# Temperature dependence of water vapor absorption coefficients for CO_2 differential absorption lidars

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<ul><li><p>Temperature dependence of water vaporabsorption coefficients for CO2 differentialabsorption lidars</p><p>Avishai Ben-David</p><p>A temperature correction of water vapor differential absorption coefficients for the C02 transition linepairs (1OR20, 1OR 18) and (10R20, 1OR22) for temperatures between -0.5 0C and 20 C is computed, witha reference temperature of 27 0C, from medium-range C02 lidar field measurements. The empiricaltemperature correction, X(T), is fitted with the polynomial X(T) = ao + a, x T + a2 x T2. For thetransition line pair (10R20, 1OR 18) the temperature dependence ranges from 1.62%/C to 3.47%/C, andthe temperature correction for the transition line pair (10R20, 10R22) ranges from 1.32%/'C to2.43%/ 0 C.</p><p>Key words: C02 lidar, differential absorption, water vapor, differential absorption lidar.</p><p>IntroductionWater vapor concentrations are routinely measuredin the atmosphere with differential absorption lidarsin the CO2 laser transition lines (9-11 ,um). In thistechnique' the laser is tuned to two wavelengths.The first wavelength is chosen such that it will beheavily absorbed by the water vapor. The secondwavelength is chosen to be outside the absorptionband and serves as a reference measurement tocalibrate the reflectivity of a target (or aerosols whenused as a diffused target) that is the source of themeasured backscattered lidar signal. The two laserwavelengths are chosen to be spaced as closely aspossible so that the only difference between the twomeasurements will be the effect of water vapor absorp-tion. The CO2 transition line 1OR20 (10.247 jim)exhibits the strongest absorption coefficient in the 9-to 11-jim wavelength range and thus is the preferredchoice for the first wavelength. The second wave-length is commonly chosen to be the transition line1OR18 (10.260 jim) or the transition line 1OR22(10.233 jm), for low-to-moderate water vapor concen-trations over reasonably short paths.</p><p>In a recent critical review paper on water vaporabsorption coefficients in the infrared, Grant2 pointedout that although there are plenty of data on the</p><p>The author is with the Science and Technology Corporation,2719 Pulaski Highway, Unit 1, Edgewood, Maryland 21040.</p><p>Received 1 April 1993.0003-6935/93/367479-05$06.00/0. 1993 Optical Society of America.</p><p>absorption coefficients at temperatures between 20 0Cand 27 0C, few reliable data exist on the temperaturedependence of water vapor absorption coefficients fortemperatures </p></li><li><p>from the lidar. The lidar beam divergence is 3.2mrad, the receiver's aperture is 25.4 cm with a4-mrad field of view, the receiver's electronic band-width is 5 MHz, and the acquisition sampling rate is50 MHz with a 10-bit resolution. Results of a totalof 100 trials at different temperature conditions wereaccumulated from a field test conducted at DugwayProving Ground, Utah, during October 1992. Allthe trials were conducted under a clear sky with thesame hard target and over the same path length overa dry desert terrain with very low and sparse vegeta-tion. Simultaneous dry- and wet-bulb temperatureswere measured with a psychrometer a few metersaway from the lidar location and at a height of 1.5 mabove the ground (approximately the height of thelaser beam). The error in the psychrometer measure-ments is estimated to be less than 0.2 0C, for whichthe error in the water vapor partial pressure is lessthan 3%. It should be noted that the lidar measure-ments are path-integrated data, whereas the psy-chrometer data are local measurements.