Uncertainties Associated with Theoretically Uncertainties Associated with Theoretically Calculated NCalculated N22 Broadened Half-widths of H Broadened Half-widths of H22O O

LinesLines

Q. MaQ. MaNASA/Goddard Institute for Space Studies & NASA/Goddard Institute for Space Studies & Department of Applied Physics and Applied Department of Applied Physics and Applied

Mathematics, Columbia UniversityMathematics, Columbia University2880 Broadway, New York, NY 100252880 Broadway, New York, NY 10025

R. H. TippingR. H. TippingDepartment of Physics and Astronomy, University of Department of Physics and Astronomy, University of

Alabama Alabama Tuscaloosa, AL 35487Tuscaloosa, AL 35487

R. R. GamacheR. R. GamacheDepartment of Environmental, Earth and Atmospheric Department of Environmental, Earth and Atmospheric

Science, University of Lowell Science, University of Lowell Lowell, MA 01854Lowell, MA 01854

I. Calculations of the half-widths I. Calculations of the half-widths With the modified Robert-Bonamy (RB) formalism, the half-With the modified Robert-Bonamy (RB) formalism, the half-

width width is given by is given by

The integrand of The integrand of is is Usually, SUsually, S22 consists of three terms S consists of three terms S2,outer,I2,outer,I, S, S2,outer,f2,outer,f, and S, and S2,middle2,middle..

For example, SFor example, S2,outer,I2,outer,I is given by is given by

In order to consider more realistic potentials, it is necessary to In order to consider more realistic potentials, it is necessary to

include a short range atom-atom model Vinclude a short range atom-atom model Vatom-atomatom-atom(t) (t)

' '2 2

2

2 2

2 2 2 2

( )( )

2, , 2( )

2 2 2 2

1

(2 1)

| ( ( ))| | ( ( )) | .

i i i i

ti t t

outer i ii i i m

i i i i i i i i i i i i

S dt dt ei

i m i m V R t i m i m i m i m V R t i m i m

12 6

12 6( ) 4 { }.

( ) ( )

ij ijatom atom ij

i a j b ij ij

V tr t r t

2 2

,min

2Re Re

1 2

0 0

( ) 2 [1 cos( Im ) ] 2 (1 ).2 2

c

b b cc c

r

n nS Svf v dv bdb S S e r dr ec c

2

2Re ( )

(1 ).

crc Se

When one calculates matrix elements of VWhen one calculates matrix elements of Vatom-atomatom-atom(t), one needs (t), one needs to express the latter as a spherical harmonic expansionto express the latter as a spherical harmonic expansion

It is necessary to limit the number of terms to be considered by It is necessary to limit the number of terms to be considered by introducing two cut-offs. introducing two cut-offs.

(1) to limit sets of irreducible tensor indices l(1) to limit sets of irreducible tensor indices l1 1 and land l22.. For lFor l1 1 = 1,2 and l= 1,2 and l22 = 0,2 # of correlations = 20. (only 8 required to be derived) = 0,2 # of correlations = 20. (only 8 required to be derived) For lFor l1 1 = 1,2,3 and l= 1,2,3 and l22 = 0,2 # of correlations = 38. (14 required …) = 0,2 # of correlations = 38. (14 required …) For lFor l1 1 = 1,2,3,4 and l= 1,2,3,4 and l22 = 0,2 # of correlations = 88. (26 required …) = 0,2 # of correlations = 88. (26 required …) For lFor l1 1 = 1,2,3,4 and l= 1,2,3,4 and l22 = 0,2,4 # of correlations = 132. (39 required …) = 0,2,4 # of correlations = 132. (39 required …)

((2) to set an upper limit of w appearing as R2) to set an upper limit of w appearing as R-2w-2w. If one chooses 8 . If one chooses 8 as the maximum of 2w, it is called as the 8-th order cut-off.as the maximum of 2w, it is called as the 8-th order cut-off.

In updating HITRAN 2006, theoretical calculations are derived In updating HITRAN 2006, theoretical calculations are derived

with the 8-th order cut-off and 20 correlations. with the 8-th order cut-off and 20 correlations.

It is the introduction of these two cut-offs that opens the It is the introduction of these two cut-offs that opens the possibility that the results derived are not converged. possibility that the results derived are not converged.

