pair identity and smooth variation rules applicable for the spectroscopic parameters of h 2 o...

Pair Identity and Smooth Variation Pair Identity and Smooth Variation Rules Applicable for the Spectroscopic Rules Applicable for the Spectroscopic

Parameters of HParameters of H22O Transitions O Transitions

Involving High J StatesInvolving High J States

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

Applied Physics and Applied Mathematics, Columbia UniversityApplied Physics and Applied Mathematics, Columbia University2880 Broadway, New York, NY 10025, USA2880 Broadway, New York, NY 10025, USA

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

Tuscaloosa, AL 35487, USATuscaloosa, AL 35487, USA

N. N. Lavrentieva N. N. Lavrentieva V. E. Zuev Institute of Atmospheric Optics SB RAS, 1, V. E. Zuev Institute of Atmospheric Optics SB RAS, 1,

Akademician Zuev square, Tomsk 634021, RussiaAkademician Zuev square, Tomsk 634021, Russia

I. Basic Idea in Analyzing Spectroscopic I. Basic Idea in Analyzing Spectroscopic Parameters of HParameters of H22O Lines O Lines

A whole system consists of one absorber HA whole system consists of one absorber H22O molecule, bath O molecule, bath molecules, and electromagnetic fields. molecules, and electromagnetic fields.

By considering this system as a black box, its inputs are the By considering this system as a black box, its inputs are the

HH22O lines of interest and its outputs are the spectroscopic O lines of interest and its outputs are the spectroscopic parameters.parameters.

Basic assumptions: (1) The outputs depend on the inputs. (2) Basic assumptions: (1) The outputs depend on the inputs. (2) Identical inputs should yield identical outputs. (3) Similar Identical inputs should yield identical outputs. (3) Similar inputs should yield similar outputs. inputs should yield similar outputs.

The inputs are the energy levels and wave functions associated The inputs are the energy levels and wave functions associated with the initial and final states of the Hwith the initial and final states of the H22O lines. O lines.

A Black Box inputsoutputs

II. Properties of the energy levels and wave II. Properties of the energy levels and wave functions of Hfunctions of H22OO

(1) One categories the H(1) One categories the H22O states into different sets of paired states {JO states into different sets of paired states {J0,J0,J, , JJ1,J1,J}, {J}, {J1,J-11,J-1, J, J2,J-12,J-1}, {J}, {J2,J-22,J-2, J, J3,J-23,J-2}, }, ···, {J···, {JJ-2,3J-2,3, J, JJ-2,2J-2,2}, {J}, {JJ-1,2J-1,2,J,JJ-1,1J-1,1}, {J}, {JJ,1J,1,J,JJ,0J,0}. }.

(2) Within each of the sets, the energy levels of two paired states with high (2) Within each of the sets, the energy levels of two paired states with high J are almost identical. For different pairs, their energy levels vary smoothly J are almost identical. For different pairs, their energy levels vary smoothly as J varies and these variation patterns are well organized. as J varies and these variation patterns are well organized.

(3) With respect to the H(3) With respect to the H22O wave functions, they are given in terms of O wave functions, they are given in terms of expansion coefficients over the symmetric top wave functions |expansion coefficients over the symmetric top wave functions |JKM>, JKM>,

(4) Within each of the sets, the coefficients of two paired states with high J (4) Within each of the sets, the coefficients of two paired states with high J have almost identical magnitudes. For different pairs, patterns of their have almost identical magnitudes. For different pairs, patterns of their coefficients are very similar and the placements of the patterns shift coefficients are very similar and the placements of the patterns shift smoothly as J varies. smoothly as J varies.

(5) The above are useful features of the inputs. By exploiting them, one can (5) The above are useful features of the inputs. By exploiting them, one can access important conclusions on the outputs without requiring to know access important conclusions on the outputs without requiring to know what really happens inside the box. what really happens inside the box.

| | . JK

K

J M U JKM

JKU

II-1 Properties of the Energy Levels of HII-1 Properties of the Energy Levels of H22OO

Fig. 1 A plot to show energy levels of H2O states with J = 11 thru 20 in the vibrational ground state. For states with J + Ka – Kc = even, their energy levels are plotted by × and their values of Ka – Kc are presented on the right side of the symbols. Meanwhile, for states with J + Ka – Kc = odd, their energy levels are plotted by ∆ and values of Ka – Kc are on the left side of the symbols.

