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Pressure broadening of oxygen by water
Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 190–198
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Pressure broadening of oxygen by water Brian J. Drouin a,n, Vivienne Payne a, Fabiano Oyafuso a, Keeyoon Sung a, Eli Mlawer b a b
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, United States Atmospheric and Environmental Research, 131 Hartwell Avenue, Lexington, MA 02421, United States
a r t i c l e in f o
abstract
Article history: Received 22 June 2013 Received in revised form 26 July 2013 Accepted 2 August 2013 Available online 9 August 2013
A need for precise air-mass retrievals utilizing the near-infrared O2 A-band has motivated measurements of the water-broadening in oxygen. Experimental challenges have resulted in very little water broadened oxygen data. Existing water broadening data for the O2 A-band is of insufficient precision for application to the atmospheric data. Line shape theory suggests that approximate O2 pressure broadening parameters for one spectral region, such as the A-band, may be obtained from comparable spectral regions such as the O2 60 GHz Q-branch, which is also used prominently in remote sensing. We have measured precise O2–H2O broadening for the 60 GHz Q-branch and the pure-rotational transitions at room temperature with a Zeeman-modulated absorption cell using a frequency-multiplier spectrometer. Intercomparisons of these data and other O2 pressure broadening data sets confirm the expectation of only minor band-to-band scaling of pressure broadening. The measurement provides a basis for fundamental parameterization of retrieval codes for the long-wavelength atmospheric measured values. Finally, we demonstrate the use of these measurements for retrievals of air-mass via remote sensing of the oxygen A-band. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Pressure broadening Atmospheric science Humidity Air mass Oxygen Water vapor
1. Introduction Oxygen is a well-mixed gas in Earth's atmosphere, with a mixing ratio that is extremely well known, allowing oxygen absorption features to be utilized in remote sensing applications for the retrieval of other atmospheric quantities. The O2 60 GHz Q-branch has long been used for the retrieval of atmospheric temperature from satellites (e.g. [1]), aircraft (e.g. [2]) and from the ground [3,4]. The pure rotational transitions in the Terahertz region may be useful for retrievals of stratospheric temperatures or air-mass, but the opacity of the water continuum reduces their utility below the tropopause. The O2 A-band at 0:76 μm has been used extensively in ground-based [5], airborne [6] and satellite [7–10] remote sensing to provide the information
n
Corresponding author. Tel.: +1 818 393 6259; fax: +1 818 354 5148. E-mail address: [email protected] (B.J. Drouin).
0022-4073/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jqsrt.2013.08.001
on atmospheric path lengths necessary to characterize cloud and aerosol abundances, to retrieve surface pressure and to retrieve column abundances of other trace gases, such as CO2 and CH4, using coincident near-infrared measurements. Current and planned spaceborne missions utilizing the O2 A-band for the purposes of greenhouse gas retrievals include the TANSO-FTS on the Japanese Greenhouse Gases Observing satellite (GOSAT) [11], the NASA Orbiting Carbon Observatory re-flight (OCO-2) [12] and the Chinese TanSat satellite instrument [13]. The accuracy of the remotely sensed quantities depends directly on the accuracy of the spectroscopic input (line positions, line intensities and lineshape) used in the forward models within the retrieval algorithms (e.g. [14–16]). The parameterization of the lineshape includes pressure broadening and may also include additional physics such as shifts, mixing, narrowing and speeddependence. For current and future remote-sensing measurements to be used to their full potential, it is necessary
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to continue to characterize and reduce uncertainties in the spectroscopic input to the models, particularly those uncertainties that could lead to spatially or seasonally dependent biases in the retrieval products. Pressure broadening by water vapor can make an additional contribution to the observed width of the lines, which in turn affects the retrieval of the target quantity. Since atmospheric water vapor is highly variable in space and time, the reduction of spectroscopic uncertainties associated with water vapor is important in order to avoid the introduction of spatially and/or temporally dependent biases in the retrieved products. Due to the experimental challenges involved, few previous studies have been performed to measure the pressure broadening of oxygen by water vapor. Here, we report new, precise measurements of O2–H2O broadening for the 60 GHz Q-branch and the pure-rotational transitions. As a linear molecule with no electric dipole moment, oxygen pressure broadening is expected to show little electronic or vibrational dependence, and so we assume that the measured values can also be applied to the O2 A-band at 0:76 μm. In Section 2, we describe results from previous studies of O2–H2O broadening in order to provide context for this new work. Section 3 contains a description of the experimental setup for the new measurements. In Section 4, we detail the approach taken to determine the O2–H2O broadening parameters from the new measurements, compare with results from previous studies and explore some of the implications for remote sensing by showing the impact on forward model calculations in the 60 GHz and 0:76 μm regions. A concise summary of the work is provided in Section 5.
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atmospheric temperature, Fanjoux et al. had extrapolated their data to compare with the measurement from [21] and had concluded that their results were relatively consistent with this datapoint for this single line, providing some support for the assumption of vibrational independence of the pressure broadening. In the O2 A-band at 0:76 μm, state-of-the-art spectroscopic techniques have produced very high quality (self and air) broadening and shift parameters for the oxygen A-band [28,29]. Other studies have obtained the temperature dependence of the pressure broadening and shift parameters [30] as well as line-mixing/collision-induced absorption [31]. O2–H2O room temperature pressure broadening was measured for six lines in the A-band by Vess et al. [32]. The water-broadened widths inferred by [32] were over 50% larger than the values implied by the earlier work [21–23,27] in other spectral regions. Due to physical constraints such as the low vapor pressure of water and the large Doppler widths of transitions in the A-band, the data of Vess et al. was not very sensitive to the water-broadening itself, and the error bars are large. In summary, the previous data for O2–H2O broadening consists of measurements of only two transitions in the 60 GHz complex [21–23], a comprehensive study of the Raman Q-branch at 1553.3 cm 1 at temperatures outside the range of interest for remote sensing of ambient atmospheric conditions [27], and a study of six lines in the 0:76 μm A-band [32], with large error bars, that was not consistent with the results of the other two studies. The single-line limitations of the millimeter region studies of [21–23] and the discrepancy between the parameters derived from [27] and the direct measurements of [32] provided a strong motivation for additional measurements.
2. Previous studies of O2–H2O broadening The new measurements described in this work have enabled the determination of precise O2–H2O broadening parameters for lines in the 60 GHz Q-branch (spanning frequencies from 47 to 119 GHz) and for pure rotational transitions between 424 and 1850 GHz. Since we are assuming that oxygen pressure broadening has little electronic or vibrational dependence, we should consider these new measurements not only in the context of previous measurements in this spectral region, but also in the context of measurements of O2–H2O broadening at other frequencies. Previous high quality measurements of spectroscopic parameters for the 60 GHz Q-branch include air and selfbroadening [17,18], line-mixing [18,19], and pressure broadening temperature dependence [19,20]. However, only two transitions in the 60 GHz Q-branch have published waterbroadening values [21–23]. While self- and air-broadening parameters for the pure rotational (S-branch) transitions have been reported by [24–26], we are not aware of previous measurements of O2–H2O broadening for these transitions. Fanjoux et al. [27] performed high temperature (between 446 and 990 K) measurements of O2–H2O broadening for the Raman Q-branch at 1553.3 cm 1, with the goal of contributing to understanding of combustion in rocket engines. While the temperature range of this study is obviously very different from the range of ambient
3. Experimental setup A room temperature apparatus designed for static gas containment was fitted with a variable temperature cold finger and was filled with a fixed amount of oxygen and water vapor. Temperature control of the cold-finger was accomplished through setting the voltage of thermoelectric (TE) coolers attached to an aluminum block encircling the cold finger. By controlling the finger temperature in the 242–280 K range the vapor pressure of water in the static gas cell was maintained at fixed values during each spectroscopic measurement. The area of the gas cell probed by the spectrometer was maintained at room temperature which fluctuated between 294 and 298 K. The spectrometer described in Drouin et al. [33], with an additional source described in Gupta et al. [34], was utilized to record the lineshapes of dozens of oxygen transitions, each as a function of water vapor pressure. In order to remove spectral features due to standing waves and water vapor absorption, Zeeman modulation was employed through application of an axial magnetic field. As in the previous work on O2 [26] the convolution method described by Pickett [35] was utilized to facilitate treatment of instrument and magnetic field effects on the lineshape. A single transition (9 at 58323.876 GHz) was measured as a function of oxygen pressure to check consistency with the
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Pressure Gauge
Lock-In Amplifier
Modulated Synthesizer
Cold Finger
Pre-amp
TE coolers
Detector
O2,H2O Multiplier(s) Wire-grid polarizer
Sample Chamber
rooftop reflector
Zeeman Coil
Fig. 1. Experimental setup.
