.074

19 2238.36292(3) 98.056(140) 0.07616(18) -0.00177(11) -0.00186(6) 0.0895(F) 106.902

20 2239.06205(3) 94.403(110) 0.07637(14) -0.00192(10) -0.00285(6) 0.0895(F) 105.859

21 2239.75424(3) 91.868(100) 0.07579(13) -0.00159(9) -0.00413(6) 0.0895(F) 106.592

22 2240.43952(3) 88.529(92) 0.07544(12) -0.00220(9) -0.00398(6) 0.0895(F) 106.96

23 2241.11777(3) 84.439(86) 0.07480(11) -0.00197(9) -0.00494(5) 0.0895(F) 106.921

24 2241.78890(3) 80.336(79) 0.07430(11) -0.00170(9) -0.00639(6) 0.0895(F) 107.175

25 2242.45307(3) 76.315(77) 0.07390(11) -0.00183(9) -0.00608(6) 0.0895(F) 107.995

26 2243.11032(2) 71.635(56) 0.07364(8) -0.00198(8) -0.00677(5) 0.0895(F) 108.018

27 2243.76050(2) 66.542(50) 0.07339(8) -0.00200(8) -0.00796(5) 0.0895(F) 107.582

28 2244.40378(2) 62.111(44) 0.07312(7) -0.00199(8) -0.00720(5) 0.0895(F) 108.133

29 2245.03995(2) 57.317(39) 0.07314(7) -0.00206(8) -0.00789(5) 0.0895(F) 108.181

30 2245.66907(2) 52.745(35) 0.07289(6) -0.00216(8) -0.00927(4) 0.0895(F) 108.368

31 2246.29122(2) 48.228(31) 0.07232(6) -0.00207(8) -0.00922(4) 0.0895(F) 108.458

32 2246.90634(2) 43.785(28) 0.07215(6) -0.00214(8) -0.0101(5) 0.0895(F) 108.382

33 2247.51438(2) 39.755(25) 0.07229(6) -0.00207(8) -0.01001(5) 0.0895(F) 108.789

34 2248.11544(2) 35.829(22) 0.07198(6) -0.00205(8) -0.00960(5) 0.0895(F) 108.94

35 2248.70947(2) 32.175(20) 0.07162(6) -0.00239(8) -0.01267(5) 0.0895(F) 109.203

36 2249.29644(2) 28.700(18) 0.07154(6) -0.00231(8) -0.01116(6) 0.0895(F) 109.329

37 2249.87636(2) 25.350(16) 0.07130(6) -0.00229(8) -0.01292(6) 0.0895(F) 108.872

38 2250.4492(2) 22.507(15) 0.07127(6) -0.00244(9) -0.01199(6) 0.0895(F) 109.507

39 2251.01499(2) 19.738(14) 0.07129(6) -0.00212(9) -0.01274(7) 0.0895(F) 109.343

40 2251.57371(2) 17.264(13) 0.07130(7) -0.00223(10) -0.01341(9) 0.0895(F) 109.332

41 2252.12542(2) 15.056(12) 0.07097(7) -0.0024(10) -0.01367(7) 0.0895(F) 109.599

42 2252.67012(2) 13.063(11) 0.07084(8) -0.00234(11) -0.01419(8) 0.0895(F) 109.697

Page 28 of 32



For Review Only

43 2253.20761(2) 11.273(10) 0.07083(8) -0.00205(11) -0.01452(8) 0.0895(F) 109.814

44 2253.73818(2) 9.693(9) 0.07087(9) -0.00281(12) -0.01512(10) 0.0895(F) 109.941

45 2254.26158(2) 8.336(8) 0.07065(10) -0.0024(13) -0.01547(11) 0.0895(F) 110.671

46 2254.77800(2) 7.052(8) 0.07087(11) -0.00329(13) -0.01619(14) 0.0895(F) 110.056

47 2255.28725(3) 6.008(7) 0.07066(12) -0.00287(14) -0.01654(12) 0.0895(F) 110.692

48 2255.78941(3) 5.056(6) 0.07058(13) -0.00316(14) -0.01691(11) 0.0895(F) 110.529

49 2256.28451(3) 4.272(5) 0.07069(13) -0.00358(15) -0.01758(18) 0.0895(F) 111.26

50 2256.77257(3) 3.558(4) 0.07089(13) -0.00402(16) -0.01869(11) 0.0895(F) 110.884

51 2257.25346(3) 2.974(3) 0.07023(13) -0.00374(16) -0.01827(11) 0.0895(F) 111.403

52 2257.72739(3) 2.461(3) 0.07055(14) -0.00459(17) -0.0185(24) 0.0895(F) 111.348

53 2258.19396(3) 2.049(2) 0.07035(14) -0.00440(19) -0.01857(15) 0.0895(F) 112.362

54 2258.65373(4) 1.682(2) 0.07077(15) -0.00510(20) -0.01935(18) 0.0895(F) 112.425

55 2259.10613(4) 1.383(2) 0.06958(16) -0.00515(22) -0.01816(41) 0.0895(F) 113.026

56 2259.55158(5) 1.126(2) 0.06985(19) -0.00513(25) -0.01829(27) 0.0895(F) 113.153

a All parameters correspond to T=296 K.

b First order line mixing coefficient using the Rosenkranz approximation.

c unitless.

Page 29 of 32



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Table 3. Measured air-broadened half-width coefficients (cm-1atm

-1 at 296 K) and line mixing parameters

(atm-1) and corresponding calculated values obtained using the EPG scaling law.