1 2

1 1 2 1 2 { }

1 2

1 1 2

1 1 2 { }

2

* *1 2 1 2 0

( , , )( )

( )

( , ) ( ) ( ) ( ( )).

ij

ijatom atom l l q w

l k l l m m m n wq

l lm k a m b lm

U l k l l n wqV t

R t

C l l l m m m D D Y ω t

II. The Coordinate RepresentationII. The Coordinate RepresentationIn the coordinate representation, the basis set | In the coordinate representation, the basis set | αα > in Hilbert > in Hilbert space arespace are

where Ωwhere Ωaaαα and Ω and Ωbbαα represent orientations of absorber molecule a represent orientations of absorber molecule a and bath molecule b, respectively.and bath molecule b, respectively.

The greatest advantage of the coordinate representation is the The greatest advantage of the coordinate representation is the interaction potential V is diagonal and can be treated as an interaction potential V is diagonal and can be treated as an ordinary function. ordinary function.

It is easy to make transformations between the state and the It is easy to make transformations between the state and the coordinate representations by using the inner productscoordinate representations by using the inner products

With this new representation, one is able not only to derive With this new representation, one is able not only to derive converged results, but also to analyze uncertainties associated converged results, but also to analyze uncertainties associated with theoretically calculated half-widths. with theoretically calculated half-widths.

| | ( ) | ( ) , a a b b

( , , ) | ( , , ) | .

a b a bV R V R

2 2 22| ( ) ( ).

i i ii i i i m a i m bi m i m

III.Three Categories of the HIII.Three Categories of the H22O LinesO Lines With the coordinate representation, one can choose any cut-offs one With the coordinate representation, one can choose any cut-offs one

wants. As a result, one can use this method as a powerful diagnostic tool wants. As a result, one can use this method as a powerful diagnostic tool to check whether values in the literature are converged or not.to check whether values in the literature are converged or not.

For convenience, one can divide all HFor convenience, one can divide all H22O lines into three categories O lines into three categories according to magnitudes of their half-widths. One can use this division to according to magnitudes of their half-widths. One can use this division to judge the convergence behavior and to estimate the uncertainty judge the convergence behavior and to estimate the uncertainty associated with them.associated with them.

For example, there are 268, 661, and 710 lines in categories 1, 2 and 3 For example, there are 268, 661, and 710 lines in categories 1, 2 and 3 (corresponding to (corresponding to > 0.075, 0.075< > 0.075, 0.075< < 0.045, and < 0.045, and < 0.045 in HITRAN < 0.045 in HITRAN 2006). 2006).

Three typical lines in these categories and their convergence checks. Three typical lines in these categories and their convergence checks. In the table, c stands for correlations, p and e stand for parabolic and In the table, c stands for correlations, p and e stand for parabolic and

“exact” trajectories. Calculated N“exact” trajectories. Calculated N2 2 broadened half-widths are given in the broadened half-widths are given in the units of cmunits of cm-1-1 atm atm-1 -1 ..

LineLine 88thth,20c,p,20c,p 2020thth,20c,p,20c,p 2020thth,38c,p,38c,p 2020thth,88c,p,88c,p 2020thth,88c,e,88c,e 2020thth,132c,p,132c,p

331,3 1,3 ← 2← 22,0 2,0 0.108771 0.108771 0.108660 0.108660 0.108763 0.108763 0.1087750.108775 0.1076560.107656 0.1087790.108779

999,0 9,0 ← 8← 86,36,3 0.0521260.052126 0.0530400.053040 0.0581420.058142 0.0584990.058499 0.0583410.058341 0.0586200.058620

17172,15 2,15 ← 16← 161,161,16 0.0258390.025839 0.0297240.029724 0.0331370.033137 0.0365910.036591 0.0316110.031611 0.0370580.037058

III-A Lines in Category 1III-A Lines in Category 1

Fig. 1 A plot to show why calculated half-widths for 31,3 ← 22,0 converge very quickly. Re(S2(rc)) derived from 20, 38, and 88 correlations and using the 20-th cut-off are plotted by black solid, dashed, and dash-dotted lines. Exp(-Re(S2(rc))) and the integrand of are given by blue and red curves. In order to show exp(-Re(S2(rc))) more clearly, their values are multiplied by 1000. There are significant differences among Re(S2(rc)) derived with different numbers of the correlations, the integrands are almost identical. This implies calculated half-widths with 20 correlations are converged.