self-broadening measurements reported by Tretyakov et al. [18]. The O2 self-broadening parameter measured with this apparatus is 1.780(38) MHz Torr 1; this value agrees well with the value 1.763(15) found by Tretyakov et al. A schematic of the experimental design is shown in Fig. 1. Measurements were made of twenty-four 60 GHz Q-branch transitions (50–119 GHz) and 11 pure rotational transitions (424–1850 GHz). All spectral and vapor pressure values were tuned digitally with a computer that simultaneously recorded the demodulated signal. After tuning the TE-cooler voltage, the water vapor pressure settles over a time of 30 min. To improve measurement efficiency all transitions within a given spectral band were measured at a given TE-cooler setting prior to re-tuning the TE-cooler. Oxygen pressure was fixed at a value between 1 and 2 Torr for each series of water pressures and the water vapor pressure was set between 0.3 and 9.0 Torr. Total pressure was measured with a 10 Torr MKS capacitance manometer at each step through each spectrum, and the averaged total pressure value was stored with the averaged spectral data. The manometer reading was calibrated upon receipt from the manufacturer and is stated to reproduce the total pressure to 0.25% down to 1 mTorr. Deviations in the temperature of the room dominate the potential systematic errors, the HVAC system maintained room temperature between 294 and 298 K, and the thermal cycles were typically shorter than the experiment durations, such that errors on the order of 1–2% are expected from datapoint to datapoint. Therefore 296(4) K is adopted as the temperature for the experiment. An example of the data set for one spectral line is shown in Fig. 2. This figure displays the typical characteristics of a pressure-broadened frequency-modulated absorption line (1) a second derivative Voigt lineshape, (2) a decrease in peak height with increasing pressure, (3) an increase in linewidth with increasing pressure, (4) a lineshift with pressure. For submillimeter transitions the integration time was chosen to enable signal-to-noise ratios (SNRs) greater than 20, which is an effective cutoff to avoid systematic errors in the linewidth measurement (noisy lines are always evaluated to larger widths). In the mm-wave range most of the lines were collected in microwindows repeated serially for each water vapor pressure, and, owing to the variability in the intensities of these transitions, the SNRs
Fig. 2. The J′ ¼ 9 transition of O2 near 61.150 GHz. The O2 partial pressure is 1.8 Torr, the total pressure (including water vapor) is given in the inset.
varied. A series of runs through these transitions enabled the optimal partial pressures and modulation depths to be determined for a majority of the transitions, with only the highest (N 425) transitions falling below the SNR of 20 cutoff in the optimal run. A few of these mm-wave lines were systematically distorted (N ¼21+ and both N ¼29 transitions), and asymmetric lineshapes and residuals were observed. For N 425, it was decided not to report the values due to low SNR, for N ¼21+, the width and shift have enlarged error bars due to the poor fit. For the 118 GHz transition the SNR was limited due to poor detector responsivity, this datapoint also has a larger error bar. Pressure broadened linewidths and lineshifts are reported in Table 1 with error bars (fit precision) determined in the convolution fitting procedure, but systematic errors (such as room temperature) up to a few percent exceed these precisions for most of the datapoints. 4. Results and analysis 4.1. Pressure broadening parameters The pressure broadened lineshapes were fitted, via the convolution method, by inter-comparisons of higher pressure
Table 1 Measured O2–H2O broadening and shift values in MHz Torr 1 for 296 K. N′
J′
N″
J″
γ
δ
3 3 5 5 7 7 7 9 9 11 11 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15 17 17 19 19 21 21 23 25
2 3 4 5 6 6 7 8 9 10 11 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15 17 17 19 19 21 21 23 25
1 1 3 3 5 5 5 7 7 9 9 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15 17 17 19 19 21 21 23 25
2 2 4 4 5 6 6 8 8 10 10 2 0 4 2 6 4 8 6 10 8 12 10 14 12 16 14 18 16 20 18 22 20 22 26
3.525(21) 3.170(13) 2.479(14) 2.700(18) 2.323(10) 2.387(11) 2.410(21) 2.227(15) 2.326(18) 2.235(16) 1.921(31) 2.507(03) 3.053(48) 2.444(12) 2.293(09) 2.061(06) 2.254(10) 2.180(05) 2.209(04) 2.090(03) 2.086(04) 2.115(06) 2.109(04) 2.026(05) 2.033(10) 1.958(04) 1.995(12) 1.915(05) 1.911(08) 1.749(05) 1.795(12) 1.922(15) 1.707(20) 1.614(22) 1.522(17)
0.089(17) 0.022(09) 0.031(04) 0.073(06) 0.059(06) 0.076(15) 0.064(04) 0.055(11) 0.188(13) 0.064(08) 0.070(12) 0.059(06) 0.062(08) 0.012(04) 0.163(04) 0.049(05) 0.004(02) 0.160(02) 0.084(01) 0.040(01) 0.039(02) 0.062(02) 0.014(02) 0.059(02) 0.022(01) 0.026(01) 0.069(03) 0.032(02) 0.034(03) 0.109(02) 0.003(03) 0.186(09) 0.042(05) 0.012(04) 0.018(10)
spectra with lower pressure spectra. The resulting ‘differential’ linewidths (and lineshifts) depend only upon the pressure broadening induced by the differing amounts of water vapor. An example regression of the differential lineshapes vs. the differential in total pressure is shown in Fig. 3. The slope of this plot is the water vapor broadening coefficient for the spectral line measured. These slopes have been determined for each of the transitions presented in this study; they are reported in Table 1 and shown in Fig. 4. Intercomparisons can be made for the two previously studied transitions, the 9+ and 1 lines at 61.15 GHz and 118.75 GHz respectively. For the 9+ transition, Setzer's reported ratio of 1.3 from Liebe's selfbroadening study gives 2.33 MHz Torr 1, which is larger than the present value determined to be 2.090(03) MHz Torr 1. For the 1 transition, the two prior measurements of 2.52(4) MHz Torr 1 [22] and 2.30(24) MHz Torr 1 [23] are in better agreement with each other than with the present value 3.053 (48) MHz Torr 1. The 1 measurement reported here is the worst signal-to-noise measurement of the present data set, and may suffer a systematic error (a larger broadening coefficient) due to the elevated noise level. For application of these parameters to other spectral bands, it is useful to define a function, shown in Eq. (1) [36] that fits the J′ dependence of the observed values [28]. We also convert the units into the more commonly used
Differential Lineshape (MHz)
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5 4
Δγ = 2.090(3)Δp
3 2 1 0
Δδ = 0.040(1)Δp 0
0.5 1 1.5 2 Differential Pressure (Torr)
2.5
Fig. 3. Differential lineshape values for the J′ ¼ 9 transition of O2 near 61.150 GHz. The slope γ ¼ Δγ=Δp corresponds to the linewidth in units of MHz Torr 1, and the slope δ ¼ Δδ=Δp corresponds to the lineshift in units of MHz Torr 1.
Fig. 4. The J′ dependence of O2–H2O broadening measured in this and other studies. Random error bars of 3% are shown for the data from this work, when precision is less than 3%. The values in Table 1 are converted into cm 1 atm 1 with the factor 0.025351 cm 1 Torr MHz 1 atm 1.
infrared units of cm 1 atm 1. This formulation is not intended to replace the fundamental measurements, which should be used for the matched transitions in remote sensing models, rather the equation is to be used as a metric to gauge the transferability of the pressure broadening from one band to another, and, if deemed acceptable, used to estimate pressure broadening when measurements are un-reliable or non-existent. γ ¼ Aγ þ
Bγ ð1 þ c1 J′ þ c2 J ′2 þ c3 J ′4 Þ
ð1Þ
A different empirical formulation was applied to the temperature dependent data of Fanjoux et al. in order to estimate the room temperature values of the fundamental Raman (vibrational) band, this formulation is given in the Appendix. The smooth red line in Fig. 5 is a fit to Eq. (1) for the 60 GHz Q-branch data in Fig. 4 and Table 1. This is the same model used by Long et al. [28] to describe their room temperature self-broadening data set for the A-band.