m

Air broadening Air line mixing

Experimental

EPG

calculation

%

difference Experimental

EPG

calculation

-50 0.07096 0.06980? 1.63 0.0055 0.0077

-49 0.07006 0.06977 0.41 0.0039 0.0076

-48 0.07143 0.06974 2.37 0.0046 0.0076

-47 0.06995 0.06971 0.34 0.0050 0.0076

-46 0.07061 0.06969 1.30 0.0050 0.0075

-45 0.07022 0.06967 0.78 0.0046 0.0075

-44 0.07130 0.06966 2.30 0.0051 0.0075

-43 0.07099 0.06965 1.89 0.0046 0.0074

-42 0.07137 0.06965 2.41 0.0043 0.0074

-41 0.07143 0.06966 2.48 0.0045 0.0073

-40 0.07078 0.06968 1.55 0.0055 0.0072

-39 0.07134 0.06970 2.30 0.0053 0.0071

-38 0.07091 0.06973 1.66 0.0049 0.0071

-37 0.07104 0.06978 1.77 0.0055 0.0070

-36 0.07105 0.06983 1.72 0.0055 0.0069

-35 0.07163 0.06990 2.42 0.0049 0.0068

-34 0.07125 0.06998 1.78 0.0054 0.0067

-33 0.07177 0.07007 2.37 0.0049 0.0066

-32 0.07230 0.07018 2.93 0.0049 0.0065

-31 0.07266 0.07031 3.23 0.0051 0.0063

-30 0.07275 0.07046 3.15 0.0051 0.0061

-29 0.07280 0.07062 2.99 0.0047 0.006

-28 0.07277 0.07081 2.69 0.0050 0.0058

-27 0.07316 0.07102 2.93 0.0050 0.0056

-26 0.07349 0.07126 3.03 0.0039 0.0053

-25 0.07360 0.07153 2.81 0.0040 0.0051

-24 0.07325 0.07183 1.94 0.0040 0.0049

-23 0.07466 0.07216 3.35 0.0040 0.0046

-22 0.07533 0.07254 3.70 0.0041 0.0043

-21 0.07548 0.07295 3.35 0.0040 0.0039

-20 0.07620 0.07341 3.66 0.0040 0.0036

-19 0.07672 0.07393 3.64 0.0038 0.0032

-18 0.07722 0.07450 3.52 0.0041 0.0027

-17 0.07844 0.07513 4.22 0.0019 0.0022

-16 0.07903 0.07584 4.04 -0.0022 0.0016

-15 0.07973 0.07663 3.89 0.0006 0.0009

-14 0.08071 0.07750 3.98 -0.0008 0.0002

-13 0.08111 0.07848 3.24 -0.0022 -0.0006

-12 0.08189 0.07956 2.85 -0.0049 -0.0016

-11 0.08299 0.08078 2.66 -0.0020 -0.0026

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For Review Only

-10 0.08398 0.08214 2.19 -0.0027 -0.0039

-9 0.08561 0.08367 2.27 -0.0040 -0.0054

-8 0.08640 0.08539 1.17 -0.0051 -0.0072

-7 0.08767 0.08733 0.39 -0.0074 -0.0095

-6 0.08887 0.08952 -0.73 -0.0103 -0.0123

-5 0.09019 0.09199 -2.00 -0.0115 -0.0161

-4 0.09113 0.09478 -4.01 -0.0135 -0.0211

-3 0.09234 0.09785 -5.97 -0.0126 -0.0287

-2 0.09562 0.10094 -5.56 -0.0174 -0.0419

-1 0.10026 0.10213 -1.87 -0.0184 -0.0737

1 0.10053 0.10432 -3.77 0.0193 0.0500

2 0.09544 0.10213 -7.01 0.0192 0.0292

3 0.09259 0.10094 -9.02 0.0163 0.0235