III-A Lines in Category 1III-A Lines in Category 1

Fig. 2 The same as Fig. 1 except that results are derived from the 8-th, Fig. 2 The same as Fig. 1 except that results are derived from the 8-th, 14-th, and 20-th order cut-offs. The calculations are based on including 14-th, and 20-th order cut-offs. The calculations are based on including 20 correlations and the “parabolic” trajectory model. The plot 20 correlations and the “parabolic” trajectory model. The plot demonstrates that with respect to the second kind of cut-off, the demonstrates that with respect to the second kind of cut-off, the calculated half-width of this line converges very quickly.calculated half-width of this line converges very quickly.

III-A. Lines in Category 1III-A. Lines in Category 1 Magnitudes of Re(SMagnitudes of Re(S22(r(rcc)) for r)) for rc c < < σσ are very large. Thus, are very large. Thus, its its

effects on the integrands of effects on the integrands of are almost diminished for r are almost diminished for rc c < < σσ.. The convergence of Re(SThe convergence of Re(S22(r(rcc)))) at rat rc c < < σσ is poor. But, the is poor. But, the

convergence of convergence of the integrands of the integrands of is very good. is very good.

Calculated half-widths for 3Calculated half-widths for 31,3 1,3 ← 2← 22,0 2,0 with low cut-offs are well with low cut-offs are well converged.converged.

Large Large Re(SRe(S22(r(rcc)))) are associated with large are associated with large . This implies that . This implies that lines in category 1 would not suffer from the convergence lines in category 1 would not suffer from the convergence difficulty. difficulty.

Because calculated Because calculated are not sensitive to variations of the short are not sensitive to variations of the short range interaction, one should not choose lines in category 1 to range interaction, one should not choose lines in category 1 to optimize the site-site potential model. In contrast, they are optimize the site-site potential model. In contrast, they are good candidates to optimize the long range potential model.good candidates to optimize the long range potential model.

Within this category, uncertainties associated with theoretically Within this category, uncertainties associated with theoretically calculated calculated are the smallest. are the smallest.

III-B Lines in Category 3III-B Lines in Category 3

Fig. 3 The same as Fig. 1 except for the line of 17Fig. 3 The same as Fig. 1 except for the line of 172,15 2,15 ← 16← 161,161,16 and multiplying exp(-Re(Sxp(-Re(S22(r(rcc)))))) by 10. Results are obtained with including 20, including 20, 38, and 88 correlations. 38, and 88 correlations.

III-B Lines in Category 3III-B Lines in Category 3

Fig. 4 The same as Fig. 2 except for the line of 17Fig. 4 The same as Fig. 2 except for the line of 172,15 2,15 ← 16← 161,161,16 and multiplying exp(-Re(Sxp(-Re(S22(r(rcc)))))) by 10. Results are obtained with adopting the 8-th, 14-th, and 20-th order cut-offs.

III-B. Lines in Category 3III-B. Lines in Category 3 In comparison with 3In comparison with 31,3 1,3 ← 2← 22,0 2,0 in category 1, magnitudes of Re(Sin category 1, magnitudes of Re(S22(r(rcc)))) for for

17172,15 2,15 ← 16← 161,16 1,16 areare one order smaller. They decrease more quickly as rone order smaller. They decrease more quickly as rc c

increases, and are close to 0 after rincreases, and are close to 0 after rc c > > σσ.. The convergence of Re(S The convergence of Re(S22(r(rcc))))

is poor.is poor.

Because the magnitudes of Because the magnitudes of Re(SRe(S22(r(rcc)))) are small, their effects on the are small, their effects on the integrand of integrand of are well preserved. are well preserved. Thus, the latter’s convergence is Thus, the latter’s convergence is poor. In addition, the latter’s magnitudes decrease very quickly and poor. In addition, the latter’s magnitudes decrease very quickly and are close to 0 for are close to 0 for rrc c > > σσ.. This implies that This implies that would be small. would be small.

The convergences of The convergences of are very poor such that with usual methods, are very poor such that with usual methods, one is not able to obtain converged results. one is not able to obtain converged results.

Dominant contributions to Dominant contributions to come from nearly head-on collisions. This come from nearly head-on collisions. This implies that both changes of the short range interaction and different implies that both changes of the short range interaction and different depictions of the trajectories would cause significant changes of depictions of the trajectories would cause significant changes of calculated calculated . .

One can choose lines in this category to optimize the site-site One can choose lines in this category to optimize the site-site potential model and to test the trajectory model.potential model and to test the trajectory model.

Uncertainties associated with theoretically calculated Uncertainties associated with theoretically calculated are the largest. are the largest.