II-2 Properties of the HII-2 Properties of the H22O Wave FunctionsO Wave Functions

Fig. 2 A plot to show properties of HFig. 2 A plot to show properties of H22O wave functions in the I R representation for O wave functions in the I R representation for three sets of pairs of states: {Jthree sets of pairs of states: {JJ,0J,0,J,JJ,1J,1}, {J}, {JJ-1,1J-1,1,J,JJ-1,2J-1,2}, and {J}, and {JJ-2,2J-2,2,J,JJ2,3J2,3}.}.

II-2 Properties of the HII-2 Properties of the H22O Wave FunctionsO Wave Functions

Fig. 3 A plot to show properties of HFig. 3 A plot to show properties of H22O wave functions in the III R representation for three sets of pairs O wave functions in the III R representation for three sets of pairs of states: {Jof states: {J0,J0,J,J,J1,J1,J}, {J}, {J1,J-11,J-1,J,J2,J-12,J-1}, and {J}, and {J2,J-22,J-2,J,J3,J-23,J-2}.}.: . : .

II-3 Boundaries for individual sets of paired states II-3 Boundaries for individual sets of paired states

In each of the sets, the pair identity and the smooth variation break down In each of the sets, the pair identity and the smooth variation break down for J is below certain boundaries.for J is below certain boundaries.

By introducing a numerical measure By introducing a numerical measure εε defined by defined by

where J, where J, 1 1 and J, and J, 22 are paired states and are paired states and = K = Ka a – K– Kcc, one can calculate how , one can calculate how εε varies with J. varies with J.

The higher the J, the smaller the The higher the J, the smaller the εε. By choosing . By choosing εε is about 1 %, one can is about 1 %, one can determine a boundary Jdetermine a boundary Jbd bd for each of the sets. The results is listed in Table.for each of the sets. The results is listed in Table.

setset JJJ,0J,0

JJJ,1 J,1

JJJ-1,1J-1,1

JJJ-1,2J-1,2

JJJ-2,2J-2,2

JJJ-2,3J-2,3

JJJ-3,3J-3,3

JJJ-3,4J-3,4

JJJ-4,4J-4,4

JJJ-4,5J-4,5

JJJ-5,5J-5,5

JJJ-5,6J-5,6

JJJ-6,6J-6,6

JJJ-6,7J-6,7

······ JJ4,J-4 4,J-4

JJ5,J-45,J-4

JJ3,J-3 3,J-3

JJ4,J-34,J-3

JJ2,J-2 2,J-2

JJ3,J-23,J-2

JJ1,J-1 1,J-1

JJ2,J-12,J-1

JJ0,J0,J

JJ1,J1,J

JJbd bd 33 55 77 99 1010 1212 1414 ······ 1919 1616 1313 1010 77

εε (%)(%)

0.630.63 0.660.66 0.490.49 0.320.32 1.081.08 0.600.60 0.320.32 ······ 1.281.28 0.550.55 1.131.13 1.001.00 0.600.60

2 1 1

22 2|| | | | | / | | , J J JK K K

K K

U U U

III. Categorizations of HIII. Categorizations of H22O lines and discovery of two O lines and discovery of two

rules applicable for all spectroscopic parametersrules applicable for all spectroscopic parameters To categorize HTo categorize H22O lines such that within individual groups, the O lines such that within individual groups, the

inputs of lines have similarities. Then, one expects their inputs of lines have similarities. Then, one expects their outputs have similarities too.outputs have similarities too.

The procedure is carried out by dividing all lines into the P, Q, The procedure is carried out by dividing all lines into the P, Q,

and R branches first and then, by categorizing them into sets and R branches first and then, by categorizing them into sets of paired lines. As example, a group consists of paired lines Jof paired lines. As example, a group consists of paired lines J′′0,J’ 0,J’ ← J″← J″1,J1,J" " and J′and J′1,J1,J′′ ← J″← J″0,J0,J"" and a group of J′ and a group of J′JJ′,0′,0 ← J″← J″JJ″,1 ″,1 and J′and J′JJ′,1′,1 ← ← J″J″JJ″,0″,0..

It turns out that the similarities of the outputs do exist. Thus, It turns out that the similarities of the outputs do exist. Thus, two rules can be established. These rules hold within certain two rules can be established. These rules hold within certain accuracy tolerances. Corresponding to 1 % accuracy of the accuracy tolerances. Corresponding to 1 % accuracy of the inputs, we choose 5 % as the accuracy tolerances.inputs, we choose 5 % as the accuracy tolerances.

The pair identity rule: Two paired lines whose J values are The pair identity rule: Two paired lines whose J values are above certain boundaries in the same groups have almost above certain boundaries in the same groups have almost identical spectroscopic parameters. identical spectroscopic parameters.

The smooth variation rule: For different pairs of states in the The smooth variation rule: For different pairs of states in the same groups, values of their spectroscopic parameters vary same groups, values of their spectroscopic parameters vary smoothly as their J values vary.smoothly as their J values vary.

