IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 2, NO. 3, MAY 2012 355

Atmospheric Attenuation of 400 GHz RadiationDue to Water Vapor

Marcus J. Weber, Student Member, IEEE, Benjamin B. Yang, Member, IEEE, Mark S. Kulie, Ralf Bennartz, andJohn H. Booske, Fellow, IEEE

Abstract—We present an experimental study of electromagneticlosses resulting from atmospheric attenuation due to water vaporon 400 GHz radiation. A hermetically sealed, high quality factorquasi-optical resonator system permits the precise control of theatmospheric water vapor content, and allows for measurement ofelectromagnetic losses. The empirically determined losses are com-pared with predictions by various different electromagnetic atten-uation models. Close agreement is demonstrated with four of themodels, while another differs by more than an order of magnitudeat higher values of water content.

Index Terms—Atmospheric electromagnetic attenuation, qualityfactor, resonator, terahertz (THz), water vapor.

I. INTRODUCTION

R ECENTLY, there has been increased interest in the tera-hertz (THz) regime, roughly defined as 0.3 THz to 3 THz,

because of proposed applications in the biomedical sciences,security, high data rate communications, and many other fields[1]–[4]. Historically, however, THz research has been hinderedby two main problems: the lack of reliable, compact, and pow-erful THz sources and atmospheric attenuation [3], [5]. Whileappreciable gains are being made in THz source development[6], there still exists the issue of atmospheric attenuation. Manyhypothesized applications for THz radiation require significantpropagation through the atmosphere where THz waves are se-verely attenuated.

Further development of THz technologies requires the abilityto quantify and predict atmospheric losses, so that engineeringdesigns may be tailored to their operating environment. A pre-dictive model which can accurately compute the anticipated at-mospheric attenuation would be valuable in the design of THztechnology. The most extensively cited atmospheric attenua-tion model for high frequency electromagnetic wave propaga-tion is the Millimeter-wave Propagation Model (MPM). TheMPM consists of several different versions of the model. We

Manuscript received December 08, 2011; revised February 08, 2012; ac-cepted February 15, 2012. Date of current version May 08, 2012. This workwas supported by the Air Force Office of Scientific Research, the Duane H. andDorothy M. Bluemke Foundation, and Northrup Grumann.

M. J. Weber, B. B. Yang, and J. H. Booske are with the Department of Elec-trical and Computer Engineering, University of Wisconsin-Madison, Madison,WI 53706 USA (e-mail: booske@engr.wisc.edu).

M. Kulie and R. Bennartz are with the Department of Atmospheric andOceanic Sciences, University of Wisconsin-Madison, Madison, WI 53706USA (e-mail: bennartz@aos.wisc.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TTHZ.2012.2189909

compare our 400 GHz data with the predictions from four dif-ferent versions of the MPM—Leibe in 1989 and 1993 [7], [8],and Rosenkranz in 1998 and 2002 [9], [10]. Reference [10] isa revised version of [9] with updates from [11]–[13]. Hewison[14] provides a detailed discussion of these different versions ofMPM. While the MPM has been shown to be very accurate formicrowave frequencies, there has been very limited comparisonwith measurements made within the THz regime. Additionally,we also compare our data to predictions made by a recently up-dated version of the monochromatic radiative transfer model, orMonoRTM (monoRTM v4.1 ) [15]–[17]. As opposed to theparametric MPM models, MonoRTM uses a combination of aphysically based line-by-line approach and the commonly usedMT CKD water vapor continuum model to characterize atmo-spheric absorption at high spectral resolutions [15]–[17]. To ourknowledge, there are few papers quantitatively comparing mea-surements of THz radiation atmospheric attenuation to theoret-ical model predictions. One recent paper [18] presents atmo-spheric attenuation data over a wide frequency band at a fewdiscrete values of water vapor content. A limited comparison totheory at a single water vapor value is provided in [18, Fig. 1].Our research complements [18] by studying the attenuation of anarrow frequency bandwidth (near 400 GHz) over a broad andhighly resolved range of water vapor concentrations.