</p><p>Figures 1 and 2 present the percentage differencebetween the water vapor partial pressure, PM, com-puted from the dry- and wet-bulb temperatures mea-sured with a psychrometer and the water vaporpartial pressure, PL, computed from the lidar measure-ments for the (R20, lOR18) and the (R20,1OR22) pairs for all 100 trials. The asterisks inthese figures denote the psychrometer-measured datapoints. Contours far from the data points resultfrom extrapolation and are therefore unreliable.It is shown in the figures that the water vapor ascomputed from the psychrometer measurements, PM,is always higher than the lidar water vapor measure-ments, PL, and the difference increases as the tempera-ture decreases. In these figures the water vaporabsorption coefficients for the transition lines OR 18,10R20, and 1OR22 are the average values2 7.127 x</p><p>4.7 5.7 6.7 7.7 8.7 9.7 10.719.5 - 19.517.5 3c ZZ'17.515-55 >F 6 15.5</p><p>( 13.5 32 \ 13.50)11.5 D 11.5</p><p>. 5 955</p><p>E48a) 5.5 40B 5.5</p><p>3.55</p><p>1.5 1.5</p><p>~4.7 5.7 6.7 7.7 8.7 9.7 10.7 05Woter Vapor (mbors)</p><p>Fig. 1. Percentage difference (PM/PL - 1) between water vaporpartial pressure, PM, measured by a psychrometer and water vaporpartial pressure, PL, computed from the lidar measurements withlaser transition line pair (lOR 20, lOR 18) as a function of dry-bulbtemperature and the psychrometer water vapor partial pressuremeasurements. Asterisks denote the psychrometer measure-ments.</p><p>19.517.5</p><p>15.50 13.5</p><p>0D 11.5, 9.5aa 7.5E0) 5.5</p><p>35</p><p>10.5.4</p><p>19.517.515.513.511.59.57.55.53.51.5-0.5</p><p>Fig. 2. Percentage difference between PM and PL as in Fig. 1 butfor lidar measurements with the laser transition line pair (10R20,1OR22).</p><p>10-6, 8.477 x 10-5, and 1.012 x 10-5 (mbars-1 m'1),respectively, at a temperature To of 27 0C and at awater vapor partial pressure of 10 Torr. Theseabsorption coefficients, a( To), are taken as referencevalues at the reference temperature To throughoutthis study. The water vapor partial pressure, PL,computed from the lidar measurements is given by</p><p>In [Sx(T1P (T) [ ~ Sxl(T)1 (1)P() 2R[ax,( T0) - ax,( T0)]' 1</p><p>where R is the range to the target, S(T) is themeasured reflected signal at a dry-bulb temperatureT, and (j, 2) are the wavelengths of the transitionline pair (1OR 20, lOR 18) or the pair (10R20, 1OR22).It is assumed in Eq. (1) that the absorption coeffi-cients, a, are linearly dependent on water vaporpartial pressure. Measurements by several au-thors3,46,7 show that the absorption coefficient isalmost linearly dependent on water vapor partialpressure for the transition line 1OR20 and has linearand quadratic dependence37 on water vapor partialpressure for the transition lines 1OR22 and lOR 18.</p><p>The standard deviation of the lidar return signalswas computed to be less than 3% for all the differenttrials. The high quality of the measurements can beseen in Fig. 3, which gives the autocorrelation of thepsychrometer measurements (dotted curves) and thecross-correlation between the water vapor computedfrom the lidar measurements with the pair (lOR20,lOR 18) and the meteorological data measured by thepsychrometer (solid curve). One-hundred data pointsmeasured at different times throughout the experi-ment were used in computing the correlation curves.In Fig. 3 the time-interval displacement representsthe displacement of the number of data points. Themaximum value of the cross-correlation is 0.9967.The cross-correlation for the pair (10R20, 1OR22)and the psychrometer measurements reaches a maxi-mum value of 0.9968 and is almost identical (not</p><p>7480 APPLIED OPTICS / Vol. 32, No. 36 / 20 December 1993</p><p>I</p></li><li><p>1.0</p><p>0.8</p><p>C._</p><p>.'</p><p>0U</p><p>0.6</p><p>0.4</p><p>0.2-</p><p>0.0 .-100 -75 -50 -25 0 25 50 75 100</p><p>Time-Interval DisplacementFig. 3. Autocorrelation of water vapor partial pressure measuredby the psychrometer (dotted curve) and cross-correlation betweenwater vapor partial pressure computed from the lidar measure-ments with the transition line pair (10R20, 1OR18) and thepsychrometer measurements (solid curve).