EXPERIMENTAL AND THEORETICAL STUDY OF WATER-VAPOR CONTINUUM ABSORPTION IN THE THZ REGION FROM 0.3 TO 2.7 THZ

V.B. PODOBEDOV, D.F. PLUSQUELLIC, K.M. SIEGRIST AND G.T. FRASER National Institute of Standards and Technology, Gaithersburg, MD 20899.

Q. MA NASA Goddard Institute for Space Studies, and Department of Applied Physics and Applied Mathematics, Columbia University, 2880 Broadway, New York, NY 10025.

R.H. TIPPING Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487.

Spectral Range

0.001

0.01

0.1

1

10

100

1 10 100 1000

Frequency, THz

0.01 0.1 1 10W

av

ele

ng

th,

mm

Wavenumber, cm-1

Continuum absorption

Atmospheric studies:Global warming, climate modelingRemote sensingWave propagations and modelsTransmissionSubmillimeter wave spectroscopy

Astrophysics:Ground-based and airborne observationsAtmospheric attenuationSystem noise temperaturePhase delay

H2O - N2 mixture absorption components

The total absorbance, A, has two parts which are measured in the experiment as their sum,

A(, T) = AL + AC,where the indexes L and C specify a local contribution from the discrete water

vapor spectrum and continuum absorption, respectively.

The continuum part, AC, may be described by the combination of three components

AC(, T) = Aself(P2H2O) + Aforeign(PN2PH2O) + Aforeign(P

2N2)

In case of wet continuum, the third term will be significantly smaller than the remaining two.

Detailed formula accounts for the absorption coefficients and temperature

exponents for water vapor and foreign gas separatelyAC(, T) = [Kself() ∙ (300/T)ns + Kfor() ∙ (300/T)nf]2L,

where Kself() and Kfor() are the absorption coefficients, is a frequency and L is a pathlength.

Kself, ns, Kfor, nf

(dB/km) = 10.Absorbance/km = 104.Absorbance/m

Expected absorption at 0.25 % (lower spectrum) and 25 % relative atmospheric humidity at T = 296 K (HITRAN 2004)

0.1

1

10

100

1000

104

105

106

20 40 60 80 100

0.001

0.01

0.1

1

10

100

1000

Abso

rptio

n Co

effic

ient,

dB/k

m

Wavenumber, cm -1Ab

sorb

ance

(bas

e10)

per

cell

THz Spectrum Features

Strong H2O vapor lines

Intensity range >105

max/min ~10

SWR Pswr=1.1-1.3

, Window limited

Measurement of continuum absorbance

-1

-0.5

0

0.5

1

10 20 30 40 50 60 70 80 90

A (

exp

eri

me

nt)

Wavenumber, cm-1

-A (

mo

de

l)

Local Contribution:

Intensity HITRAN04Linewidth HITRAN04x1.11Lineshape VVWCut-off (±0) 100 cm-1

A@>0 0

Experiment:

Instrument FTSResolution 0.03-0.12 cm-1

Pathlength 23.3 m

Experiment

Model

Self Continuum

H2O vapor at P=2.13 kPa, T=293 K

Far-IR Multipass Cell (core)

In

Out

Pathlength: 2.4 – 48 mInput aperture: 60 mmOptics: F/2

Experimental absorption spectraPH2O =0.67 kPa, PN2 = 70 kPa, T1=293 K, T2=333 K

0

0.2

0.4

0.6

0.8

1

1.2

10 20 30 40 50 60 70 80 900

100

200

300

400

500

Ab

sorb

ance

(ba

se 1

0)

Wavenumber, cm-1

Ab

sorp

tion

Coe

ffic

ient

, dB

/km

T stab.

H2O in

(P, T) stab.

Spectrum 1

N2 in

(P,T) stab.

Spectrum 2One T- set

Experimental continuum absorbance

0

0.05

0.1

0.15

0.2

0.25

10 20 30 40 50 60 70 80 900

20

40

60

80

100

Ab

sorb

ance

(ba

se 1

0)

Wavenumber, cm-1

293 K

333 K

313 K

Ab

sorp

tion

Coe

ffic

ien

t, d

B/k

m

0

0.05

0.1

0.15

10 30 50 70 900

16

32

48

64

Abs

orb

ance

(ba

se 1

0)Wavenumber, cm -1

293 K 323 K

333 K

293 K

Abs

orp

tion

Coe

ffic

ient

, dB

/km

Self

P = 2.13 kPa

Foreign

Fitting the continuum data

0.2

0.4

0.6

0.8

1

1.2

290 300 310 320 330 340N

orm

aliz

ed A

bsor

ban

ce F

acto

r

Temperature, K

n=5.7

n=4.1

n=6.3

I. A=A(300/T)n II. A=A

2-fit(300/T)n

I. 5 (T) data points II. 8() x 5(T) data matrix

0

0.05

0.1

0.15

290 300 310 320 330 340

A=A(300/T)n

Ab

so

rba

nc

e10

Temperature, K

84 cm-1

22.5 cm-1

Continuum absorption coefficients, Kself and Kfor, (dB/km)/(kPa.THz)2

and temperature exponents, ns and nf, obtained from each transmittance window. Same parameters shown below the dashed

line were determined from the complete set of 2-fitted curves

__________________________________________________________________________________________

Window center, Kself ns Kfor nf

(cm-1) Exp. Exp. Exp. Theory Exp. Theory__________________________________________________________________________________________

