This paper describes the procedures and algorithms for the laboratory calibration and field data retrieval of the NASA Langley/Ames Diode Laser Hygrometer as implemented during the NASA Transport and Chemical Evolution Over the Pacific (TRACE-P) mission during February–April 2000. The calibration is based on a National Institute of Standards and Technology traceable dew point hygrometer using relatively high humidity and short optical path length. Two near-infrared water vapor absorption lines of widely different strengths are used to increase the dynamic range of the instrument in the course of a flight. The laboratory results are incorporated into a numerical model of the second harmonic spectrum for each of the two spectral window regions using spectroscopic parameters from the HITRAN database and other sources, allowing water vapor retrieval at upper tropospheric and lower stratospheric temperatures and humidity levels. The data retrieval algorithm is simple, numerically stable, and accurate. A comparison with other water vapor instruments on board the NASA DC-8 and ER-2 aircraft is presented.
 Water plays an important role in the chemistry, dynamics, and radiation budget of the Earth's atmosphere. For the Transport and Chemical Evolution Over the Pacific (TRACE-P) mission, water vapor measurements are required to understand the HOx chemistry that controls the transformation and loss of many chemical constituents being studied. Understanding cloud processes and determining air parcel history also requires accurate water vapor measurements. In the troposphere, water exists in all three phases, so measurements of water most often must be able to distinguish the vapor phase from the liquid and solid phases. The NASA Langley/Ames Diode Laser Hygrometer (DLH) was designed and built to measure gas-phase water in the free-stream region of the NASA DC-8 aircraft, between the fuselage and the cowling of engine 1. The instrument is described in detail elsewhere [Diskin et al., 2002], so only a brief description will be given here.
 The DLH instrument is a near-infrared (NIR) spectrometer operating near 1.4 μ to detect individual rotation-vibration lines of H2O in either the (101) combination band or the (200) overtone band. Second harmonic detection [Sachse et al., 1977, 1987; Reid and Labrie, 1981; Podolske and Loewenstein, 1993, and references therein] and long path length are utilized to achieve high sensitivity, and two or more lines of different strengths are used to meet the dynamic range requirements for atmospheric water. The beam of a NIR diode laser is quasicollimated (divergence ∼10 mrad) and transmitted through a quartz window secured in a DC-8 window plate, toward the cowling of the left-side outboard engine. There it strikes a sheet of retroreflector material (3M Corporation Scotchlite Diamond Grade VIP reflective sheeting Series 3990) and returns to the fuselage window from which it originally emerged. Inside the window a portion of the return beam is passed through a narrowband interference filter, collected by a Fresnel lens, and focused onto a detector. The total path length outside of the aircraft is 2850 cm, with an estimated uncertainty of 13 cm (0.5%), considering both static and dynamic errors. The sample volume of this external path is completely exchanged every 40–70 ms, depending on aircraft velocity. The laser wavelength is sinusoidally modulated at 4 kHz, and the signal detector output is synchronously demodulated at 8 kHz and is recorded to produce the second harmonic signal. The DC component from the signal detector is also recorded to allow power normalizing of the second harmonic (2f) signal. The 2f and DC signals have matched 6-Hz bandwidths and are recorded at 20 samples s−1. The laser radiation that is emitted from the rear facet of the diode laser crystal is sent through a short (25 mm) reference cell containing pure water vapor and onto a second detector. The reference detector output is synchronously demodulated at 12 kHz (3f), the central zero crossing of which is subsequently used to lock the laser wavelength to the center of the chosen absorption line. During data flights an operator interacts with the control computer to select when to switch between the prominent (P) and weak (W) water lines and when to unlock the laser to perform a scan over the wavelength region around the line in order to acquire a second harmonic baseline. The computer control program systematically blocks the laser beam for brief intervals to measure detector DC zero and logs the time of all system activities. The instrument internal optical path of 20 cm is continuously purged with dry air, containing <2 ppmv of water.
 Given the long open path design of DLH, exposing the sampling volume to known standard air samples at pressures and mixing ratios typical of the upper troposphere and lower stratosphere is not feasible. Therefore the instrument is calibrated prior to and after each aircraft mission using two short cells (75 cm and 300 cm), constructed such that they could be operated over a range of 10–1013.25 hPa. Room air, whose humidity is adjusted and controlled, flows through the calibration cell in use for a given set of conditions. Using air with dew points in the range of −10°C to +10°C of 0.0028–0.012) provides the same absorption signal in the 75-cm cell as air with 75–320 ppmv in 2850 cm and in the 300-cm cell as air with 295–1260 ppmv in 2850 cm. Using the high mixing ratios in the short cells does require accounting for water self-broadening in modeling the second harmonic response in the calibration runs.