</p><p>shown) with the cross-correlation of the pair (10R20,lOR18) with the psychrometer measurements. Fig-ure 3 shows that the cross-correlation curve is almostidentical with the autocorrelation curve of the psy-chrometer measurements, and thus it shows that thepath-integrated lidar measurements are closely re-lated to the local psychrometer measurements.</p><p>Analysis and DiscussionLaboratory measurements 3 48 show a positive tem-perature dependence of the water vapor absorptioncoefficient for transition line 1OR20 (i.e., the absorp-tion coefficient increases with increased tempera-ture), whereas for most other weak CO2 transitionlines, including lines 1OR22 and lOR 18, the tempera-ture dependence is negative (i.e., the absorption coef-ficient decreases with increased temperature). Apositive temperature dependence for other transitionlines, 1OR40, 9P38, 9R36, was also observed byHinderling et al.46 The positive temperature depen-dence of transition line 1OR20 is thought to originatefrom the coincidence of line 1OR20 with a weakrotational transition.3 9 Hinderling et al." modeledthe positive temperature dependence of transitionline 1OR20 with a pure rotational model, where themain parameters are the energy of the lower rota-tional state and the rotational partition function, andstated that because the absorption is almost linearlydependent on water vapor pressure it is unlikely thatself-broadening effects in near-line center regions aresignificant. The data of Hinderling et al." on thenegative temperature dependence indicate that atleast two molecules are involved in the absorptionprocess of the continuum and that the absorption isbest modeled by simultaneous contribution of waterdimers and a collisional broadening mechanism (i.e., adominant quadratic pressure dependence). It shouldbe noted that in his review paper Grant2 indicated thepossibility of contamination by impurities at 27 C inthe data given by Loper et al. 3 and some inconsistency</p><p>im the continuum absorption temperature depen-dence in the data of Hiderling et al.4</p><p>As shown in Figs. 1 and 2, the partial pressure ofthe water vapor computed from the lidar measure-ments for temperatures < 20 C with the absorptioncoefficients at To is always lower than the water vaporpartial pressure measured by the psychrometer.This suggests that the value of the differential absorp-tion coefficients used in Eq. (1) should be decreasedand thus is given by</p><p>ax1 (T) - x 2(T) = [ax1 (To) - CA2(To)]x [1 + X(T) (T - TO)], (2)</p><p>where the empirical temperature correction, X(T),for the wavelength pair (,, X2) is given by</p><p>PL(T)X(T)= T-T 0 (3)</p><p>Figures 4 and 5 show the empirical temperaturecorrection, X(T), of the differential absorption coeffi-cients for wavelength pairs (lOR20, lOR 18) and(10R20, 1OR22), respectively. In these figures aleast-squares curve fit (solid curve) in the formX(T)[1/ 0C] = ao + alT + a 2T2 (T in C) was used to fitthe data points (circles). The curve-fit coefficients(ao, al, a2) are (1.64 x 10-2, -4.33 x 10-4, 6.76 x10-5) and (1.32 x 10-2, -4.09 x 10-5, 2.98 x 10-5) forthe wavelength pairs (10R20, lOR18) and (10R20,1OR22), respectively.</p><p>For an error e of 3% in lidar measurements S(T),the uncertainty, AX(T), inX(T) is estimated by</p><p>AX(T) =(ln~ 1 + E)XT)=PM(T)2R[uax,(T) - ax,(T)](T - TO) (4)</p><p>The normalized uncertainty, AX(T)/X(T), in comput-ing X(T) is shown in Figs. 4 and 5 (dotted curves).The temperature coefficients X(T), for T = 10 C and10 Torr water vapor partial pressure and for T = 0 C</p><p>x</p><p>3</p><p>2</p><p>13</p><p>12</p><p>1 1</p><p>10 X.x</p><p>8</p><p>70 5 10 15 20</p><p>Temperature (C)Fig. 4. Empirical temperature correction X(T) of the differentialabsorption coefficients for the transition line pair (10R20, lOR18)as a function of dry-bulb temperature.