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Fig. 5. Comparison of band models and scaled band models. The models (see Eq. (1) and Table 2) are depicted with the solid and dotted lines representing each data set (all at 296 K). The values in Table 1 are converted into cm 1 atm 1 with the factor 0.025351 cm 1 Torr MHz 1 atm 1 for modeling with Eq. (1). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
To facilitate comparisons and examine previous assumptions used in atmospheric retrievals this same model was applied to the self-broadening room temperature 60 GHz Q-branch data of Tretyakov et al. [18]. 4.2. Assumption of no state dependence Since the new millimeter and sub-millimeter measurements presented here have far smaller error bars than existing direct measurements of H2O broadening in the O2 A-band, we wish to apply this new data to the A-band. In order to do this, we must assume that the pressure broadening has little or no vibrational or electronic state dependence. In this section, we examine whether this assumption is reasonable. First we compare the self-broadening of the O2 60 GHz Q-branch with the self-broadening of O2 A-band. From a fundamental point-of-view the pressure broadening of these bands differs for two reasons: (1) the upper-states differ in electronic state and (2) the upper quantum states differ by J 7 1. The pressure-broadening parameter depends primarily upon the cross-section of the molecule averaged over both the ground and the excited state, such that these two bands have half of the pressure broadening contributions in common. The first difference, in regard to the electronic nature of the excited state, is actually fairly minor since the 1 Σ þ g state actually contains the same electronic configuration (1s2 2s2 2π 6 2π n2 ) as the 3 Σ g ground electronic state, thus the molecule retains its geometry in both a nuclear (Δr ¼ 2 pm, or 1.6%) and electronic sense. A caveat that remains is that the excited electronic state does not contain a magnetic dipole. The second difference, which arises from the selection rules that govern the observable transitions in different bands can be thought of as a quantum shift in the dependent variable that accounts for the difference in the average J value between the upper and lower states. Between Q-branches the shift is moot, but P,R, and S branches will shift by 1/2, 1/2 and 1 quanta respectively. The relative P and R shifts are intrinsically accounted in the parameterization of Eq. (1) which uses J′. Equivalently many parameterizations define m¼ J for R-branches and m ¼J+1 for
P-branches. However, we expect the Q-branch and S-branch values (for matched J′) to fall below and above the P,R branch values by amounts related to the magnitude of the J′dependence (δγ=δJ′). Typically, J′dependence of pressure broadening is a monotonic decreasing function that reflects the diminishing probability of collisional energy transfer with increasing molecular rotation. When this function is slow enough (say o 10%=J) then the change based solely on different selection rules will be systematic shifts of 75%. There are many possible intercomparisons of pressure broadening parameters that could be made, however, the precision of the self-broadening data sets of the 60 GHz Q-branch [18] and the A-band [28] enables tests of these potential differences to accuracies of a few percent. Inspection of the dotted solid black and solid blue curves plotted in Fig. 5 reveals that the self-broadening in these two bands has common origins at J′ ¼ 1, diverge to 6% disagreement at J′ ¼ 11–15, before converging again at J′ ¼ 29. Above J′ ¼ 27 the 60 GHz Q-branch data is an extrapolation whereas the A-band data extend above J′ ¼ 39. The disagreement above J′ ¼ 29 may be attributed to the formula (Eq. (1)) which is designed to approach a horizontal asymptote just below the data range. For statistical comparisons we limit the range to J′ ¼ 1–29. Considering the two potential sources for differences in pressure-broadening, the two functions can be analyzed in terms of their mean difference of 4% and their standard deviation of 2%. The mean difference is perhaps attributable to the electronic energy differences, and their variance is perhaps attributable to the quantum shift associated with the selection rules. Overall, the statistical differences are not much greater than the experimental uncertainties (0.5–2%) and indicate that the band-to-band invariance of the pressure-broadening of oxygen introduces minimal biases. For fundamental spectroscopic parameters, such as N2 and O2 broadening for the Earth atmosphere, such an assumption can bias retrievals (by more than the noise) when SNR 450. However, for pressure broadening from a minor species, the assumption would have an impact scaled down with the species concentration, e.g. for an atmosphere with 7 cm total column of precipitable water vapor (PWV), the water broadening contributes significantly to total pressure broadening linewidth ( 8%), but the error induced by an assumption of the pressure broadening that has a 4% bias will be 0:3%. Although the self-broadening widths display only minor scaling from one oxygen band to another, water broadening involves an electric dipole moment, which introduces stronger intermolecular interactions compared with the dominant quadrupole–quadrupole interaction of the O2–O2 system [37]. As a test of the transferability of oxygen–water broadening data, inter-comparisons can be made between three bands, the 60 GHz Q-branch, the pure rotation S-branch, and the isotropic Raman Q-branch. In comparison with the Qbranches the selection rules produce no ambiguity in the parameterization, but the comparison with the pure rotation S-branch is obviously best when the polynomial is quantum shifted. (This is analogous to utilizing the m quantum number when comparing P and R branches, essentially
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Table 2 Best fit values of coefficients in Eq. (1) for O2–O2 [18], for O2–O2 [28] and for O2–H2O (this work). Units are cm 1 atm 1. Parameter
O2–O2 [18]
O2–O2 [28]
O2–H2O
Aγ Bγ c1 c2 c3
60 GHz 1.1524(827) 1.2484(710) 0.1573(251) 5.63(114) 10 3 6.99(237) 10 6
A-band 0.9581 1.3612 0.07180 2.334 10 3 3.025 10 6
60 GHz 1.409(210) 1.854(246) 0.382(236) 2.50(194) 10 2 4.06(388) 10 5
defining a common quantum for intercomparison of bands.) This quantum shift is visible for the pure rotational data set plotted in Fig. 4 which lies higher than the 60 GHz Q-branch data. A straightforward statistical comparison (J′ o11) of fits to Eq. (1) reveals 19.4% average difference and 30.2% variance. Applying a quantum shift produces a 2.9% average difference and a 10.9% standard deviation. Even better statistics are obtained with a comparison between extrapolated room temperature values from Fanjoux et al. (see Appendix), where a 4.9% average difference and 8.0% standard deviation are obtained in comparison with the 60 GHz Q-branch. These inter-comparisons support the validity of the assumption that band-to-band variability for oxygen water broadening is at least no worse than 10%. Because of the agreement among these data sets we report only the more precise polynomial expansion based on the 60 GHz Q-branch (see Table 2) measurements, which are the most extensive in quantum coverage. We recommend these values to be applied where high-precision pressure broadening measurements are not available. Note that pressure shifts are expected to have state dependence, so the values reported here should only be used in their respective bands. Extension of these invariant pressure broadening assumptions to the A-band implies that the directly measured water broadened width values for the A-band [32] are systematically biased, by more than 50%. This bias is larger than the given uncertainties. In the A-band the water broadening coefficient (at room temperature) is a minor component of the Lorentzian linewidth, 0–2%. Furthermore, the dynamic range of the change in linewidth with water vapor was also about 1%. Considering these potential issues with the A-band measurements, we have more confidence in the transference of the 60 GHz Q-branch data set for use in atmospheric A-band retrievals. 4.3. Forward model calculations and implications for remote sensing In order to assess the impact of the new data and the implications for atmospheric remote sensing, we have implemented the new data in two existing forward models – one used in the microwave (60 GHz) region and one used in the near-infrared/visible (0:76 μm) region. The model used here to demonstrate the impact in the microwave region is the Monochromatic Radiative Transfer Model (MonoRTM) [38–40], developed and distributed by Atmospheric and Environmental Research. MonoRTM is publicly available for download from http:// rtweb.aer.com MonoRTM is used to train fast radiation codes for assimilation of satellite measurements into