22.5 3.94 5.4 0.178 0.178 4.1 5.0228.3 4.91 7.8 0.178 0.188 4.3 4.7534.3 3.75 6.8 0.169 0.175 4.6 4.8345.0 3.94 9.6 0.188 0.177 6.3 4.2850.3 3.89 9.5 0.186 0.177 5.8 4.2966.4 3.66 8.0 0.182 0.163 5.7 3.9470.1 3.89 9.3 0.183 0.176 6.2 4.0384.1 2.98 7.9 0.172 0.172 5.4 4.07- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2- fitted (Exp.) 3.83(300/T)8.8 8.8 0.185(300/T)5.7 - 5.7 -

Comparison of the continuum absorption coefficients, Kself and Kfor, (dB/km)/(kPa.THz)2 and temperature exponents, ns and nf, from

different studies

Reference Rosenkranz A. Bauer J. Pardo CKD Present workRange, THz<0.8 <0.35 0.35-1.1 **) 0.3-2.7

Experiment Theory

*) a) b) c)

Kself 7.8 8.9-9.5 - 4.18 3.83 4.00 -ns 7.5 7.8-8.5 - 6.9 8.8 8.5 -

Kfor 0.236 0.25-0.28 0.26 0.41 0.185 0.231 0.163-0.188nf 3.0 4.5-4.6 3.0 3.0 5.7 4.8 3.94-5.02

Notes on modeling parameters:

*) Range of data for different parameters [6]**) Calculations at 50 cm-1

a) Basic set: cut-off = 100 cm-1, A=0 beyond the cut-offb) Same as in a) except cut-off = 25 cm-1, A=0 beyond the cut-offc) Same as in a)

CONCLUSIONS

1. The contributions to the absorbance resulting from the structureless H2O – H2O and H2O - N2 continua have been measured in the temperature range from 293 to 333 K with spectral resolution of 0.04 to 0.12 cm-1.

2. Within experimental uncertainty, both the H2O - H2O and H2O – N2

continua demonstrate nearly quadratic dependencies of absorbance on frequency with some deviation near the 2.5 THz window.

3. The absorption coefficients of 3.83 and 0.185 (dB/km)/(kPa.THz)2 were measured for self- and foreign-gas continuum, respectively. The corresponding temperature exponents were found to be 8.8 and 5.7.

4. Absorption coefficients and temperature exponents were also found in each THz window.

ACKNOWLEDGMENTS

This work was supported in part by the NASA Upper Atmospheric Research grant, NNH05AB21I.

Two of the authors (Q. Ma and R. H. Tipping) acknowledge financial support from NASA under grants NNG06GB23G, and FCCS-547.

Q. Ma wishes to acknowledge financial support from the Biological and Environmental Research Program (BER), U.S. Department of Energy, Interagency Agreement No. DE-AI02-93ER61744.

Far-wing cut-off

0

0.05

0.1

0.15

0.2

0.25

10 20 30 40 50 60 70 80 900

20

40

60

80

100

Ab

sorb

ance

(ba

se 1

0)

Wavenumber, cm-1

293 K

333 K

313 K

Ab

sorp

tion

Coe

ffic

ien

t, d

B/k

m

0

0.05

0.1

0.15

0.2

0.25

0

20

40

60

80

100

290 300 310 320 330 340

A1

0

T, K

, d

B/k

m

Self/For_25_100

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

4

8

12

16

20

24

28

32

0 50 100 150 200 250 300 350 400

25 vs 100 cm-1 cut-off

A

bso

rban

ce1

0

Wavenumber, cm -1

A

bso

rpti

on

Co

eff

icie

nt,

dB

/km

H2O 2.13 kPa

H2O/N

2: 0.67/70 kPa

Exp. uncertainty

H2O 2.13 kPa

Self-continuum Absorption

H2O vapor at P=2.13 kPa

0

0.05

0.1

0.15

0.2

0.25

10 20 30 40 50 60 70 80 900

20

40

60

80

100

Ab

sorb

ance

(ba

se 1

0)

Wavenumber, cm-1

293 K

333 K

313 K

Ab

sorp

tion

Coe

ffic

ien

t, d

B/k

m

Foreign Continuum Absorbance

0

0.05

0.1

0.15

10 30 50 70 900

16

32

48

64A

bsor

ban

ce (

base

10)

Wavenumber, cm -1

293 K 323 K

333 K

293 K

Ab

sorp

tion

Coe

ffic

ient

, dB

/km

H2O/N2 : 1.43/78.5 0.67/70 kPa

Multipass cell efficiency

0

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60

7.5/0.5

7.5

/0.5

Wavenumber, cm-1

Ab

sorb

an

ce (

ba

se 1

0)

-2.6032

-2.6

03

2

Atmospheric absorption (T = 297 K, ~7 g H2O per m3):

1 - single pass cell, 2 - multipass cell

1

2