</p><p>20 December 1993 / Vol. 32, No. 36 / APPLIED OPTICS 7481</p><p>(3)</p></li><li><p>3.5</p><p>a</p><p>xcX</p><p>2.5</p><p>1.5</p><p>0.5</p><p>19</p><p>17</p><p>15 </p><p>13 x</p><p>11</p><p>90 5 10 15 20</p><p>Temperature (C)Fig. 5. Empirical temperature correction as in Fig. 4 but for thetransition line pair (1OR20, 1OR22).</p><p>and 3.2 Torr water vapor partial pressure werecomputed from Loper et al.,3 using their absorptioncoefficient measurements and their empirical correc-tion for the pressure dependence of the absorptioncoefficients for these temperature values. Their tem-perature coefficients are noted by the triangle in Figs.4 and 5. The pressure values 10 Torr and 3.2 Torrfor T = 0 C and 10 C, respectively, are close to thepsychrometer measurements of Figs. 1 and 2.</p><p>The temperature correction, X(T), at a tempera-ture within a few degrees of 27 C is given by Grant etal.10 as 2.1%/C for the transition lines (10R20,lOR18). The results presented here (Fig. 4) showthe temperature correction to be approximately3.5%/C at 20 0C. It should be noted that the tem-perature correction X(T) [1/C] computed from thelidar and psychrometer measurements [Eq. (3)] maybe biased higher than the true temperature correc-tion X(T) as T approaches To, for which the denomi-nator approaches zero, while the numerator, becauseof error in measurements, is never equal to zero.However, the total temperature correction X(T) x(TO - T) decreases with increasing temperature, as isshown in Fig. 6, where the empirical least-squaresquadratic fits for the transition line pairs (lOR20,lOR 18), shown by the solid curve and (lOR20, 1OR22),shown by the dashed curve, are used.</p><p>50</p><p>E-4x</p><p>EH</p><p>x</p><p>P</p><p>40</p><p>30</p><p>20</p><p>10</p><p>Table 1. Temperature Correction of Water Vapor AbsorptionCoefficient Measurements</p><p>TemperatureCorrection Water Vapor</p><p>(%/IC) PartialTransition Pressure</p><p>Source Line 10 C 0 C (Torr)Hinderling 1OR20 1.89 1.73 6.07-15.26</p><p>et al.aLoper et al.b 1OR20 1.41 1.19 3.2</p><p>1.12 101OR22 -1.2 -2.19 3.2</p><p>-2.3 10lOR 18 -1.0 -1.62 3.2</p><p>-2.39 10</p><p>aRef. 4.bRef. 3.</p><p>The temperature corrections for the transitionlines 1OR22, 1OR20, and 1OR18 are computed fromthe measurements of Loper et al.3 and Hinderling etal.4 and are given in Table 1. Loper et al. 3 give anempirical pressure correction to the absorption coeffi-cients for only 10 C and 27 0C and give absorptioncoefficient measurements only at 3.2 Torr for 0 C.Thus the temperature correction is computed fromLoper et al.3 for 3.2 Torr only for 0 C. In this paperthe temperature corrections for the differential ab-sorption coefficients for the transition line pairs(1OR20, lOR18) and 1OR20, 1OR22) were measured.It is shown in Figs. 4 and 5 that there is reasonablygood agreement between the present measurementsand those of Loper et al.3 More laboratory experi-ments at a wide variety of water vapor partial pres-sures and temperatures are needed to determine thequadratic pressure dependence of absorption coeffi-cients for transition lines 1OR22 and OR18 as afunction of temperature and thus to improve theaccuracy of the temperature correction, X(T), for asingle transition line and for the differential absorp-tion coefficients that can be measured with a lidar.</p><p>This work was suDDorted by the U.S. Army Edge-wood Research, Development, and Engineering Cen-ter (ERDEC), Aberdeen Proving Ground, Maryland,under Grant DAAA15-93-D-0001. The author</p><p>(lOR20-10R18) thanks David Cohn, John Becker, Louis Klaras, and---- (lOR20-lOR22) Hans Marciniak of the Passive and Laser Sensor</p><p>Laboratory at Hughes Aircraft Company, El Se-gundo, California, for designing and building the lidarsystem and is especially grateful to David Cohn andJohn Becker for their help in the field test. Thecontributions of Cynthia Swim of ERDEC and of Jay</p><p>*. Fox of the U.S. Army Night Vision and Electro-OpticsDirectorate, Fort Belvoir, Virginia, to the design of</p><p>5.... I.... . . the lidar system are greatly appreciated.5 10 1...</p></li></ul>