IV. Demonstrations of the two rules by MeasurementsIV. Demonstrations of the two rules by Measurements

Fig. 4Fig. 4 Demonstrations of the pair identity and smooth variation rules for line Demonstrations of the pair identity and smooth variation rules for line strengths, air- and Nstrengths, air- and N22-broadened half-widths, and induced shifts in a group of paired -broadened half-widths, and induced shifts in a group of paired lines J′lines J′3,J’-2 3,J’-2 ← J″← J″0,J0,J" " and J′and J′2,J’-2 2,J’-2 ← J″← J″1,J1,J" " in the R branch. The measured values by Toth are in the R branch. The measured values by Toth are plotted byplotted by × × and and ∆∆, respectively. The spin degeneracy factor is excluded for the , respectively. The spin degeneracy factor is excluded for the strength.strength. The boundary of this group is JThe boundary of this group is Jbd bd = 13.= 13.

IV. Demonstration of the two rules by MeasurementsIV. Demonstration of the two rules by Measurements

Fig. 5 Demonstration of the pair identity and smooth variation rules in a Fig. 5 Demonstration of the pair identity and smooth variation rules in a group of paired lines of Jgroup of paired lines of J''0,J' 0,J' ← J"← J"1,J"-1 1,J"-1 and and JJ''1,J' 1,J' ← J"← J"2,J"-1 2,J"-1 in the Q branch of the in the Q branch of the νν2 2 band. The air-broadened half-widths (in cmband. The air-broadened half-widths (in cm -1-1/bar) are from measurements /bar) are from measurements by Yamada. The boundary of this group is about by Yamada. The boundary of this group is about JJbdbd = 10.= 10.

V. Comparison between HITRAN HV. Comparison between HITRAN H22O 2006 and 2009O 2006 and 2009

Fig. 6Fig. 6 Comparisons between air-broadened half-widths in HITRAN HComparisons between air-broadened half-widths in HITRAN H22O O 2006 and 2009. They are plotted by2006 and 2009. They are plotted by × × and ∆, respectively. The 1639 lines and ∆, respectively. The 1639 lines of the Hof the H22O pure rotational band are arranged according to the ascending O pure rotational band are arranged according to the ascending order of the half-width values of HITRAN Horder of the half-width values of HITRAN H22O 2009.O 2009.


Fig. 7 The same as Fig. 6 except for values of the temperature exponent Fig. 7 The same as Fig. 6 except for values of the temperature exponent (T exponent) n. There are dramatically differences between these two (T exponent) n. There are dramatically differences between these two versions of n. Among 1639 lines, there are 245 lines whose T exponent n versions of n. Among 1639 lines, there are 245 lines whose T exponent n become negative. become negative.


Table 2. Relative differences of parameters in HITRAN HTable 2. Relative differences of parameters in HITRAN H22O 2006 and 2009.O 2006 and 2009.

Rough estimations of uncertainties associated with all the spectroscopic Rough estimations of uncertainties associated with all the spectroscopic parameters. parameters. (1) For the line position and intensity, their uncertainties are less than the (1) For the line position and intensity, their uncertainties are less than the accuracy tolerance.accuracy tolerance.(2) For the half-widths, shift, and T exponent, their uncertainties are larger (2) For the half-widths, shift, and T exponent, their uncertainties are larger than the accuracy tolerance.than the accuracy tolerance.Conclusions: For positions and intensities of lines, two rules enable one Conclusions: For positions and intensities of lines, two rules enable one to identify errors. For other parameters, they enable one to identify errors to identify errors. For other parameters, they enable one to identify errors and to improve accuracies. and to improve accuracies.

Number of linesNumber of lines

differencedifference IntensityIntensity Air-widthAir-width Self-widthSelf-width shiftshift T-expon.T-expon.

> 50 %> 50 % 2525 143143 246246 572572 630630

30 - 50 %30 - 50 % 88 165165 280280 121121 360360

10 – 30 %10 – 30 % 1313 369369 601601 420420 421421

< 10 %< 10 % 15931593 962962 512512 526526 228228

unchangedunchanged 15851585 150150 107107 158158 2020

VI-1. Screening HITRAN HVI-1. Screening HITRAN H22O O

2009 2009 (Example 1 in the R branch)(Example 1 in the R branch)

Fig. 8 Six spectroscopic Fig. 8 Six spectroscopic parameters for a group of paired parameters for a group of paired lines Jlines J′′JJ′,1 ′,1 ← J″← J″J″,0 J″,0 and and JJ′′JJ′,0 ′,0 ← J″← J″J″,1 J″,1 in the R branch. Their values in in the R branch. Their values in HITRAN HHITRAN H22O 2009 are plotted by O 2009 are plotted by ×× and and ∆∆, respectively. The , respectively. The boundary of this group is Jboundary of this group is Jbd bd = 3.= 3.