III-C Lines in Category 2III-C Lines in Category 2

Fig. 5 The same as Fig. 1 except for the line of Fig. 5 The same as Fig. 1 except for the line of 99,0 ← 86,3 and multiplying and multiplying exp(-Re(Sexp(-Re(S22(r(rcc)))))) by 10. Results are obtained with including 20, 38, and 88 by 10. Results are obtained with including 20, 38, and 88 correlations.correlations.

III-C Lines in Category 2III-C Lines in Category 2

Fig. 6 The same as Fig. 2 except for the line of Fig. 6 The same as Fig. 2 except for the line of 99,0 ← 86,3 and multiplying and multiplying exp(-Re(Sexp(-Re(S22(r(rcc)))))) by 10. Results are obtained with adopting the 8-th, 14-th, by 10. Results are obtained with adopting the 8-th, 14-th, and 20-th order cut-offs.and 20-th order cut-offs.

III-C. Lines in Category 2III-C. Lines in Category 2 In comparison with 3In comparison with 31,3 1,3 ← 2← 22,0 2,0 and 17and 172,15 2,15 ← 16← 161,161,16,,

magnitudes of Re(Smagnitudes of Re(S22(r(rcc)))) for 9for 99,0 9,0 ← 8← 8 6,3 6,3 are are intermediate. intermediate.

The convergence of The convergence of Re(SRe(S22(r(rcc)) is poor. is poor.

Because magnitudes of Because magnitudes of Re(SRe(S22(r(rcc)))) are intermediate, its effects are intermediate, its effects on the integrand of on the integrand of are partially preserved and partially are partially preserved and partially suppressed suppressed for for rrc c > > σσ. .

The convergence of calculated The convergence of calculated for for 999,0 9,0 ← 8← 8 6,3 6,3 is worse than is worse than 331,3 1,3 ← 2← 22,02,0, but is better 17, but is better 172,15 2,15 ← 16← 161,161,16. .

Calculated Calculated for this line is smaller than for this line is smaller than 331,3 1,3 ← 2← 22,02,0, but larger , but larger than 17than 172,15 2,15 ← 16← 161,161,16. .

Uncertainties associated with theoretically calculated Uncertainties associated with theoretically calculated are the are the intermediate.intermediate.

III-D Comparisons among lines in three categoriesIII-D Comparisons among lines in three categories

Fig. 7 A plot to show comparisons among calculated integrands of Fig. 7 A plot to show comparisons among calculated integrands of for for the three lines of interest. For each of them, we plots two results derived the three lines of interest. For each of them, we plots two results derived from the lowest choice of the cut-offs (i.e., the 8-th and 20 correlations) from the lowest choice of the cut-offs (i.e., the 8-th and 20 correlations) and from a higher one (i.e., the 20-th and 88 correlations) by a dot-dashed and from a higher one (i.e., the 20-th and 88 correlations) by a dot-dashed and a solid curves, respectively. Meanwhile, the curves for different lines and a solid curves, respectively. Meanwhile, the curves for different lines are distinguished by three colors. are distinguished by three colors.

III-D Comparisons among three lines in different categoriesIII-D Comparisons among three lines in different categories

Fig. 8 A plot to show percentage contributions to Fig. 8 A plot to show percentage contributions to at 296 K from at 296 K from collisions whose closet distances ranging from rcollisions whose closet distances ranging from rc,min c,min to rto rcc. Results . Results derived for 3derived for 31,3 1,3 ← 2← 22,02,0, 9, 99,0 9,0 ← 8← 86,36,3, and 17, and 172,15 2,15 ← 16← 161,16 1,16 are represented are represented by a black, red, and green curves, respectively. The calculations by a black, red, and green curves, respectively. The calculations are carried out with the 20-th order and including 88 correlations.are carried out with the 20-th order and including 88 correlations.

IV Convergence checkIV Convergence check

Fig. 9 Calculated NFig. 9 Calculated N22-broadened half-widths of the 1639 lines of the H-broadened half-widths of the 1639 lines of the H22O pure rotational O pure rotational band. These results are derived by including 20, 38, 88, and 132 correlations and by band. These results are derived by including 20, 38, 88, and 132 correlations and by adopting the 20-th order cut-off. They are plotted by symbolsadopting the 20-th order cut-off. They are plotted by symbols □□, , ++, , ×,×, and ∆ respectively. and ∆ respectively.