numerical weather prediction models and for satellite retrieval algorithms (e.g. [41]). The model is also used within the Department of Energy (DoE) Atmospheric Radiation Measurement (ARM) program for groundbased retrieval of the atmospheric state (e.g. [42]). MonoRTM versions numbered v4.2 and below only account for air- and self-broadening of lines for O2 as well as for other molecules. Differences between air- and H2Obroadening have not been accounted for in this model up to now. We note that the difference between air- and H2Obroadening of O2 has been accounted for in other widely used microwave radiative transfer models, namely the Millimeter-wave Propagation Model [43] and the Rosenkranz model [44,45]. Since the MPM-93 version, this model has utilized information from the measurements of [21,23] to calculate a single estimated scaling factor (1.1 ) for H2O–O2 broadening relative to air–O2 broadening that was applied to all lines in the 60 GHz complex. To further demonstrate the impact for remote sensing in the microwave region, we have integrated the MonoRTM output over specific sub-bands to simulate the quantities that are measured by the Special Sensor Microwave Imager/Sounder (SSMIS), which views the atmosphere with a constant Earth incidence angle of 531, which corresponds to an airmass of 1.5. SSMIS is a microwave radiometer system flown on board the Defense Meteorological Satellite Program (DMSP) F-16, F-17 and F-18 satellites. The model used here to demonstrate the impact in the O2 A-band at 0:76 μm is the forward model for the Orbiting Carbon Observatory 2 Level 2 Full Physics (OCO-2 L2FP) retrieval algorithm [7] calculated on a 0.01 cm 1 grid. This forward model uses pre-calculated absorption coefficient (ABSCO) tables (see [46] and references therein for further details). ABSCO tables associated with Level 2 version 3.3 and earlier did not account for the difference between airand H2O-broadening of O2. Subsequent versions will incorporate the data produced from this work. For retrieval impacts we define three wet (slant path 3.5 cm PWC) atmospheric models: (1 – [ref.]) a reference atmosphere with water broadening equal to air broadening; (2 – [1.8 ]) water broadening of 1.8 that of air broadening; and (3 – [this work]) water broadening given by the model fit to the 60 GHz data in this work. For the atmospheric profile, we used a sample profile from July 20, 2012, from the radiosonde-based “Merged Sounding” [47] product at the Department of Energy (DoE) Atmospheric Radiation Measurement (ARM) site at Lamont, Oklahoma. The second case is designed to provide a rough agreement with the water-broadening A-band measurements of Vess et al. [32]. A fourth case, [1.1 ] for the 60 GHz Q-branch
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region is taken from the MPM algorithm attributed to Rosenkranz. We ran these cases through the MonoRTM and OCO-2-L2FP algorithm and plotted the systematic shifts in the output which are above or near the noise level of typical atmospheric data retrieved via the models. In Fig. 6 the results are displayed as optical depth and change in optical depth for both bands, and then as brightness temperature (BT) or % Transmission (T) for the 60 GHz Q-branch and A-bands respectively. Several qualitative observations are readily discernable from inspection of the changes to the atmospheric spectral models. For the 60 GHz Q-branch the effects of water broadening are noticed at the edges of the band where the higher J transitions are no longer saturated. In the microwave the effects must be filtered through the relatively wide bandwidth of the sensing measurements. Although sharp spectral features result from the changes in lineshape, only two channels are affected by the changes in the brightness temperature variable, however, it is precisely these channels that are useful for temperature
measurement in the lower atmosphere. Here, the Rosenkranz model is accounting for some of the ‘wet’ atmosphere bias ( 0:2 mK GHz1 ), but the new data implies a stronger effect of ( 0:5 mK GHz1 ). In the microwave spectra the strong blending, mixing and saturation of the atmospheric line profiles preclude any interpretation of the changes in J-dependence of the models. Although this change is small compared with the radiometric noise of a receiver such as SSMIS, it will bias averaged results, which are routinely used to determine climatologies and longterm trends. The models of the A-band show that the wellresolved oxygen features are systematically different on a line-by-line basis, with differences consistent with just a change in width and peak height. Here the correlation of the width with peak height can be seen in the different residual band shapes between this work and the 1.8 air broadening assumptions. In the differential percent transmission (ΔT) the impact on X CO2 retrievals can be inferred directly, with the 1.8 factor producing changes in retrieved air mass of up to 0.2% and the values from this
Fig. 6. Results of optical depth calculations for ‘wet’ atmospheric models with different assumptions for H2O–O2 broadening coefficients. The microwave Qbranch optical depth (upper) and brightness temperature (lower) are shown on the left. The O2 A-band optical depth (upper) and transmittance (lower) are shown on the right. Cyan traces are the modeled value for the reference atmosphere, differences are given for three different models in red [1.8 ] (to match [32]), black [1.1 ], and blue [this work]. Details of the atmospheric conditions are given in the text. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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work implying 5–10 less change. Since an atmosphere with 3.5 cm PWC is a modestly humid atmosphere, and X CO2 is desired to be fit to 0.3%, it is clear that an assumption such as the [1.8 ] can negatively affect the retrieval and introduce bias instead of resolve it. 5. Conclusion Accurate and precise measurements of waterbroadening of oxygen transitions at room temperature are realized at millimeter and submillimeter wavelengths. These measurements compare favorably with expectations from previous millimeter and Raman studies, but cast doubt on the validity of water-broadening measurements in the oxygen A-band. Based on intercomparisons and evaluations of the laboratory data, as well as testing in the context of forward models used in atmospheric retrieval algorithms, we recommend the widespread application of the presently measured water broadening values across the oxygen spectrum.
197
Table 4 Calculated 446 K O2–H2O broadening and temperature exponent fitted from data in Fanjoux et al. and extrapolated room temperature values. Quanta J′
n
Γ(J′,446) cm 1 atm 1
Γ(J′,296)
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
0.6477 0.6145 0.7137 0.8116 0.8449 0.8213 0.7796 0.7401 0.7079 0.6825 0.6626 0.6468 0.6341 0.6237 0.6151 0.6078 0.6017 0.5964
0.0412 0.0380 0.0384 0.0384 0.0380 0.0373 0.0365 0.0356 0.0346 0.0335 0.0324 0.0313 0.0302 0.0290 0.0279 0.0267 0.0255 0.0243
0.0537 0.0489 0.0515 0.0536 0.0537 0.0523 0.0502 0.0482 0.0462 0.0443 0.0426 0.0408 0.0391 0.0375 0.0359 0.0342 0.0326 0.0311
Acknowledgments Portions of this research were carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
pressure broadening value for any J′ quantum at any temperature ΓðJ′; TÞ ¼ ΓðJ′; 446Þð446=TÞnðJ′Þ
ð4Þ
The values obtained from this expression are listed in Table 4.