The atmospheric attenuation predictive models require thespecification of atmospheric parameters such as temperature,pressure, relative humidity, hydrosol content, and frequency inorder to predict attenuation due to the main atmospheric com-ponents: water vapor, gaseous oxygen, and hydrosols [7]–[10],[15]–[17]. The largest contributor to atmospheric attenuation iswater vapor because THz waves excite different rotational andvibrational states of the water molecules in the atmosphere [1].For this reason, we have focused our research on studying theatmospheric losses on THz regime radiation due to water vaporcontent. We present attenuation data ranging from 130 parts permillion (ppm) to greater than 16 500 ppm, or 0.5% relative hu-midity to roughly 60% relative humidity (RH) at 22.777 C anda pressure of 983 hPa. We acknowledge that measurementswith varying pressure and temperature are required to more ac-curately and completely represent real-atmospheric parameters,however, our experimental setup does not allow for this at thispoint. Moreover, the method used in our study to acquire and pa-rameterize the attenuation data both enables but also constrainsus to studying only radiation attenuation by water vapor. Otherresearchers have examined discrepancies between model pre-dictions and measurements regarding high-frequency attenua-tion by other gas phase species such as O (see [11]–[13], [19]and references cited therein). Assessing the predictive accuracy

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356 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 2, NO. 3, MAY 2012

of models for attenuation by non-water-vapor gas phase speciesis beyond the scope of this study.

II. METHOD FOR DATA COLLECTION

A. High- Quasi-Optical Resonator System

We have conducted atmospheric attenuation measurements at400 GHz using a high- quasi-optical resonator system, whichwas originally designed for materials property measurements[20]–[24]. We have adapted the hardware setup by adding a her-metically sealed enclosure and water content measurement de-vices for the atmospheric attenuation experiments. The enclo-sure walls are comprised of acrylic glass and sealed with caulkand rubber seals. Molecular sieve desiccant is used to decreasethe amount of water content within the enclosure, while evapo-rated water is used to achieve higher water content levels whichare not climatically obtainable. By varying the amount of desic-cant sealed in the setup, the enclosure will reach a steady stateat different water content levels.

Two instruments were used to measure the water vapor con-centration. We used a data logger to record higher water vaporlevels ( 10% RH). The data logger measures both RH and tem-perature so that, along with pressure, the water vapor parts permillion (ppm) may be computed. According to our calibrationresults, the data logger has a worst case accuracy of 0.9% RHand 0.5 C for measurement of RH and temperature, respec-tively. A moisture analyzer is used to measure lower water vaporlevels ( 10% RH) and reports the data in ppm. The moistureanalyzer is accurate to 5% of the reported value. Both instru-ments sampled the environment every minute. Ambient pressurereadings were obtained, with a max error of 0.5 hPa, from anautomated instrument suite located on top of a nearby buildingthat continuously collects standard weather observations. Thesepressure readings were corrected for the 50 m height differ-ence between the weather station and the surface using coinci-dent temperature and relative humidity observations. The meanand standard deviation of the ambient pressure over the durationof the lab measurements was 983.31 4.85 hPa. Observed RH,temperature, and pressure values coinciding with the dates andtimes of the laboratory attenuation measurements are reportedin the Appendix.

This experimental setup operates at higher frequencies thanprevious resonator-based approaches for precisely measuringatmospheric attenuation [25], [26]. Using a resonator systemoffers the advantage of simulating long propagation distanceswhile allowing for more precise control of the experimental en-vironment. Fig. 1 shows a schematic of the hardware setup.