 The calibration cells are constructed of 15-cm inside diameter polyvinyl chloride pipe, with glass windows glued to the ends. The humidity- and pressure-controlled air flows in very near one end and out near the other end. The cells are 75 cm and 300 cm long to afford a range of path lengths and are of sufficient diameter to avoid reflective multipathing within the cell.
 To adapt the instrument for calibration, the laser transmitter is first demounted from the transceiver. Next the laser transmitter is mounted as close to the entrance window of the calibration cell as possible, and the sample beam detector is mounted as close to the exit window as possible. The small regions between the windows and the transmitter/detector are purged with dry nitrogen gas to avoid a spurious water absorption signal from outside the calibration cell.
 The gas handling system is shown in Figure 1. Room air is drawn through a temperature-controlled saturator to set the moisture content of the gas stream. The temperature bath is a Neslab Model NTE-110. The air is next sampled by a National Institute of Standards and Technology (NIST) traceable dew point hygrometer (EdgeTech Model 300) and then is passed through a pressure controller (Vacuum General 80-1). The EdgeTech accuracy, as stated by the manufacturer, is 0.2°C in dew point, corresponding to a mixing ratio accuracy of ∼1.5% in the dew point range used during calibration. This controller serves to drop the sample air from atmospheric pressure to the nominal operating pressure (100–800 hPa). Sample air then passes through the calibration cell, out through a mass flow controller (Alicat MC-12), and, finally, to a diaphragm pump. The ambient pressure and the cell pressure are measured with Barocell Model 1174 capacitance manometers. Room temperature is measured with an Omega Model DP116 resistance temperature device thermometer, and the cell temperature is measured with an Omega Model 660 Type T thermocouple thermometer.
 The purpose of the calibration runs is to determine the modulation amplitude of the sinusoidal laser wavelength modulation and the line strength of the P and W H2O lines. These two parameters will then be used in the numerical model of the second harmonic water spectrum to allow the retrieval of the water vapor mixing ratio from DLH flight data. The basic structure of the calibration data consists of two three-dimensional arrays (2f values and DC values) versus laser current modulation amplitude, pressure, and water vapor mixing ratio, acquired as follows. First, the saturator is adjusted to achieve a selected dew point (and hence water vapor volume mixing ratio) in the range of −10° to +10°C of 0.0028–0.012). Next the absorption cell pressure is set to a selected value in the range of 100–800 hPa. At a fixed water vapor volume mixing ratio and cell pressure (p) the modulation amplitude is adjusted over a fixed range of 24 settings of the modulation amplitude, and the 2f and DC signals are recorded. This is repeated for each of five cell pressure values and three dew point values. In addition to the room air runs described, a set of runs at 1013 hPa with dry nitrogen and the 24 modulation settings is made to measure the 2f “zero.” The detector DC “zero” is also measured by blocking the laser beam with thin metalized plastic foil beam stops. Finally, the 2f and DC values for all the room air runs are zero corrected and are used to calculate the normalized 2f (NTF = 2f/DC).
 Each data set (fixed and p, varying modulation) is fit to the functional form of Reid and Labrie  to retrieve two parameters: the tuning rate of the laser and laser driver combination (TR) (cm−1/mV input) and the line strength scaling (SS); see Appendix A for more detail. The line strengths given by Toth  tend to be smaller than the values in HITRAN 86 and HITRAN 96 [Rothman et al., 1998] by ∼10–30% and are in better agreement with our measurements. The best fits to the calibration data were found by starting with the line strength values of Toth  (SToth) and scaling them up from 0 to 5%. Figure 2 shows the data for 3 pressures and 20 modulation values at constant along with the fit for the 400.9-hPa data set. The shape of the fit curve in Figure 2 is determined by the ratio of the sinusoidal laser frequency modulation (“mV modulation amplitude” × TR parameter) to the absorption line width (combined Lorentz and Doppler broadening). The peak height of the curve is determined primarily by the scaled line strength (SS × SToth) as well as by the absorption line width.
 The analyzed results of these calibration experiments (TR and SS for each pressure/dew point pair considered) were used to give a mean tuning rate and line strength for both the P and W lines and an estimate of the uncertainties of these parameters. The best fit tuning rate was 8.845E-4 cm−1/mV with a 1σ standard deviation of 0.7% for the P line and 8.894E-4 cm−1/mV with a standard deviation of 1.3% for the W line. The best fit line strengths were determined to be 1.043 times the Toth value for the P line with a standard deviation of 2.8% and 1.005 times the Toth value for the W line with a standard deviation of 3.9%. The parameters from these calibration runs were then used to select a single modulation amplitude that was a suitable compromise for the range of pressures expected in flight. The strategy is to pick a modulation amplitude that slightly overmodulates at low pressure and slightly undermodulates at high pressure compared to the optimum but will still be within ∼25% of the optimum response. With a modulation amplitude chosen, the parameters of the retrieval algorithm were determined.