Appendix A References To obtain H2O broadened half-widths of O2 the Raman Q-branch at 296 K, first the reported widths for 446 K were fitted to the equation ΓðJ′; 446Þ ¼ ðp3 nJ ′3 þ p2 nJ ′2 þ p1 nJ′ þ p0 Þ=ðq2 J ′2 þ q1 nJ′ þ q0 Þ
ð2Þ which is a simple polynomial expansion in the J′ quantum number. This formulation allows a smooth extrapolation or interpolation throughout the spectrum. A similar equation was used to fit the power-law exponents nðJ′Þ ¼ ðp3 nJ ′3 þ p2 nJ ′2 þ p1 nJ′ þ p0 Þ=ðJ ′3 þ q2 nJ ′2 þ q1 nJ′ þ q0 Þ
ð3Þ again, the formulation allows a smooth extrapolation or interpolation throughout the spectrum. The coefficients of these polynomials are given in Table 3. Combination of these formulae into the power-law expression enables the Table 3 Values of the functions ΓðJ′; 446Þ and nðJ′Þ fitted from data in Fanjoux et al. Parameter
ΓðJ′; 446Þ
n(J′)
p3 p2 p1 p0 q2 q1 q0
0.5306 5.385 40.14 20.42 13.31 82.35 47.09
0.0006242 0.04711 0.03517 0.1903 0.02948 3.864 0.0
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Contents lists available at ScienceDirect
Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Pressure broadening of oxygen by water Brian J. Drouin a,n, Vivienne Payne a, Fabiano Oyafuso a, Keeyoon Sung a, Eli Mlawer b a b
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, United States Atmospheric and Environmental Research, 131 Hartwell Avenue, Lexington, MA 02421, United States
a r t i c l e in f o
abstract
Article history: Received 22 June 2013 Received in revised form 26 July 2013 Accepted 2 August 2013 Available online 9 August 2013
A need for precise air-mass retrievals utilizing the near-infrared O2 A-band has motivated measurements of the water-broadening in oxygen. Experimental challenges have resulted in very little water broadened oxygen data. Existing water broadening data for the O2 A-band is of insufficient precision for application to the atmospheric data. Line shape theory suggests that approximate O2 pressure broadening parameters for one spectral region, such as the A-band, may be obtained from comparable spectral regions such as the O2 60 GHz Q-branch, which is also used prominently in remote sensing. We have measured precise O2–H2O broadening for the 60 GHz Q-branch and the pure-rotational transitions at room temperature with a Zeeman-modulated absorption cell using a frequency-multiplier spectrometer. Intercomparisons of these data and other O2 pressure broadening data sets confirm the expectation of only minor band-to-band scaling of pressure broadening. The measurement provides a basis for fundamental parameterization of retrieval codes for the long-wavelength atmospheric measured values. Finally, we demonstrate the use of these measurements for retrievals of air-mass via remote sensing of the oxygen A-band. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Pressure broadening Atmospheric science Humidity Air mass Oxygen Water vapor
1. Introduction Oxygen is a well-mixed gas in Earth's atmosphere, with a mixing ratio that is extremely well known, allowing oxygen absorption features to be utilized in remote sensing applications for the retrieval of other atmospheric quantities. The O2 60 GHz Q-branch has long been used for the retrieval of atmospheric temperature from satellites (e.g. [1]), aircraft (e.g. [2]) and from the ground [3,4]. The pure rotational transitions in the Terahertz region may be useful for retrievals of stratospheric temperatures or air-mass, but the opacity of the water continuum reduces their utility below the tropopause. The O2 A-band at 0:76 μm has been used extensively in ground-based [5], airborne [6] and satellite [7–10] remote sensing to provide the information
n
Corresponding author. Tel.: +1 818 393 6259; fax: +1 818 354 5148. E-mail address: [email protected] (B.J. Drouin).
0022-4073/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jqsrt.2013.08.001
on atmospheric path lengths necessary to characterize cloud and aerosol abundances, to retrieve surface pressure and to retrieve column abundances of other trace gases, such as CO2 and CH4, using coincident near-infrared measurements. Current and planned spaceborne missions utilizing the O2 A-band for the purposes of greenhouse gas retrievals include the TANSO-FTS on the Japanese Greenhouse Gases Observing satellite (GOSAT) [11], the NASA Orbiting Carbon Observatory re-flight (OCO-2) [12] and the Chinese TanSat satellite instrument [13]. The accuracy of the remotely sensed quantities depends directly on the accuracy of the spectroscopic input (line positions, line intensities and lineshape) used in the forward models within the retrieval algorithms (e.g. [14–16]). The parameterization of the lineshape includes pressure broadening and may also include additional physics such as shifts, mixing, narrowing and speeddependence. For current and future remote-sensing measurements to be used to their full potential, it is necessary
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to continue to characterize and reduce uncertainties in the spectroscopic input to the models, particularly those uncertainties that could lead to spatially or seasonally dependent biases in the retrieval products. Pressure broadening by water vapor can make an additional contribution to the observed width of the lines, which in turn affects the retrieval of the target quantity. Since atmospheric water vapor is highly variable in space and time, the reduction of spectroscopic uncertainties associated with water vapor is important in order to avoid the introduction of spatially and/or temporally dependent biases in the retrieved products. Due to the experimental challenges involved, few previous studies have been performed to measure the pressure broadening of oxygen by water vapor. Here, we report new, precise measurements of O2–H2O broadening for the 60 GHz Q-branch and the pure-rotational transitions. As a linear molecule with no electric dipole moment, oxygen pressure broadening is expected to show little electronic or vibrational dependence, and so we assume that the measured values can also be applied to the O2 A-band at 0:76 μm. In Section 2, we describe results from previous studies of O2–H2O broadening in order to provide context for this new work. Section 3 contains a description of the experimental setup for the new measurements. In Section 4, we detail the approach taken to determine the O2–H2O broadening parameters from the new measurements, compare with results from previous studies and explore some of the implications for remote sensing by showing the impact on forward model calculations in the 60 GHz and 0:76 μm regions. A concise summary of the work is provided in Section 5.
191
atmospheric temperature, Fanjoux et al. had extrapolated their data to compare with the measurement from [21] and had concluded that their results were relatively consistent with this datapoint for this single line, providing some support for the assumption of vibrational independence of the pressure broadening. In the O2 A-band at 0:76 μm, state-of-the-art spectroscopic techniques have produced very high quality (self and air) broadening and shift parameters for the oxygen A-band [28,29]. Other studies have obtained the temperature dependence of the pressure broadening and shift parameters [30] as well as line-mixing/collision-induced absorption [31]. O2–H2O room temperature pressure broadening was measured for six lines in the A-band by Vess et al. [32]. The water-broadened widths inferred by [32] were over 50% larger than the values implied by the earlier work [21–23,27] in other spectral regions. Due to physical constraints such as the low vapor pressure of water and the large Doppler widths of transitions in the A-band, the data of Vess et al. was not very sensitive to the water-broadening itself, and the error bars are large. In summary, the previous data for O2–H2O broadening consists of measurements of only two transitions in the 60 GHz complex [21–23], a comprehensive study of the Raman Q-branch at 1553.3 cm 1 at temperatures outside the range of interest for remote sensing of ambient atmospheric conditions [27], and a study of six lines in the 0:76 μm A-band [32], with large error bars, that was not consistent with the results of the other two studies. The single-line limitations of the millimeter region studies of [21–23] and the discrepancy between the parameters derived from [27] and the direct measurements of [32] provided a strong motivation for additional measurements.
2. Previous studies of O2–H2O broadening The new measurements described in this work have enabled the determination of precise O2–H2O broadening parameters for lines in the 60 GHz Q-branch (spanning frequencies from 47 to 119 GHz) and for pure rotational transitions between 424 and 1850 GHz. Since we are assuming that oxygen pressure broadening has little electronic or vibrational dependence, we should consider these new measurements not only in the context of previous measurements in this spectral region, but also in the context of measurements of O2–H2O broadening at other frequencies. Previous high quality measurements of spectroscopic parameters for the 60 GHz Q-branch include air and selfbroadening [17,18], line-mixing [18,19], and pressure broadening temperature dependence [19,20]. However, only two transitions in the 60 GHz Q-branch have published waterbroadening values [21–23]. While self- and air-broadening parameters for the pure rotational (S-branch) transitions have been reported by [24–26], we are not aware of previous measurements of O2–H2O broadening for these transitions. Fanjoux et al. [27] performed high temperature (between 446 and 990 K) measurements of O2–H2O broadening for the Raman Q-branch at 1553.3 cm 1, with the goal of contributing to understanding of combustion in rocket engines. While the temperature range of this study is obviously very different from the range of ambient
3. Experimental setup A room temperature apparatus designed for static gas containment was fitted with a variable temperature cold finger and was filled with a fixed amount of oxygen and water vapor. Temperature control of the cold-finger was accomplished through setting the voltage of thermoelectric (TE) coolers attached to an aluminum block encircling the cold finger. By controlling the finger temperature in the 242–280 K range the vapor pressure of water in the static gas cell was maintained at fixed values during each spectroscopic measurement. The area of the gas cell probed by the spectrometer was maintained at room temperature which fluctuated between 294 and 298 K. The spectrometer described in Drouin et al. [33], with an additional source described in Gupta et al. [34], was utilized to record the lineshapes of dozens of oxygen transitions, each as a function of water vapor pressure. In order to remove spectral features due to standing waves and water vapor absorption, Zeeman modulation was employed through application of an axial magnetic field. As in the previous work on O2 [26] the convolution method described by Pickett [35] was utilized to facilitate treatment of instrument and magnetic field effects on the lineshape. A single transition (9 at 58323.876 GHz) was measured as a function of oxygen pressure to check consistency with the
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Pressure Gauge
Lock-In Amplifier
Modulated Synthesizer
Cold Finger
Pre-amp
TE coolers
Detector
O2,H2O Multiplier(s) Wire-grid polarizer
Sample Chamber
rooftop reflector
Zeeman Coil
Fig. 1. Experimental setup.