Custom software was created in order to establish and con-trol the necessary parameters for each experiment. This softwarecontrols the synthesizer, which provides a source for microwaveradiation ( 11 GHz). The microwave radiation is then deliv-ered to the amplifier multiplier chain (AMC) where the radia-tion is converted to THz regime radiation ( 400 GHz) throughharmonic mixing and amplification. The THz radiation beamis reshaped and directed into the resonator with a pair of fo-cusing mirrors and coupled into the cavity via a single couplingfilm. Radiation is returned out of the cavity and separated fromthe incident radiation by a pair of wire grids. The Golay Cell,in conjunction with the lock-in amplifier, samples the returnedTHz power and provides data to the software. The synthesizer’s

Fig. 1. A schematic representation of the high-� quasi-optical resonatorsystem. THz radiation is directed and coupled into the cavity (comprised ofthe spherical mirror, the coupling film, and the flat mirror) and the returnedradiation is sampled by the Golay Cell.

Fig. 2. Raw data collected by the Golay Cell for five different measurementsat different values of water content. The central frequency and amplitude of thepeaks increases as the water content is decreased.

output frequency, and accordingly the THz radiation, is incre-mentally varied over a specified frequency range, providing re-turned power data versus frequency.

B. Measurement of the Quality Factor

Raw data collected from five different measurements areshown in Fig. 2. Each measurement spanned a 54 MHz bandand was conducted at different water content levels as indicatedin the figure. An incremental frequency resolution of 0.18 MHz,giving 300 data points, was used to scan each peak in orderto achieve a balance between frequency resolution and scantime, which was about 34 min. While each scan spanned 54MHz, only data points within 7 half-width-at-half-maximum ofthe central frequency were used (typically 35–40 data points).Furthermore, the data points that were used in the curve fit werecollected in less than 5 min. A finer resolution giving moredata points can be achieved, but this increases the required scantime for each peak and allows for larger water content variationduring and between each scan. Additionally, a shorter totalscan time could have reduced time between scans; however, thecentral frequency of the peaks would drift out of the scannedrange more frequently.

The relationship between the output peaks and the watercontent levels reveals two expected results. First, the height ofthe peaks decreases as the water content level increases, which

WEBER et al.: ATMOSPHERIC ATTENUATION OF 400 GHz RADIATION DUE TO WATER VAPOR 357

implies an increase in absorption. Second, the center frequencyof the peaks move to higher frequency as the water level isdecreased indicating that the refractive index of the atmosphereis decreasing towards the value of vacuum. Quality factors

are determined from the raw data by fitting the data to theLorentzian function.

The maximum obtained was 5.21 10 at the very min-imum water content levels while the lowest quality factor wasapproximately 3.44 10 at the highest water levels. These num-bers show that the varies sensitively with the water contentlevel, and confirms that our cavity is sensitive enough to deter-mine losses due to water vapor attenuation.

The factor can be related to the atmospheric attenuationcoefficient by the following equations:

(1)

(2)

(3)

where is the attenuation coefficient, in Np/m, due to watercontent and is the average fractional power retained perwavelength (ignoring losses due to water vapor). (1) shows thedefinition of the quality factor while (3) is derived from (1) bysolving for . The term takes into account attenua-tion due to the conductivity of the mirrors, losses introduced bythe coupling film, diffractive losses, and losses due to dry aircomponents such as gaseous oxygen and nitrogen. By makinga reference measurement of , we may discern the powerlosses due to only the water content. This reference measure-ment is accomplished by measuring , the factor,while the enclosure is dried down to the lowest possible watercontent level.

III. ELECTROMAGNETIC LOSSES DUE TO WATER VAPOR

The results of the water content attenuation coefficient mea-surements at 400 GHz are shown in Fig. 3, in dB/km. These re-sults were obtained from averaging five measurements withapproximately the same water content levels. The averagewas then used to determine the average attenuation constant ateach RH, with the use of (2) and (3), and the determined atten-uation constants are plotted in Fig. 3. The x-axis of Fig. 3 isbased on the observed water vapor mixing ratios but, to ease in-terpretation, shown as an equivalent RH at a fixed temperatureof 22.777 C. Actual values of the atmospheric parameters andthe measured attenuation at each data point are included in theAppendix.