IV Convergence checkIV Convergence check

Fig. 10 Calculated NFig. 10 Calculated N22-broadened half-widths of the 1639 lines of the H-broadened half-widths of the 1639 lines of the H22O pure rotational O pure rotational band. These results are derived by adopting the 8-th, 14-th, and 20-th order cut-offs and band. These results are derived by adopting the 8-th, 14-th, and 20-th order cut-offs and by including 20 correlation functions. They plotted by symbols by including 20 correlation functions. They plotted by symbols ++, , ×,×, and ∆, respectively. and ∆, respectively.

V. MODIFICATION OF THE RB FORMALISMV. MODIFICATION OF THE RB FORMALISM

There is a subtle derivation error in applying the There is a subtle derivation error in applying the Linked-Cluster Theorem.Linked-Cluster Theorem.

After making the correction, the expressions for the After making the correction, the expressions for the half-width and shift differ from the original ones. half-width and shift differ from the original ones.

For example, in the RB formalismFor example, in the RB formalism

and in the modified RB formalismand in the modified RB formalism

where <A >where <A >j2 j2 is a notation foris a notation for

2

21 2

0 0

Re( )( ) 2 1 cos( Im( )) ,

2

b

RB j

n Sv f v dv bdb S S e

c

2

2 2

)2mod 1 2

0 0

Re(( ) 2 [1 cos( Im( )) ].

2

jbifiedRB j j

Snvf v dv bdb S S e

c

2

2

22 2

( ) /(2 1) ( ) / . j bj

E j kTA j e A j Q

V. MODIFICATION OF THE RB FORMALISMV. MODIFICATION OF THE RB FORMALISM

Fig. 11 Relative errors of calculated Fig. 11 Relative errors of calculated resulting from the subtle error in resulting from the subtle error in developing the RB formalism. The percentage errors are measured by developing the RB formalism. The percentage errors are measured by ((modifiedRB modifiedRB - - RBRB) / ) / modifiedRB modifiedRB %. The calculations are carried out with the 20-th %. The calculations are carried out with the 20-th order, 88 correlations, and the “parabolic” trajectory. In the plot, the 1639 order, 88 correlations, and the “parabolic” trajectory. In the plot, the 1639 lines are arranged in a ascending order of their half-width values. lines are arranged in a ascending order of their half-width values.

VI Comparison between calculated half-widths and VI Comparison between calculated half-widths and HITRAN 2006HITRAN 2006

Fig. 12 Comparisons between calculated Fig. 12 Comparisons between calculated from the 8-th order, 20 correlations, and the from the 8-th order, 20 correlations, and the “parabolic” trajectory and air-broadened half-widths in HITRAN. The former are plotted by “parabolic” trajectory and air-broadened half-widths in HITRAN. The former are plotted by symbols symbols ×× and the latter are given by symbols ∆, respectively. The calculated N and the latter are given by symbols ∆, respectively. The calculated N22--broadened half-widths have been adjusted to air-broadened ones by multiplying by 1/1.09.broadened half-widths have been adjusted to air-broadened ones by multiplying by 1/1.09.

VI Comparison between calculated half-widths and VI Comparison between calculated half-widths and HITRAN 2006HITRAN 2006

Fig. 13 The same as Fig. 12 except that calculated half-widths are derived Fig. 13 The same as Fig. 12 except that calculated half-widths are derived by using the 20-th order cut-off, including 88 correlations, and adopting by using the 20-th order cut-off, including 88 correlations, and adopting the “exact” trajectory model.the “exact” trajectory model.

VII Comparison between HITRAN 2006 and 2009VII Comparison between HITRAN 2006 and 2009

Fig. 14 Comparisons between air-broadened half-widths in HITRAN 2006 and 2009. They are plotted Fig. 14 Comparisons between air-broadened half-widths in HITRAN 2006 and 2009. They are plotted by × and ∆, respectively. The H2O lines of the pure rotational band are arranged according to the by × and ∆, respectively. The H2O lines of the pure rotational band are arranged according to the ascending order of their air-broadened half-widths in HITRAN 2009. Among 1639 lines, there are 1489 ascending order of their air-broadened half-widths in HITRAN 2009. Among 1639 lines, there are 1489 lines whose half-widths have been modified. There are 677 lines with relative differences are above lines whose half-widths have been modified. There are 677 lines with relative differences are above 10%, 313 lines within 4 – 10%, and 649 lines with less than 4 % including those without changes.10%, 313 lines within 4 – 10%, and 649 lines with less than 4 % including those without changes.