self-broadening measurements reported by Tretyakov et al. [18]. The O2 self-broadening parameter measured with this apparatus is 1.780(38) MHz Torr 1; this value agrees well with the value 1.763(15) found by Tretyakov et al. A schematic of the experimental design is shown in Fig. 1. Measurements were made of twenty-four 60 GHz Q-branch transitions (50–119 GHz) and 11 pure rotational transitions (424–1850 GHz). All spectral and vapor pressure values were tuned digitally with a computer that simultaneously recorded the demodulated signal. After tuning the TE-cooler voltage, the water vapor pressure settles over a time of 30 min. To improve measurement efficiency all transitions within a given spectral band were measured at a given TE-cooler setting prior to re-tuning the TE-cooler. Oxygen pressure was fixed at a value between 1 and 2 Torr for each series of water pressures and the water vapor pressure was set between 0.3 and 9.0 Torr. Total pressure was measured with a 10 Torr MKS capacitance manometer at each step through each spectrum, and the averaged total pressure value was stored with the averaged spectral data. The manometer reading was calibrated upon receipt from the manufacturer and is stated to reproduce the total pressure to 0.25% down to 1 mTorr. Deviations in the temperature of the room dominate the potential systematic errors, the HVAC system maintained room temperature between 294 and 298 K, and the thermal cycles were typically shorter than the experiment durations, such that errors on the order of 1–2% are expected from datapoint to datapoint. Therefore 296(4) K is adopted as the temperature for the experiment. An example of the data set for one spectral line is shown in Fig. 2. This figure displays the typical characteristics of a pressure-broadened frequency-modulated absorption line (1) a second derivative Voigt lineshape, (2) a decrease in peak height with increasing pressure, (3) an increase in linewidth with increasing pressure, (4) a lineshift with pressure. For submillimeter transitions the integration time was chosen to enable signal-to-noise ratios (SNRs) greater than 20, which is an effective cutoff to avoid systematic errors in the linewidth measurement (noisy lines are always evaluated to larger widths). In the mm-wave range most of the lines were collected in microwindows repeated serially for each water vapor pressure, and, owing to the variability in the intensities of these transitions, the SNRs
Fig. 2. The J′ ¼ 9 transition of O2 near 61.150 GHz. The O2 partial pressure is 1.8 Torr, the total pressure (including water vapor) is given in the inset.
varied. A series of runs through these transitions enabled the optimal partial pressures and modulation depths to be determined for a majority of the transitions, with only the highest (N 425) transitions falling below the SNR of 20 cutoff in the optimal run. A few of these mm-wave lines were systematically distorted (N ¼21+ and both N ¼29 transitions), and asymmetric lineshapes and residuals were observed. For N 425, it was decided not to report the values due to low SNR, for N ¼21+, the width and shift have enlarged error bars due to the poor fit. For the 118 GHz transition the SNR was limited due to poor detector responsivity, this datapoint also has a larger error bar. Pressure broadened linewidths and lineshifts are reported in Table 1 with error bars (fit precision) determined in the convolution fitting procedure, but systematic errors (such as room temperature) up to a few percent exceed these precisions for most of the datapoints. 4. Results and analysis 4.1. Pressure broadening parameters The pressure broadened lineshapes were fitted, via the convolution method, by inter-comparisons of higher pressure
Table 1 Measured O2–H2O broadening and shift values in MHz Torr 1 for 296 K. N′
J′
N″
J″
γ
δ
3 3 5 5 7 7 7 9 9 11 11 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15 17 17 19 19 21 21 23 25
2 3 4 5 6 6 7 8 9 10 11 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15 17 17 19 19 21 21 23 25
1 1 3 3 5 5 5 7 7 9 9 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15 17 17 19 19 21 21 23 25
2 2 4 4 5 6 6 8 8 10 10 2 0 4 2 6 4 8 6 10 8 12 10 14 12 16 14 18 16 20 18 22 20 22 26
3.525(21) 3.170(13) 2.479(14) 2.700(18) 2.323(10) 2.387(11) 2.410(21) 2.227(15) 2.326(18) 2.235(16) 1.921(31) 2.507(03) 3.053(48) 2.444(12) 2.293(09) 2.061(06) 2.254(10) 2.180(05) 2.209(04) 2.090(03) 2.086(04) 2.115(06) 2.109(04) 2.026(05) 2.033(10) 1.958(04) 1.995(12) 1.915(05) 1.911(08) 1.749(05) 1.795(12) 1.922(15) 1.707(20) 1.614(22) 1.522(17)
0.089(17) 0.022(09) 0.031(04) 0.073(06) 0.059(06) 0.076(15) 0.064(04) 0.055(11) 0.188(13) 0.064(08) 0.070(12) 0.059(06) 0.062(08) 0.012(04) 0.163(04) 0.049(05) 0.004(02) 0.160(02) 0.084(01) 0.040(01) 0.039(02) 0.062(02) 0.014(02) 0.059(02) 0.022(01) 0.026(01) 0.069(03) 0.032(02) 0.034(03) 0.109(02) 0.003(03) 0.186(09) 0.042(05) 0.012(04) 0.018(10)
spectra with lower pressure spectra. The resulting ‘differential’ linewidths (and lineshifts) depend only upon the pressure broadening induced by the differing amounts of water vapor. An example regression of the differential lineshapes vs. the differential in total pressure is shown in Fig. 3. The slope of this plot is the water vapor broadening coefficient for the spectral line measured. These slopes have been determined for each of the transitions presented in this study; they are reported in Table 1 and shown in Fig. 4. Intercomparisons can be made for the two previously studied transitions, the 9+ and 1 lines at 61.15 GHz and 118.75 GHz respectively. For the 9+ transition, Setzer's reported ratio of 1.3 from Liebe's selfbroadening study gives 2.33 MHz Torr 1, which is larger than the present value determined to be 2.090(03) MHz Torr 1. For the 1 transition, the two prior measurements of 2.52(4) MHz Torr 1 [22] and 2.30(24) MHz Torr 1 [23] are in better agreement with each other than with the present value 3.053 (48) MHz Torr 1. The 1 measurement reported here is the worst signal-to-noise measurement of the present data set, and may suffer a systematic error (a larger broadening coefficient) due to the elevated noise level. For application of these parameters to other spectral bands, it is useful to define a function, shown in Eq. (1) [36] that fits the J′ dependence of the observed values [28]. We also convert the units into the more commonly used
Differential Lineshape (MHz)
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193
5 4
Δγ = 2.090(3)Δp
3 2 1 0
Δδ = 0.040(1)Δp 0
0.5 1 1.5 2 Differential Pressure (Torr)
2.5
Fig. 3. Differential lineshape values for the J′ ¼ 9 transition of O2 near 61.150 GHz. The slope γ ¼ Δγ=Δp corresponds to the linewidth in units of MHz Torr 1, and the slope δ ¼ Δδ=Δp corresponds to the lineshift in units of MHz Torr 1.
Fig. 4. The J′ dependence of O2–H2O broadening measured in this and other studies. Random error bars of 3% are shown for the data from this work, when precision is less than 3%. The values in Table 1 are converted into cm 1 atm 1 with the factor 0.025351 cm 1 Torr MHz 1 atm 1.
infrared units of cm 1 atm 1. This formulation is not intended to replace the fundamental measurements, which should be used for the matched transitions in remote sensing models, rather the equation is to be used as a metric to gauge the transferability of the pressure broadening from one band to another, and, if deemed acceptable, used to estimate pressure broadening when measurements are un-reliable or non-existent. γ ¼ Aγ þ
Bγ ð1 þ c1 J′ þ c2 J ′2 þ c3 J ′4 Þ
ð1Þ
A different empirical formulation was applied to the temperature dependent data of Fanjoux et al. in order to estimate the room temperature values of the fundamental Raman (vibrational) band, this formulation is given in the Appendix. The smooth red line in Fig. 5 is a fit to Eq. (1) for the 60 GHz Q-branch data in Fig. 4 and Table 1. This is the same model used by Long et al. [28] to describe their room temperature self-broadening data set for the A-band.