Errors in the measurement of translate into error in deter-mination of the attenuation constant. The main factors of errorin all measurements of include a changing resonator lengthdue to thermal expansion and contraction, variations in watercontent during individual scans and across averaged scans, lim-ited frequency resolution in data collection, and fluctuationsin power levels from the AMC. The power variation is due tochanging the frequency of the AMC before the device can reacha thermal equilibrium at a given frequency as well as changingtemperature in the enclosure.

Fig. 3. Comparison of MPM [7]–[10] and MonoRTM [15]–[17] predictions,with the measured attenuation data at 400 GHz. Thicker error bars representone standard deviation difference from the data point, and the thinner error barsare the absolute maximum deviation in measurement.

As shown in (3), the attenuation constant depends on twomeasured values: the measured at the given RH andwhich is a function of the at the driest conditions. Each atten-uation data point on the graph was achieved using the averagemeasured at each RH and the average value obtained fromthe average dry . Therefore, errors in measurement ofresult in error of determination of the attenuation constant at allRH values. Using (3), it can be shown, to the first order, thatsmall errors in and can affect the measurement of thewater attenuation coefficient by the following equation:

(4)

where and are small errors in and ,respectively. From (4), a 2% error in , with a typical of4.0 10 , introduces an 11% percent error in measurementof the attenuation constant while a worst-case 10% error inresults in 55% error in . Meanwhile, an error in of1.3 10 %, the worst-case measured deviation, correspondsto 4.5% error in measurement of .

The thicker error bars seen in Fig. 3 represent one standarddeviation away from the average value while the thinner errorbars represent the absolute minimum and maximum attenuationcoefficients measured. The thinner error bars take into accountthe maximum errors in measurement of at each water contentvalue and also the maximum error in measurement of .Furthermore, the maximum error bars were estimated using thesmallest measured at each RH point while also using thegreatest value. Conversely, the minimum error bars wereestablished using the largest measured at the RH point whileusing the smallest value.

While each of the mentioned factors for error in measurementof are present at all water content values, limited frequencyresolution and RH fluctuations during a scan introduce propor-tionally more error at the lowest water vapor levels. This ex-plains the larger error bars seen at low RH. As stated earlier,the frequency resolution was selected in order to provide a sub-stantial number of points to define a peak, while also tryingto minimize the amount of time per scan. Since peaks fittedat lower values of water content have a significantly smallerfull-width-at-half-maximum (FWHM) than peaks at high levelsof water vapor, there are less data points available to accurately

358 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 2, NO. 3, MAY 2012

characterize the resonance curves at low RH. Additionally, aswater content levels approach very low values of RH, smallchanges in absolute water content constitute larger changes inpercent change of water content. On average, the scans at thelowest water content values had higher percent changes in watervapor levels than the scans at the higher and intermediate waterlevels.

Also shown in Fig. 3 are water vapor attenuation predictionsobtained with four different MPM models and MonoRTM. TheMPM model predictions contain effects relating to water vaporline and “self-” and “foreign-broadened” continuum absorp-tion. As can be seen in Fig. 3, the Liebe [7], Rosenkranz [9],Rosenkranz [10], and MonoRTM [15]–[17] models producesimilar attenuation results throughout the entire range of rela-tive humidity values at the 400 GHz frequency considered inthis experiment. Additionally, the attenuation values calculatedby these models also consistently reside within the standarddeviation uncertainty range of the measurements, with only twonotable exceptions near 38% and 52% relative humidityvalues. Sensitivity analyses regarding the impact of uncer-tainties in temperature, pressure, and relative humidity wereperformed using MonoRTM and disturbances of 0.5 C, 5 hPa,and 0.9 RH, respectively. The maximum resulting uncertaintiesin attenuation were smaller than 1 dB/km. The similarity be-tween the agreeable MPM models is not completely surprisingsince the Rosenkranz models rely on the same basic frameworkas Liebe [7], with slight modifications to account for differencesin how each respective model characterizes various absorptioncomponents. Previous atmospheric remote sensing validationstudies of these MPM models at lower microwave frequen-cies (e.g., 20–160 GHz), have noted variable and statisticallysignificant frequency-, humidity-, and temperature-dependentdifferences between these models [14], [27], and [28]. Inour study, Liebe [7], Rosenkranz [9], Rosenkranz [10], andMonoRTM [15]–[17] are in excellent agreement with the data.In contrast, the Liebe [8] model produces attenuation valuesthat are consistently biased high compared to the measureddata and other MPM model attenuation values, especially atRH values exceeding about 20%. Hewison [14] states that [8]differs from [7] in its treatment of certain water vapor linesand in its characterization of temperature dependency of watervapor continuum absorption. Refer to [14] for a more detailedcomparison between the versions of MPM. The divergence ob-served with the Liebe [8] model continually grows and exceedsan order of magnitude at the very highest water content levels.This model is a distinct outlier compared to the other threeMPM versions and MonoRTM and seems ill-suited to accu-rately capture attenuation characteristics near 400 GHz, similarto previous MPM comparison studies between 150–160 GHz[14], [28].