ParameterParameter Questionable LinesQuestionable Lines

PositionPosition NoneNone

IntensityIntensity NoneNone

Air-Air-

Half-widthHalf-width

999,0 9,0 ← 8← 88,18,1, , 999,1 9,1 ← 8← 88,08,0,,

101010,0 10,0 ← 9← 99,19,1, 10, 1010,1 10,1 ← 9← 99,09,0,,

111111,0 11,0 ← 10← 1010,110,1, 11, 1111,1 11,1 ← 10← 1010,010,0

Self-Self-


131313,0 13,0 ← 12← 1212,112,1,13,1313,1 13,1 ← 12← 1212,012,0

Induced Induced shiftshift

999,0 9,0 ← 8← 88,18,1, , 999,1 9,1 ← 8← 88,08,0,,

101010,0 10,0 ← 9← 99,19,1, 10, 1010,1 10,1 ← 9← 99,09,0,,

111111,0 11,0 ← 10← 1010,110,1, 11, 1111,1 11,1 ← 10← 1010,010,0,,

121212,0 12,0 ← 11← 1111,111,1, 12, 1212,1 12,1 ← 11← 1111,011,0,,

131313,0 13,0 ← 12← 1212,112,1, 13, 1313,1 13,1 ← 12← 1212,012,0,,

141414,0 14,0 ← 13← 1313,113,1, 14, 1414,1 14,1 ← 13← 1313,013,0

T T exponentexponent

999,0 9,0 ← 8← 88,18,1, , 999,1 9,1 ← 8← 88,08,0,,

101010,0 10,0 ← 9← 99,19,1, 10, 1010,1 10,1 ← 9← 99,09,0,,

111111,0 11,0 ← 10← 1010,110,1, 11, 1111,1 11,1 ← 10← 1010,010,0

VI-1. SVI-1. Suggested values of the air-broadened half-width for lines uggested values of the air-broadened half-width for lines

in in the ethe example 1 of the R branchxample 1 of the R branch

Fig. 9 Based on the two rules, suggested air-broadened half-widths for the group of Fig. 9 Based on the two rules, suggested air-broadened half-widths for the group of paired lines Jpaired lines J′′JJ′,1 ′,1 ← J″← J″J″,0 J″,0 and and JJ′′JJ′,0 ′,0 ← J″← J″J″,1 J″,1 in the R branch are plotted by in the R branch are plotted by ++. Meanwhile, . Meanwhile, the original values in HITRAN Hthe original values in HITRAN H22O 2009 are given by O 2009 are given by ×× and and ∆∆, respectively. , respectively.

LinesLines HITRAN HITRAN 20092009

Suggest-Suggest-ed ed

valuesvalues

889,0 9,0 ← 7← 78,1 8,1

889,1 9,1 ← 7← 78,08,0

0.02720.0272

0.02720.0272

0.02640.0264

999,0 9,0 ← 8← 88,1 8,1

999,1 9,1 ← 8← 88,08,0

0.01340.0134

0.01340.0134

0.01950.0195

10109,0 9,0 ← 9← 98,1 8,1

10109,1 9,1 ← 9← 98,08,0

0.01240.0124

0.01240.0124

0.01610.0161

11119,0 9,0 ← 10← 108,1 8,1

11119,1 9,1 ← 10← 108,08,0

0.02030.0203

0.02030.0203

0.01560.0156



Fig. 10 The same as Fig. 8 except Fig. 10 The same as Fig. 8 except for a group of paired lines Jfor a group of paired lines J′′3,J3,J′-2 ′-2 ← ← J″J″0,J″ 0,J″ and and JJ′′2,J2,J′-2 ′-2 ← J″← J″1,J″ 1,J″ in the R in the R branch. The boundary of this branch. The boundary of this group is Jgroup is Jbd bd = 13.= 13.