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Fig. 5. Comparison of band models and scaled band models. The models (see Eq. (1) and Table 2) are depicted with the solid and dotted lines representing each data set (all at 296 K). The values in Table 1 are converted into cm 1 atm 1 with the factor 0.025351 cm 1 Torr MHz 1 atm 1 for modeling with Eq. (1). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
To facilitate comparisons and examine previous assumptions used in atmospheric retrievals this same model was applied to the self-broadening room temperature 60 GHz Q-branch data of Tretyakov et al. [18]. 4.2. Assumption of no state dependence Since the new millimeter and sub-millimeter measurements presented here have far smaller error bars than existing direct measurements of H2O broadening in the O2 A-band, we wish to apply this new data to the A-band. In order to do this, we must assume that the pressure broadening has little or no vibrational or electronic state dependence. In this section, we examine whether this assumption is reasonable. First we compare the self-broadening of the O2 60 GHz Q-branch with the self-broadening of O2 A-band. From a fundamental point-of-view the pressure broadening of these bands differs for two reasons: (1) the upper-states differ in electronic state and (2) the upper quantum states differ by J 7 1. The pressure-broadening parameter depends primarily upon the cross-section of the molecule averaged over both the ground and the excited state, such that these two bands have half of the pressure broadening contributions in common. The first difference, in regard to the electronic nature of the excited state, is actually fairly minor since the 1 Σ þ g state actually contains the same electronic configuration (1s2 2s2 2π 6 2π n2 ) as the 3 Σ g ground electronic state, thus the molecule retains its geometry in both a nuclear (Δr ¼ 2 pm, or 1.6%) and electronic sense. A caveat that remains is that the excited electronic state does not contain a magnetic dipole. The second difference, which arises from the selection rules that govern the observable transitions in different bands can be thought of as a quantum shift in the dependent variable that accounts for the difference in the average J value between the upper and lower states. Between Q-branches the shift is moot, but P,R, and S branches will shift by 1/2, 1/2 and 1 quanta respectively. The relative P and R shifts are intrinsically accounted in the parameterization of Eq. (1) which uses J′. Equivalently many parameterizations define m¼ J for R-branches and m ¼J+1 for
P-branches. However, we expect the Q-branch and S-branch values (for matched J′) to fall below and above the P,R branch values by amounts related to the magnitude of the J′dependence (δγ=δJ′). Typically, J′dependence of pressure broadening is a monotonic decreasing function that reflects the diminishing probability of collisional energy transfer with increasing molecular rotation. When this function is slow enough (say o 10%=J) then the change based solely on different selection rules will be systematic shifts of 75%. There are many possible intercomparisons of pressure broadening parameters that could be made, however, the precision of the self-broadening data sets of the 60 GHz Q-branch [18] and the A-band [28] enables tests of these potential differences to accuracies of a few percent. Inspection of the dotted solid black and solid blue curves plotted in Fig. 5 reveals that the self-broadening in these two bands has common origins at J′ ¼ 1, diverge to 6% disagreement at J′ ¼ 11–15, before converging again at J′ ¼ 29. Above J′ ¼ 27 the 60 GHz Q-branch data is an extrapolation whereas the A-band data extend above J′ ¼ 39. The disagreement above J′ ¼ 29 may be attributed to the formula (Eq. (1)) which is designed to approach a horizontal asymptote just below the data range. For statistical comparisons we limit the range to J′ ¼ 1–29. Considering the two potential sources for differences in pressure-broadening, the two functions can be analyzed in terms of their mean difference of 4% and their standard deviation of 2%. The mean difference is perhaps attributable to the electronic energy differences, and their variance is perhaps attributable to the quantum shift associated with the selection rules. Overall, the statistical differences are not much greater than the experimental uncertainties (0.5–2%) and indicate that the band-to-band invariance of the pressure-broadening of oxygen introduces minimal biases. For fundamental spectroscopic parameters, such as N2 and O2 broadening for the Earth atmosphere, such an assumption can bias retrievals (by more than the noise) when SNR 450. However, for pressure broadening from a minor species, the assumption would have an impact scaled down with the species concentration, e.g. for an atmosphere with 7 cm total column of precipitable water vapor (PWV), the water broadening contributes significantly to total pressure broadening linewidth ( 8%), but the error induced by an assumption of the pressure broadening that has a 4% bias will be 0:3%. Although the self-broadening widths display only minor scaling from one oxygen band to another, water broadening involves an electric dipole moment, which introduces stronger intermolecular interactions compared with the dominant quadrupole–quadrupole interaction of the O2–O2 system [37]. As a test of the transferability of oxygen–water broadening data, inter-comparisons can be made between three bands, the 60 GHz Q-branch, the pure rotation S-branch, and the isotropic Raman Q-branch. In comparison with the Qbranches the selection rules produce no ambiguity in the parameterization, but the comparison with the pure rotation S-branch is obviously best when the polynomial is quantum shifted. (This is analogous to utilizing the m quantum number when comparing P and R branches, essentially
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Table 2 Best fit values of coefficients in Eq. (1) for O2–O2 [18], for O2–O2 [28] and for O2–H2O (this work). Units are cm 1 atm 1. Parameter
O2–O2 [18]
O2–O2 [28]
O2–H2O
Aγ Bγ c1 c2 c3
60 GHz 1.1524(827) 1.2484(710) 0.1573(251) 5.63(114) 10 3 6.99(237) 10 6
A-band 0.9581 1.3612 0.07180 2.334 10 3 3.025 10 6
60 GHz 1.409(210) 1.854(246) 0.382(236) 2.50(194) 10 2 4.06(388) 10 5
defining a common quantum for intercomparison of bands.) This quantum shift is visible for the pure rotational data set plotted in Fig. 4 which lies higher than the 60 GHz Q-branch data. A straightforward statistical comparison (J′ o11) of fits to Eq. (1) reveals 19.4% average difference and 30.2% variance. Applying a quantum shift produces a 2.9% average difference and a 10.9% standard deviation. Even better statistics are obtained with a comparison between extrapolated room temperature values from Fanjoux et al. (see Appendix), where a 4.9% average difference and 8.0% standard deviation are obtained in comparison with the 60 GHz Q-branch. These inter-comparisons support the validity of the assumption that band-to-band variability for oxygen water broadening is at least no worse than 10%. Because of the agreement among these data sets we report only the more precise polynomial expansion based on the 60 GHz Q-branch (see Table 2) measurements, which are the most extensive in quantum coverage. We recommend these values to be applied where high-precision pressure broadening measurements are not available. Note that pressure shifts are expected to have state dependence, so the values reported here should only be used in their respective bands. Extension of these invariant pressure broadening assumptions to the A-band implies that the directly measured water broadened width values for the A-band [32] are systematically biased, by more than 50%. This bias is larger than the given uncertainties. In the A-band the water broadening coefficient (at room temperature) is a minor component of the Lorentzian linewidth, 0–2%. Furthermore, the dynamic range of the change in linewidth with water vapor was also about 1%. Considering these potential issues with the A-band measurements, we have more confidence in the transference of the 60 GHz Q-branch data set for use in atmospheric A-band retrievals. 4.3. Forward model calculations and implications for remote sensing In order to assess the impact of the new data and the implications for atmospheric remote sensing, we have implemented the new data in two existing forward models – one used in the microwave (60 GHz) region and one used in the near-infrared/visible (0:76 μm) region. The model used here to demonstrate the impact in the microwave region is the Monochromatic Radiative Transfer Model (MonoRTM) [38–40], developed and distributed by Atmospheric and Environmental Research. MonoRTM is publicly available for download from http:// rtweb.aer.com MonoRTM is used to train fast radiation codes for assimilation of satellite measurements into