IV. CONCLUSION

The results reported in this paper demonstrate that a hermeti-cally sealed, quasi-optical resonator system provides a compactand accurate method to measure atmospheric attenuation of ter-ahertz (THz) regime radiation. In particular, we have obtainednew measurements of the attenuation of 400 GHz radiation as afunction of water vapor concentration over a wide band of rela-tive humidity (RH) values ranging from less than 1% to roughly

TABLE IATMOSPHERIC PARAMETERS AND ATTENUATION VALUES

60% at 22.777 C and 983 hPa. Attenuation is a monotonicallyincreasing function of water vapor concentration, ranging from0.66 dB/km at 0.5% RH to 29.9 dB/km at 58.7% RH. Thedata agree with, and thus validate, three separate versions of theMillimeter Propagation Model (MPM) and MonoRTM: Liebein 1989 [7], Rosenkranz in 1998 [9], Rosenkranz in 2002 [10],and monoRTM v4.1 . A fourth version of the MPM, Liebe ’93,predicts attenuation rates significantly larger than the data orthe other three MPM versions. These results, therefore, confirmthe accuracy of applying appropriately selected versions of theMPM and MonoRTM for prediction of atmospheric attenuationof THz regime radiation.

APPENDIX

See Table I.

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[13] A. F. Krupnov, G. Y. Golubiatnikov, V. N. Markov, and D. A. Sergeev,“Pressure broadening of the rotational line of oxygen at 425 GHz,” J.Mol. Spect., vol. 215, no. 2, pp. 309–311, Oct. 2002.

[14] T. J. Hewison, “Aircraft validation of clear air absorption models atmillimeter wavelengths (89–183 GHz),” Journal of Geophysical Re-search, vol. 111, no. D14303, pp. 1–11, July 2006.

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Marcus J. Weber (M’10) received the B.S. degreein electrical engineering from the University of Wis-consin-Madison in 2012, and is currently working to-ward the M.S. degree from Stanford University, Stan-ford, CA.

In 2008, he was a software engineering internat GE Healthcare. He also participated in threecooperative education semesters at NASA JohnsonSpace Center from 2009 to 2011. Additionally, hehas worked as an undergraduate researcher since2010. His research interests are broad and include

next generation solid-state devices, high-frequency research and applications,and optoelectronics.

Mr. Weber received both the Stanford Graduate Fellowship and the NSFGraduate Research Fellowship. He is also a member of the Tau Beta Pi and hasreceived various undergraduate academic awards, including the Polygon Out-standing Senior Award.

Benjamin Bing-Yeh Yang (M’02) received the B.S.degree in electrical engineering and the B.S. degreein mathematics, both in 2005, and the M.S. degree inelectrical engineering in 2006 from the University ofUtah, and the Ph.D. degree in electrical engineeringin 2011 from the University of Wisconsin-Madison.