VII Comparison between HITRAN 2006 and 2009VII Comparison between HITRAN 2006 and 2009

Fig. 15 A comparison of the temperature exponents n listed in the HITRAN 2006 and 2009. Fig. 15 A comparison of the temperature exponents n listed in the HITRAN 2006 and 2009. There are dramatically differences between these two versions of n. Among 1639 lines, There are dramatically differences between these two versions of n. Among 1639 lines, there are 245 lines whose temperature exponent n become negative. It is worth there are 245 lines whose temperature exponent n become negative. It is worth mentioning that the lines with negative n values are those with high Jmentioning that the lines with negative n values are those with high Ji i and Jand Jf f and with and with small half-widths. small half-widths.

An example to show the convergence problem associated with nAn example to show the convergence problem associated with n

Fig. 16 The T dependence of the half-width for the line 16Fig. 16 The T dependence of the half-width for the line 1614,2 14,2 ← 15← 1513,3 13,3 in the range from 220 in the range from 220 K – 340 K derived from adopting different cut-offs and including different numbers of the K – 340 K derived from adopting different cut-offs and including different numbers of the correlation functions. In the plot, a negative slope means a negative n and a positive correlation functions. In the plot, a negative slope means a negative n and a positive slope means a positive n.slope means a positive n.In HITRAN 2006, n = 0.38 and in HITRAN 2009, n = - 0.79.In HITRAN 2006, n = 0.38 and in HITRAN 2009, n = - 0.79.

VII Comments on HITRAN 2009VII Comments on HITRAN 2009 TThere are significant differences between air-broadened half-here are significant differences between air-broadened half-

widths listed in HITRAN 2006 and 2009. Among 1639 lines, widths listed in HITRAN 2006 and 2009. Among 1639 lines, there are 1489 lines whose half-widths have been modified. there are 1489 lines whose half-widths have been modified. There are 677 lines with relative differences above 10 %, 313 There are 677 lines with relative differences above 10 %, 313 lines within 4 – 10 %, and 649 lines with less than 4 % including lines within 4 – 10 %, and 649 lines with less than 4 % including those without changes.those without changes.

The modification of HITRAN 2006 is necessary. But, in the 2009 The modification of HITRAN 2006 is necessary. But, in the 2009 version, many theoretically calculated results are not version, many theoretically calculated results are not converged. In addition, the potential model used in these converged. In addition, the potential model used in these theoretical calculations is poor.theoretical calculations is poor.

With respect to the temperature exponents n, there are With respect to the temperature exponents n, there are dramatically differences between these two versions. Among dramatically differences between these two versions. Among 1639 lines, there are 245 lines whose temperature exponent n 1639 lines, there are 245 lines whose temperature exponent n become negative. become negative.

In general, lines with negative n values are those with large JIn general, lines with negative n values are those with large J i i

and Jand Jf f and with small half-widths. Thus, there are serious and with small half-widths. Thus, there are serious convergence problems associated with those calculated n. We convergence problems associated with those calculated n. We are open to accept negative n values. But, we believe some of are open to accept negative n values. But, we believe some of these negative values of n in HITRAN 2009 are not correct.these negative values of n in HITRAN 2009 are not correct.

IX. ConclusionsIX. Conclusions With the current RB formalism,With the current RB formalism, calculated half-widths for calculated half-widths for

lines in category 1 have small uncertainties. Thus, one can lines in category 1 have small uncertainties. Thus, one can achieve the accuracy requirement set by HITRAN.achieve the accuracy requirement set by HITRAN.

For lines in category 3, calculated half-widths contain larger For lines in category 3, calculated half-widths contain larger uncertainties. It is impossible to meet this goal.uncertainties. It is impossible to meet this goal.

For lines in category 2, the situations are in between these two For lines in category 2, the situations are in between these two extremes.extremes.

When theorists optimize the potential models, they need to When theorists optimize the potential models, they need to select lines properly.select lines properly.

When experimentalists determine the measurement priority, When experimentalists determine the measurement priority, they can add another consideration that their measured data they can add another consideration that their measured data for lines in category 3 have an extra reliability advantage.for lines in category 3 have an extra reliability advantage.

When people update HITRAN for lines in category 3, it would be When people update HITRAN for lines in category 3, it would be helpful to know there are large uncertainties associated with helpful to know there are large uncertainties associated with theoretically calculated values.theoretically calculated values.