numerical weather prediction models and for satellite retrieval algorithms (e.g. [41]). The model is also used within the Department of Energy (DoE) Atmospheric Radiation Measurement (ARM) program for groundbased retrieval of the atmospheric state (e.g. [42]). MonoRTM versions numbered v4.2 and below only account for air- and self-broadening of lines for O2 as well as for other molecules. Differences between air- and H2Obroadening have not been accounted for in this model up to now. We note that the difference between air- and H2Obroadening of O2 has been accounted for in other widely used microwave radiative transfer models, namely the Millimeter-wave Propagation Model [43] and the Rosenkranz model [44,45]. Since the MPM-93 version, this model has utilized information from the measurements of [21,23] to calculate a single estimated scaling factor (1.1 ) for H2O–O2 broadening relative to air–O2 broadening that was applied to all lines in the 60 GHz complex. To further demonstrate the impact for remote sensing in the microwave region, we have integrated the MonoRTM output over specific sub-bands to simulate the quantities that are measured by the Special Sensor Microwave Imager/Sounder (SSMIS), which views the atmosphere with a constant Earth incidence angle of 531, which corresponds to an airmass of 1.5. SSMIS is a microwave radiometer system flown on board the Defense Meteorological Satellite Program (DMSP) F-16, F-17 and F-18 satellites. The model used here to demonstrate the impact in the O2 A-band at 0:76 μm is the forward model for the Orbiting Carbon Observatory 2 Level 2 Full Physics (OCO-2 L2FP) retrieval algorithm [7] calculated on a 0.01 cm 1 grid. This forward model uses pre-calculated absorption coefficient (ABSCO) tables (see [46] and references therein for further details). ABSCO tables associated with Level 2 version 3.3 and earlier did not account for the difference between airand H2O-broadening of O2. Subsequent versions will incorporate the data produced from this work. For retrieval impacts we define three wet (slant path 3.5 cm PWC) atmospheric models: (1 – [ref.]) a reference atmosphere with water broadening equal to air broadening; (2 – [1.8 ]) water broadening of 1.8 that of air broadening; and (3 – [this work]) water broadening given by the model fit to the 60 GHz data in this work. For the atmospheric profile, we used a sample profile from July 20, 2012, from the radiosonde-based “Merged Sounding” [47] product at the Department of Energy (DoE) Atmospheric Radiation Measurement (ARM) site at Lamont, Oklahoma. The second case is designed to provide a rough agreement with the water-broadening A-band measurements of Vess et al. [32]. A fourth case, [1.1 ] for the 60 GHz Q-branch
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region is taken from the MPM algorithm attributed to Rosenkranz. We ran these cases through the MonoRTM and OCO-2-L2FP algorithm and plotted the systematic shifts in the output which are above or near the noise level of typical atmospheric data retrieved via the models. In Fig. 6 the results are displayed as optical depth and change in optical depth for both bands, and then as brightness temperature (BT) or % Transmission (T) for the 60 GHz Q-branch and A-bands respectively. Several qualitative observations are readily discernable from inspection of the changes to the atmospheric spectral models. For the 60 GHz Q-branch the effects of water broadening are noticed at the edges of the band where the higher J transitions are no longer saturated. In the microwave the effects must be filtered through the relatively wide bandwidth of the sensing measurements. Although sharp spectral features result from the changes in lineshape, only two channels are affected by the changes in the brightness temperature variable, however, it is precisely these channels that are useful for temperature
measurement in the lower atmosphere. Here, the Rosenkranz model is accounting for some of the ‘wet’ atmosphere bias ( 0:2 mK GHz1 ), but the new data implies a stronger effect of ( 0:5 mK GHz1 ). In the microwave spectra the strong blending, mixing and saturation of the atmospheric line profiles preclude any interpretation of the changes in J-dependence of the models. Although this change is small compared with the radiometric noise of a receiver such as SSMIS, it will bias averaged results, which are routinely used to determine climatologies and longterm trends. The models of the A-band show that the wellresolved oxygen features are systematically different on a line-by-line basis, with differences consistent with just a change in width and peak height. Here the correlation of the width with peak height can be seen in the different residual band shapes between this work and the 1.8 air broadening assumptions. In the differential percent transmission (ΔT) the impact on X CO2 retrievals can be inferred directly, with the 1.8 factor producing changes in retrieved air mass of up to 0.2% and the values from this
Fig. 6. Results of optical depth calculations for ‘wet’ atmospheric models with different assumptions for H2O–O2 broadening coefficients. The microwave Qbranch optical depth (upper) and brightness temperature (lower) are shown on the left. The O2 A-band optical depth (upper) and transmittance (lower) are shown on the right. Cyan traces are the modeled value for the reference atmosphere, differences are given for three different models in red [1.8 ] (to match [32]), black [1.1 ], and blue [this work]. Details of the atmospheric conditions are given in the text. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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work implying 5–10 less change. Since an atmosphere with 3.5 cm PWC is a modestly humid atmosphere, and X CO2 is desired to be fit to 0.3%, it is clear that an assumption such as the [1.8 ] can negatively affect the retrieval and introduce bias instead of resolve it. 5. Conclusion Accurate and precise measurements of waterbroadening of oxygen transitions at room temperature are realized at millimeter and submillimeter wavelengths. These measurements compare favorably with expectations from previous millimeter and Raman studies, but cast doubt on the validity of water-broadening measurements in the oxygen A-band. Based on intercomparisons and evaluations of the laboratory data, as well as testing in the context of forward models used in atmospheric retrieval algorithms, we recommend the widespread application of the presently measured water broadening values across the oxygen spectrum.
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Table 4 Calculated 446 K O2–H2O broadening and temperature exponent fitted from data in Fanjoux et al. and extrapolated room temperature values. Quanta J′
n
Γ(J′,446) cm 1 atm 1
Γ(J′,296)
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
0.6477 0.6145 0.7137 0.8116 0.8449 0.8213 0.7796 0.7401 0.7079 0.6825 0.6626 0.6468 0.6341 0.6237 0.6151 0.6078 0.6017 0.5964
0.0412 0.0380 0.0384 0.0384 0.0380 0.0373 0.0365 0.0356 0.0346 0.0335 0.0324 0.0313 0.0302 0.0290 0.0279 0.0267 0.0255 0.0243
0.0537 0.0489 0.0515 0.0536 0.0537 0.0523 0.0502 0.0482 0.0462 0.0443 0.0426 0.0408 0.0391 0.0375 0.0359 0.0342 0.0326 0.0311
Acknowledgments Portions of this research were carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
pressure broadening value for any J′ quantum at any temperature ΓðJ′; TÞ ¼ ΓðJ′; 446Þð446=TÞnðJ′Þ
ð4Þ
The values obtained from this expression are listed in Table 4.
Appendix A References To obtain H2O broadened half-widths of O2 the Raman Q-branch at 296 K, first the reported widths for 446 K were fitted to the equation ΓðJ′; 446Þ ¼ ðp3 nJ ′3 þ p2 nJ ′2 þ p1 nJ′ þ p0 Þ=ðq2 J ′2 þ q1 nJ′ þ q0 Þ
ð2Þ which is a simple polynomial expansion in the J′ quantum number. This formulation allows a smooth extrapolation or interpolation throughout the spectrum. A similar equation was used to fit the power-law exponents nðJ′Þ ¼ ðp3 nJ ′3 þ p2 nJ ′2 þ p1 nJ′ þ p0 Þ=ðJ ′3 þ q2 nJ ′2 þ q1 nJ′ þ q0 Þ
ð3Þ again, the formulation allows a smooth extrapolation or interpolation throughout the spectrum. The coefficients of these polynomials are given in Table 3. Combination of these formulae into the power-law expression enables the Table 3 Values of the functions ΓðJ′; 446Þ and nðJ′Þ fitted from data in Fanjoux et al. Parameter
ΓðJ′; 446Þ
n(J′)
p3 p2 p1 p0 q2 q1 q0
0.5306 5.385 40.14 20.42 13.31 82.35 47.09
0.0006242 0.04711 0.03517 0.1903 0.02948 3.864 0.0
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