ParameterParameter Questionable linesQuestionable lines

PositionsPositions NoneNone

IntensityIntensity 21213,19 3,19 ← 20← 200,200,20, 21, 212,19 2,19 ← 20← 201,201,20

Air-Air-


17173,15 3,15 ← 16← 160,160,16, 17, 172,15 2,15 ← 16← 161,161,16,,

18183,16 3,16 ← 17← 170,170,17, 18, 182,16 2,16 ← 17← 171,171,17,,

19193,17 3,17 ← 18← 180,180,18, 19, 192,17 2,17 ← 18← 181,181,18

Self-Self-


18183,16 3,16 ← 17← 170,170,17, 18, 182,16 2,16 ← 17← 171,171,17,,

19193,17 3,17 ← 18← 180,180,18, 19, 192,17 2,17 ← 18← 181,181,18,,

20203,18 3,18 ← 19← 190,190,19, 20, 202,18 2,18 ← 19← 191,191,19


14143,12 3,12 ← 13← 130,130,13, 14, 142,12 2,12 ← 13← 131,131,13,,

15153,13 3,13 ← 14← 140,140,14, 15, 152,13 2,13 ← 14← 141,141,14,,

16163,14 3,14 ← 15← 150,150,15, 16, 162,14 2,14 ← 15← 151,151,15,,

18183,16 3,16 ← 17← 170,170,17, 18, 182,16 2,16 ← 17← 171,171,17,,

19193,17 3,17 ← 18← 180,180,18, 19, 192,17 2,17 ← 18← 181,181,18


15153,13 3,13 ← 14← 140,140,14, 15, 152,13 2,13 ← 14← 141,141,14,,

16163,14 3,14 ← 15← 150,150,15, 16, 162,14 2,14 ← 15← 151,151,15,,

21213,19 3,19 ← 20← 200,200,20, 21, 212,19 2,19 ← 20← 201,201,20

VI-2. Suggested values of the induced shift for lines in VI-2. Suggested values of the induced shift for lines in the example 2 of the R branchthe example 2 of the R branch

Fig. 11 Based on the two rules, suggested induced shifts (in units of 10 Fig. 11 Based on the two rules, suggested induced shifts (in units of 10 -3 -3 × × cmcm-1 -1 atmatm-1-1) for the group of paired lines J) for the group of paired lines J′′3,3,JJ′-2 ′-2 ← J″← J″0,J″ 0,J″ and and JJ′′2,2,JJ′-2 ′-2 ← J″← J″1,J″ 1,J″

in the R branch are plotted by in the R branch are plotted by ++. Meanwhile, the original values in . Meanwhile, the original values in HITRAN HHITRAN H22O 2009 are given by O 2009 are given by ×× and and ∆∆, respectively. , respectively.



valuesvalues

14143,12 3,12 ← 13← 130,130,13

14142,12 2,12 ← 13← 131,131,13

3.003.00

1.141.14

2.112.11

15153,13 3,13 ← 14← 140,140,14

15152,13 2,13 ← 14← 141,141,14

3.123.12

1.741.74

2.342.34

16163,14 3,14 ← 15← 150,150,15

16162,14 2,14 ← 15← 151,151,15

2.912.91

1.611.61

2.462.46

17173,15 3,15 ← 16← 160,160,16

17172,15 2,15 ← 16← 161,161,16

2.662.66

2.642.64

2.502.50

18183,16 3,16 ← 17← 170,170,17

18182,16 2,16 ← 17← 171,171,17

3.353.35

6.986.98

2.032.03

19193,17 3,17 ← 18← 180,180,18

19192,17 2,17 ← 18← 181,181,18

0.480.48

0.470.47

1.221.22

20203,18 3,18 ← 19← 190,130,13

20202,18 2,18 ← 19← 191,191,19

0.860.86

0.860.86

1.021.02

21213,19 3,19 ← 20← 200,200,20

21212,19 2,19 ← 20← 201,201,20

1.551.55

1.551.55

1.411.41



Fig. 12 The same as Fig. 8 Fig. 12 The same as Fig. 8 except for a group of paired except for a group of paired lines Jlines J′′3,J3,J′-3 ′-3 ← J″← J″2J″-1 2J″-1 and and JJ′′4,J4,J′-3 ′-3 ← J← J″″1,J″-1 1,J″-1 in the R branch. The in the R branch. The boundary of this group is Jboundary of this group is Jbd bd = = 16.16.



IntensityIntensity 19193,16 3,16 ← 18← 182,172,17, 19, 194,16 4,16 ← 18← 181,171,17,,