4 0.09157 0.09785 -6.86 0.0141 0.0193

5 0.08975 0.09478 -5.60 0.0120 0.0161

6 0.08936 0.09199 -2.94 0.0110 0.0133

7 0.08800 0.08952 -1.73 0.0104 0.0111

8 0.08539 0.08733 -2.27 0.0088 0.0092

9 0.08497 0.08539 -0.49 0.0065 0.0075

10 0.08404 0.08367 0.44 0.0056 0.0060

11 0.08349 0.08214 1.62 0.0043 0.0047

12 0.08220 0.08078 1.73 0.0039 0.0036

13 0.08082 0.07956 1.56 0.0035 0.0025

14 0.07998 0.07848 1.88 0.0019 0.0015

15 0.07931 0.07750 2.28 0.0013 0.0005

16 0.07937 0.07663 3.45 0.0006 -0.0003

17 0.07804 0.07584 2.82 -0.0018 -0.0011

18 0.07703 0.07513 2.47 -0.0012 -0.0019

19 0.07616 0.07450 2.18 -0.0019 -0.0026

20 0.07637 0.07393 3.19 -0.0029 -0.0033

21 0.07579 0.07341 3.14 -0.0041 -0.0039

22 0.07544 0.07295 3.30 -0.0040 -0.0046

23 0.07480 0.07254 3.02 -0.0049 -0.0051

24 0.07430 0.07216 2.88 -0.0064 -0.0057

25 0.07390 0.07183 2.80 -0.0061 -0.0062

26 0.07364 0.07153 2.87 -0.0068 -0.0067

27 0.07339 0.07126 2.90 -0.0080 -0.0072

28 0.07312 0.07102 2.87 -0.0072 -0.0077

29 0.07314 0.07081 3.19 -0.0079 -0.0082

30 0.07289 0.07062 3.11 -0.0093 -0.0087

31 0.07232 0.07046 2.57 -0.0092 -0.0092

32 0.07215 0.07031 2.55 -0.0101 -0.0096

33 0.07229 0.07018 2.92 -0.0100 -0.0101

34 0.07198 0.07007 2.65 -0.0096 -0.0105

35 0.07162 0.06998 2.29 -0.0127 -0.0109

36 0.07154 0.06990 2.29 -0.0112 -0.0113

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For Review Only

37 0.07130? 0.06983 2.06 -0.0129 -0.0118

38 0.07127 0.06978 2.09 -0.0120 -0.0122

39 0.07129 0.06973 2.19 -0.0127 -0.0126

40 0.07130 0.06970 2.24 -0.0134 -0.0130

41 0.07097 0.06968 1.82 -0.0137 -0.0134

42 0.07084 0.06966 1.67 -0.0142 -0.0138

43 0.07083 0.06965 1.67 -0.0145 -0.0143

44 0.07087 0.06965 1.72 -0.0151 -0.0147

45 0.07065 0.06966 1.40 -0.0155 -0.0151

46 0.07087 0.06967 1.69 -0.0162 -0.0156

47 0.07066 0.06969 1.37 -0.0165 -0.0161

48 0.07058 0.06971 1.23 -0.0169 -0.0166

49 0.07069 0.06974 1.34 -0.0176 -0.0171

50 0.07089 0.06977 1.58 -0.0187 -0.0176

51 0.07023 0.06980 0.61 -0.0183 -0.0184

52 0.07055 0.06983 1.02 -0.0185 -0.0192

53 0.07035 0.06987 0.68 -0.0186 -0.0204

54 0.07077 0.06991 1.22 -0.0194 -0.0219

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for review only - university of toronto t-spacefor review only 3 strow et al. [8] who reported line...

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