In 2002, he was a lab technician at the Universityof Utah’s HEDCO cleanroom facility. From 2003 to2005 he was an NSF IGERT fellow at the Universityof Utah. During his time at the University of Wis-consin-Madison, he held various teaching assistant

and research assistant positions. He also completed a summer internship at L-3Communications, Electron Devices in 2006. Since July of 2011, he has beenworking at Sandia National Laboratories in the Validation and Failure AnalysisDepartment. His past and current research interests include terahertz system en-gineering, nonlinear optics, microelectromechanical systems, and failure anal-ysis and reliability techniques for next-generation integrated circuits, photo-voltaic and power electronics technologies.

Dr. Yang is also a member of ASM International and the Electronic DeviceFailure Analysis Society. He is the recipient of the 2011 IEEE InternationalConference on Plasma Science best student paper award, the Gerald HoldridgeTeaching Excellence Award at the University of Wisconsin-Madison, and theEngineering Service Scholar Award at the University of Utah.

Mark S. Kulie received the B.S.E. degree in meteo-rology from the University of Michigan, Ann Arbor,in 1993, the M.S. degree in atmospheric sciencesfrom North Carolina State University in 1996, andthe Ph.D. degree in atmospheric and oceanic sciencesfrom the University of Wisconsin-Madison in 2010.

From 1997 to 2001, he was a scientist at the NASAGoddard Space Flight Center in Greenbelt, M.D. andworked on ground-based radar validation efforts forthe Tropical Rainfall Measuring Mission. From 2010to 2011, he was a Post-Doctoral Research Associate

at the University of Wisconsin-Madison Space Science and Engineering Center(SSEC). He is currently an Assistant Researcher at SSEC working primarily onmicrowave precipitation remote sensing using a combination of ground-based,airborne, and spaceborne instruments.

Ralf Bennartz received the Ph.D. degree in 1997from the Free University of Berlin and the M.S.degree in atmospheric physics from the Universityof Hamburg, in 1994.

Since 2002, he has been with the faculty of the At-mospheric and Oceanic Sciences Department at theUniversity of Wisconsin-Madison and principal in-vestigator at the University of Wisconsin’s Space Sci-ence and Engineering Center. His research interestsinclude satellite remote sensing and atmospheric ra-diative transfer in the near-infrared and microwave

spectral range.Prof. Bennartz is also past editor (2006–2010) of the American Meteorolog-

ical Society’s Journal of Applied Meteorology and Climatology.

360 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 2, NO. 3, MAY 2012

John H. Booske (S’82–M’85–SM’93–F’07)received the Ph.D. degree in nuclear engineeringfrom the University of Michigan, Ann Arbor, in1985.

From 1985 to 1989, he was a Research Scientistwith the University of Maryland, College Park,researching magnetically confined hot ion plasmasand sheet-electron-beam free electron lasers. Since1990, he has been with the faculty of the Departmentof Electrical and Computer Engineering, Universityof Wisconsin, Madison (UW), where he is currently

the Chair of the department, Director of the Wisconsin Collaboratory forEnhanced Learning (a learning space that supports IT-assisted, peer-collab-orative learning) and the Duane H. and Dorothy M. Bluemke Professor ofEngineering. From 2001 to 2005, he served as Director of the UW Interdisci-plinary Materials Science Program. His research interests include experimental

and theoretical study of coherent electromagnetic radiation, its sources and itsapplications, spanning the RF, microwave, millimeter-wave, and THz regimes.His recent research activities include vacuum electronics, microfabricationof millimeter-wave and THz regime sources and components, high-powermicrowaves, advanced cathodes, physics of the interaction of THz radiation andmaterials, microwave-generated plasma discharges and biological applicationsof electric and electromagnetic fields.

Prof. Booske was a coeditor of Microwave and Radio Frequency Applica-tions (American Ceramic Society, 2003) and Microwave and Millimeter-WavePower Electronics (IEEE/Wiley, 2005). He has been a Guest Editor of the IEEETRANSACTIONS ON PLASMA SCIENCE. He received the University of WisconsinVilas Associate Award for research and the U.S. National Science FoundationPresidential Young Investigator Award. He has received many teaching awards,including the UW Chancellor’s Distinguished Teaching Award. He is a Fellowof the American Physical Society.