20203,17 3,17 ← 19← 192,182,18, 20, 204,17 4,17 ← 19← 191,181,18

Air-Air-


18183,15 3,15 ← 17← 172,162,16, 18, 184,15 4,15 ← 17← 171,161,16,,

19193,16 3,16 ← 18← 182,172,17, 19, 194,16 4,16 ← 18← 181,171,17,,

20203,17 3,17 ← 19← 192,182,18, 20, 204,17 4,17 ← 19← 191,181,18

Self-Self-


18183,15 3,15 ← 17← 172,162,16, 18, 184,15 4,15 ← 17← 171,161,16


17173,14 3,14 ← 16← 162,152,15, 17, 174,14 4,14 ← 16← 161,151,15,,

18183,15 3,15 ← 17← 172,162,16, 18, 184,15 4,15 ← 17← 171,161,16,,

19193,16 3,16 ← 18← 182,172,17, 19, 194,16 4,16 ← 18← 181,171,17,,

20203,17 3,17 ← 19← 192,182,18, 20, 204,17 4,17 ← 19← 191,181,18


19193,16 3,16 ← 18← 182,172,17, 19, 194,16 4,16 ← 18← 181,171,17

VI-4. Screening HITRAN HVI-4. Screening HITRAN H22O 2009O 2009 (Example 1 in the Q branch)(Example 1 in the Q branch)

Fig. 13 The same as Fig. 8 except for a group of paired lines JFig. 13 The same as Fig. 8 except for a group of paired lines J′′JJ′,0 ′,0 ← J″← J″J″-1,1 J″-1,1 and and JJ′′JJ′,1 ′,1 ← ← J″J″J″-1,2 J″-1,2 in the Q branch. The boundary of this group is Jin the Q branch. The boundary of this group is Jbd bd = 5.= 5.

VI-5. Screening HITRAN HVI-5. Screening HITRAN H22O 2009O 2009 (Example 2 in the Q branch)(Example 2 in the Q branch)

Fig. 14 The same as Fig. 8 except for a group of paired lines JFig. 14 The same as Fig. 8 except for a group of paired lines J′′2,2,JJ′-2 ′-2 ← J″← J″1,J″-1 1,J″-1 and and JJ′′33JJ′-2 ′-2

← J″← J″2,J″-1 2,J″-1 in the Q branch. The boundary of this group is Jin the Q branch. The boundary of this group is Jbd bd = 13.= 13.

VI-6. Screening HITRAN HVI-6. Screening HITRAN H22O 2009O 2009 (Example 1 in the P branch)(Example 1 in the P branch)

Fig. 15 The same as Fig. 8 except for a group of paired lines JFig. 15 The same as Fig. 8 except for a group of paired lines J′′2,2,JJ′-2 ′-2 ← J″← J″1,J″ 1,J″ and and JJ′′3,3,JJ′-2 ′-2

← J″← J″0,J″ 0,J″ in the P branch. The boundary of this group is Jin the P branch. The boundary of this group is Jbd bd = 13.= 13.

VI-7. Screening HITRAN 2009VI-7. Screening HITRAN 2009

(Example 1 in the Q branch of the (Example 1 in the Q branch of the vv2 2 band)band)

Fig. 16 The same as Fig. 8 Fig. 16 The same as Fig. 8 except for a group of paired except for a group of paired lines Jlines J′′0,0,JJ′ ′ ← J″← J″1,J″-1 1,J″-1 and and JJ′′1,1,JJ′ ′ ← J← J″″2,J″ -1 2,J″ -1 in the Q branch of the in the Q branch of the vv2 2

bandband. The boundary J. The boundary Jbd bd ≈ 10.≈ 10.




Air-Air-


15150,15 0,15 ← 15← 151,141,14, 15, 151,15 1,15 ← 15← 152,142,14,,

16160,16 0,16 ← 16← 161,151,15, 16, 161,16 1,16 ← 16← 162,152,15,,

17170,17 0,17 ← 17← 171,161,16, 17, 171,17 1,17 ← 17← 172,162,16,,

18180,18 0,18 ← 18← 181,171,17, 18, 181,18 1,18 ← 18← 182,172,17,,

19190,19 0,19 ← 19← 191,181,18, 19, 191,19 1,19 ← 19← 192,182,18

Self-Self-


14140,14 0,14 ← 14← 141,131,13, 14, 141,14 1,14 ← 14← 142,132,13,,

15150,15 0,15 ← 15← 151,141,14, 15, 151,15 1,15 ← 15← 152,142,14,,

16160,16 0,16 ← 16← 161,151,15, 16, 161,16 1,16 ← 16← 162,152,15,,

19190,19 0,19 ← 19← 191,181,18, 19, 191,19 1,19 ← 19← 192,182,18


15150,15 0,15 ← 15← 151,141,14, 15, 151,15 1,15 ← 15← 152,142,14,,

16160,16 0,16 ← 16← 161,151,15, 16, 161,16 1,16 ← 16← 162,152,15,,

17170,17 0,17 ← 17← 171,161,16, 17, 171,17 1,17 ← 17← 172,162,16,,

18180,18 0,18 ← 18← 181,171,17, 18, 181,18 1,18 ← 18← 182,172,17


19190,19 0,19 ← 19← 191,181,18, 19, 191,19 1,19 ← 19← 192,182,18

VI-7. Suggested values of the air-broadened half-width VI-7. Suggested values of the air-broadened half-width for lines in the example 1 of the Q branch of the for lines in the example 1 of the Q branch of the νν2 2 bandband