3. Retrieval Algorithm
 The DLH instrument provides a data stream of its basic instrument outputs (2f, DC, laser current) at a 20-Hz sampling rate as well as an auxiliary data stream of instrument mode and laser status. Included in the DLH data stream are the static temperature (T) and static pressure (p), which are continuously provided to DLH in real time at 1 Hz by the DC-8 data system (either the DC-8 Air Data System or the Information Collection and Transmission System).
 The retrieval of the water vapor volume mixing ratio from DLH data requires several spectral parameters: line strength (S), Doppler width (γD), and pressure-broadened width (γL). All three are functions of temperature, and γL is also a function of pressure. For S we start with the values from Toth  at 296 K, scale them with a factor determined during calibration, and then correct for temperature using the lower-state energy E″ from HITRAN 96 and the partition function approximation Q(T) given by HITRAN 96. The Doppler width is calculated using the standard formula [Demtroder, 1982]. γL0 is taken from HITRAN 96, as is the temperature exponent n. γL is then calculated as
With these parameters, plus the absorption path length and the laser modulation amplitude (a), both the DC and 2f values can be calculated for any value of p, T, and expected during flight operations. The spectral regions around both the W and P lines contain other H2O lines, so in order to account for these, an entire 1.5-cm−1 region, including five separate lines, is calculated. Figure 3 shows the calculated direct transmission and normalized 2f signals for the W line for a temperature of 229 K and a pressure of 304 hPa (9.1 km conditions), with an of 500 ppmv, a path length of 2850 cm, and a modulation amplitude of 0.11 cm−1. Figure 4 shows the same quantities for the P line region, calculated using the same conditions as for Figure 3. The normalized 2f (NTF) value at line center is determined from these spectra and is saved for subsequent parameterization.
 The retrieval algorithm splits the data into four separate regions: 0–1000 ppmv for the P line (P2), 1000–5000 ppmv for the P line (P4), 0–10,000 ppmv for the W line (W2), and 10,000–50,000 ppmv for the W line (W4). For each region a three-dimensional array of normalized second harmonic values (NTF) is calculated. The pressure ranged over 101.3–1013 hPa in increments of 50.7 hPa, the temperature ranged from 200 to 300 K in increments of 5 K, and 21 values of spanning the appropriate range were used. For the standard humidity ranges (P2 and W2) the best simple approximation found was
For each (p,T) pair the best value for B and C were determined via multilinear least squares fitting. The set of coefficients B(p,T) and C(p,T) were then approximated to allow interpolation to other p and T values by
where T′ = (T − 250). C(p,T) is treated similarly to B(p,T). Finally, the pressure dependence is modeled as
for m = 0–3. C, again, is treated similarly. The resulting set of 42 coefficients can then be used to calculate B(p,T) and C(p,T) for any pressure and temperature encountered in flight. This quadratic form requires inversion to retrieve from NTF, B(p,T), and C(p,T):
where the discriminant D is defined as
 After the first field mission with DLH it was discovered that an ability to retrieve water vapor mixing ratios at higher mixing ratios than originally expected was required. The P4 and W4 algorithm uses the approximation:
With this form, no inversion is required. However, NTF must be checked to ensure that it does not exceed the maximum value for which the quartic expansion is valid. As with the P2 and W2 algorithms, the four coefficients E, F, G, and H are first fit to third-order polynomials in T′. However, for the pressure approximation, seventh-order polynomials rather than sixth-order are used. The order of the pressure polynomials was chosen to give the smallest residuals while keeping the order reasonable. More terms did not significantly improve the fits. These four algorithms (P2, W2, P4, W4) return water vapor mixing ratios which are always within 3% of the original values used to calculate the algorithm coefficients for all pressures, temperatures, and water vapor mixing ratios used and typically agree to better than 1% in RMS.
4. Data Reduction
 The reduction of flight data proceeds in several stages. Each raw data set is first visually scanned by an analyst using the data analysis package Igor Pro (Wavemetrics, Incorporated), and sections are marked as either valid water vapor data, detector zero data, laser scan data, or invalid data. The detector DC zero sections, which occur for 5 s every 15 min, are then processed, and cubic spline interpolation is used to generate an effective DC offset array for the entire flight.
 Next the second harmonic scans are analyzed. Several times per flight, the laser frequency is unlocked from the absorption line and scanned across the spectral region from well before the absorption lines until well after. A linear least squares fit is then applied to the 2f baseline, with the absorption region excluded. In Figure 5 a typical 2f and DC flight spectrum is shown, along with the baseline regions used in the fit marked and the baseline fit line. The fit value at the absorption line center is then taken as the 2f zero value. Because the scans are infrequent and alternate between the P and W lines, only average P and W offset values are determined for subsequent analysis.