Fig. 17 Based on the two rules, suggested air-broadened half-widths (in cmFig. 17 Based on the two rules, suggested air-broadened half-widths (in cm -1 -1 atmatm-1-1) ) for the group of paired lines Jfor the group of paired lines J′′0,0,JJ′ ′ ← J″← J″1,J″-1 1,J″-1 and and JJ′′1,1,JJ′ ′ ← J″← J″2,J″ -1 2,J″ -1 in the Q branch of the in the Q branch of the vv2 2

bandband are plotted by are plotted by ++. Meanwhile, the original values in HITRAN H. Meanwhile, the original values in HITRAN H22O 2009 are given O 2009 are given by by ×× and and ∆∆, respectively. , respectively.



valuesvalues

15150,15 0,15 ← 15← 151,141,14

15151,15 1,15 ← 15← 152,142,14

0.01400.0140

0.01700.0170

0.01500.0150

16160,16 0,16 ← 16← 161,151,15

16161,16 1,16 ← 16← 16215215

0.01440.0144

0.00900.0090

0.01300.0130

17170,17 0,17 ← 17← 171,161,16

17171,17 1,17 ← 17← 172,162,16

0.00920.0092

0.01250.0125

0.01150.0115

18180,18 0,18 ← 18← 181,171,17

18181,18 1,18 ← 18← 182,172,17

0.01080.0108

0.01080.0108

0.00990.0099

19190,19 0,19 ← 19← 191,181,18

19191,19 1,19 ← 19← 192,182,18

0.00640.0064

0.00640.0064

0.00730.0073

VI-8. Screening HITRAN 2009VI-8. Screening HITRAN 2009 (Example 1 in the P branch of the (Example 1 in the P branch of the vv2 2 band)band)

Fig. 18 The same as Fig. 8 except for Fig. 18 The same as Fig. 8 except for a group of paired lines Ja group of paired lines J′′1,1,JJ′ ′ ← J″← J″0,J″ 0,J″

and and JJ′′0,0,JJ′ ′ ← J″← J″1,J″ 1,J″ in the P branch of in the P branch of the the vv2 2 bandband. The boundary J. The boundary Jbd bd ≈≈ 7. 7.




Air-Air-


12121,12 1,12 ← 13← 130,130,13, 12, 120,12 0,12 ← 13← 131,131,13,,

13131,13 1,13 ← 14← 140,140,14, 13, 130,13 0,13 ← 14← 141,141,14,,

14141,14 1,14 ← 15← 150,150,15, 14, 140,14 0,14 ← 15← 151,151,15,,

16161,16 1,16 ← 17← 170,170,17, 16, 160,16 0,16 ← 17← 171,171,17,,

17171,17 1,17 ← 18← 180,180,18, 17, 170,17 0,17 ← 18← 181,181,18,,

19191,19 1,19 ← 20← 200,200,20, 19, 190,19 0,19 ← 20← 201,201,20

Self-Self-


771,7 1,7 ← 8← 80,80,8, 7, 70,7 0,7 ← 8← 81,81,8,,

881,8 1,8 ← 9← 90,90,9, 8, 80,8 0,8 ← 9← 91,91,9,,

991,9 1,9 ← 10← 100,100,10, 9, 90,9 0,9 ← 10← 101,101,10,,

13131,13 1,13 ← 14← 140,140,14, 13, 130,13 0,13 ← 14← 141,141,14,,

16161,16 1,16 ← 17← 170,170,17, 16, 160,16 0,16 ← 17← 171,171,17,,

18181,18 1,18 ← 19← 190,190,19, 18, 180,18 0,18 ← 19← 191,191,19,,


13131,13 1,13 ← 14← 140,140,14, 13, 130,13 0,13 ← 14← 141,141,14,,

14141,14 1,14 ← 15← 150,150,15, 14, 140,14 0,14 ← 15← 151,151,15,,

18181,18 1,18 ← 19← 190,190,19, 18, 180,18 0,18 ← 19← 191,191,19,,

19191,19 1,19 ← 20← 200,200,20, 19, 190,19 0,19 ← 20← 201,201,20


18181,18 1,18 ← 19← 190,190,19, 18, 180,18 0,18 ← 19← 191,191,19,,

19191,19 1,19 ← 20← 200,200,20, 19, 190,19 0,19 ← 20← 201,201,20

VI-9. Screening HITRAN 2009 VI-9. Screening HITRAN 2009 (Example 1 in the R branch of the (Example 1 in the R branch of the vv2 2 band)band)

Fig. 19 The same as Fig. 8 except for a group of paired lines JFig. 19 The same as Fig. 8 except for a group of paired lines J′′1,1,JJ′ ′ ← J″← J″0,J″ 0,J″ and and JJ′′0,0,JJ′ ′ ← ← J″J″1,J″ 1,J″ in the R branch of the in the R branch of the vv2 2 bandband. The boundary J. The boundary Jbd bd ≈ 7.≈ 7.

VI-10. Screening HITRAN 2009 VI-10. Screening HITRAN 2009 (Example 2 in the R branch of the (Example 2 in the R branch of the vv2 2 band)band)

Fig. 20 The same as Fig. 8 except for a group of paired lines JFig. 20 The same as Fig. 8 except for a group of paired lines J′′JJ′,0 ′,0 ← J″← J″J″,1 J″,1 and and JJ′′JJ′,1 ′,1 ← ← J″J″J″,0 J″,0 in the R branch of the in the R branch of the vv2 2 bandband. The boundary J. The boundary Jbd bd ≈ 3.≈ 3.

VII. Predicting spectroscopic parameters for HITEMPVII. Predicting spectroscopic parameters for HITEMP

Fig. 21 A plot to show NFig. 21 A plot to show N22-broadened half-widths for two groups of paired lines with J˝ -broadened half-widths for two groups of paired lines with J˝ = 26 = 26 ······ 50 predicted from an extrapolation method. One is a group of J′ 50 predicted from an extrapolation method. One is a group of J′0,J’ 0,J’ ← J″ ← J″1,J1,J" " and and J′J′1J’ 1J’ ← J″ ← J″0J0J“ “ in the R branch and another is a group of J′in the R branch and another is a group of J′2,J’-2 2,J’-2 ← J″← J″1,J1,J"-1 "-1 and J′and J′3J’-2 3J’-2 ← J″← J″2J2J"-2 "-2 in the Q branch. For the former, theoretically calculated values with J″ = 6, ∙∙∙, 25 and in the Q branch. For the former, theoretically calculated values with J″ = 6, ∙∙∙, 25 and those predicted ones are given by × and ∆. For the latter, calculated values with J″ = those predicted ones are given by × and ∆. For the latter, calculated values with J″ = 12, ∙∙∙, 25 and predicted ones are given by + and □.12, ∙∙∙, 25 and predicted ones are given by + and □.

VIII. ConclusionsVIII. Conclusions Two basic rules (i.e., the pair identity and the smooth variation rules) Two basic rules (i.e., the pair identity and the smooth variation rules)

are applicable for all the spectroscopic parameters of Hare applicable for all the spectroscopic parameters of H22O lines whose O lines whose J values are above certain boundaries in the same groups. J values are above certain boundaries in the same groups.

Different groups of lines have different boundaries. The latter can be Different groups of lines have different boundaries. The latter can be calculated from the identity requirements for the energy levels and calculated from the identity requirements for the energy levels and wave functions of paired Hwave functions of paired H22O states.O states.

The rule hold within certain accuracy tolerance. The latter could vary The rule hold within certain accuracy tolerance. The latter could vary as the parameter of interest varies. In general, the 5 % accuracy as the parameter of interest varies. In general, the 5 % accuracy tolerance is suggested for the half-widths, shifts, and T exponents. tolerance is suggested for the half-widths, shifts, and T exponents.

The 5 % accuracy tolerance is poorer than the accuracies associated The 5 % accuracy tolerance is poorer than the accuracies associated with line positions and intensities, but is better than those with other with line positions and intensities, but is better than those with other parameters. In addition, the current theoretical calculations and parameters. In addition, the current theoretical calculations and measurements for high J lines cannot reach such high accuracies. measurements for high J lines cannot reach such high accuracies.

The present work can be extended for lines in vibrationaly excited The present work can be extended for lines in vibrationaly excited states. Of course, one needs to check the properties of the energy states. Of course, one needs to check the properties of the energy levels and wave functions of vibrationaly excited states first and levels and wave functions of vibrationaly excited states first and recalculate corresponding boundaries.recalculate corresponding boundaries.

The idea of the present work is simple and general. One can applied it The idea of the present work is simple and general. One can applied it for other molecules whose energy levels and wave functions have for other molecules whose energy levels and wave functions have similarities. similarities.

pair identity and smooth variation rules applicable for the spectroscopic parameters of h 2 o...

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