 Following offset determination, both the DC and 2f data arrays are offset-corrected and scaled for their respective lock-in amplifier gain. Next the DC values are screened for values below a selected cutoff value and are marked as invalid if too small. This cutoff value is chosen somewhat empirically to account for errors in determining the DC offset or possible laser-mode impurities. The cutoff value is determined by making a conservative estimate of the uncertainty in the DC offset determination and by setting the cutoff such that the offset uncertainty is 5% of the cutoff value. Then the normalized second harmonic array is generated, with invalid data marked as required.
 The final reduction step applies the appropriate retrieval algorithms. For each section of data where the P line was in use, both the P2 and P4 algorithms are applied. For each data point, if the P2 discriminant (D) is >0 and the retrieved is within the valid range for P2, this value is selected as the correct one. If not, the P4 value is checked for the condition that it is within the valid range for P4 and for the condition that NTF is less than or equal to the maximum NTF value for that pressure and temperature for which the P4 coefficients were calculated. If the P4 value passes both tests, it is selected as the correct value. If neither the P2 nor P4 algorithm returns a valid result, a “no value” marker is put in the data stream. For the sections of data where the W line is in use the same procedure as for the P line is used but using the W2 or W4 coefficients. Finally, the high-mixing-ratio portions of the data > 0.005) are compared with the two-stage frost point hygrometer data to confirm that the DC cutoff value chosen earlier is working effectively at removing potential artifacts due to uncertainty in the DC offset value or in the slight laser-mode impurity. The final data stream is then averaged using a 1-s running mean and is output in a project-specified text format at a rate of 1 sample s−1 for submission to the project data archive. The original 20 sample s−1 data stream is also made available to individual project investigators interested in fine temporal-scale and spatial-scale variations in water vapor.
5. Instrument Intercomparison
 To illustrate the performance of DLH under relatively dry conditions, an intercomparison with four other water vapor instruments is shown in Figure 6. The data were taken on 23 January 2000 during the NASA Stratospheric Aerosol and Gas (SAGE) III Ozone Loss and Validation Experiment (SOLVE) mission out of Kiruna, Sweden. The DC-8 flew a level leg at a pressure altitude of 11.3 km (Figure 6 (top)), and the ER-2 descended to a pressure altitude of ∼11.2 km to rendezvous with the DC-8. The aircraft did not fly in close proximity throughout the intercomparison. Rather, the aircraft were separated somewhat in time and space but flew the same flight track, at a heading of 9.3°. In addition, the winds at this altitude were 35.2 m s−1 (±10%) at 359.9°. The water data were therefore plotted versus aircraft latitude as the flight track was nearly north-south in orientation. Horizontal advection is accounted for by using different axes for the DC-8 and ER-2 aircraft. Assuming the wind velocity is constant, we calculate that the air parcel that the ER-2 sampled at a latitude of 64.351° (the beginning of Figure 6) was sampled by the DC-8 at a latitude of 64.380° 89 s earlier. Similarly, the air parcel that the ER-2 sampled at a latitude of 66.841° just before it descended (the end of Figure 6) was sampled by the DC-8 at a latitude of 67.028° 593 s earlier. Owing to a slight cross-track component of the wind and its variation during the intercomparison leg, it is expected that the sampling coherence of the two aircraft will decrease throughout the track.
 The uppermost trace is that of the Jet Propulsion Laboratory (JPL) laser hygrometer on the DC-8 (JLH DC-8). This is an open-path NIR laser spectrometer, which uses a short optical path (50 cm total path length) near the fuselage. The next trace down is the JPL laser hygrometer on the ER-2 (JLH ER-2) [May, 1998], which uses a multipass Herriott cell (1120 cm total path length) for greater sensitivity to stratospheric water mixing ratios. The middle trace is the DLH instrument [Diskin et al., 2002] described in section 1. There is a gap in the DLH data between latitudes 65.7° and 66.4°, when the operator was conducting preplanned scans of the laser current. The trace below that is the Harvard Lyman α hygrometer (HW) [Weinstock et. al., 1994; Hintsa et al., 1999]. The lowermost trace is the NASA Langley cryogenic dew point hygrometer (CD) [Vay et al., 1998; Busen and Buck, 1993, 1995]. This instrument is meant for use in the lower to middle troposphere and is near its limit of performance under the condition of this intercomparison. All data sets are plotted at the highest time resolutions available from the SOLVE project archive: These time resolutions are 1, 1.28, 1.55, and 4 s point−1 for DLH and CD, JLH ER-2, JLH DC-8, and HW, respectively, and appear to be sufficient to capture all the atmospheric variation of water encountered.
 Several features of Figure 6 are worth pointing out. For most of the intercomparison the ER-2 was flying ∼100 m below the DC-8. If there was a strong vertical gradient in water, this would affect our ability to compare the data from the two aircraft. Fortunately, at the very beginning of the track the ER-2 sampled the altitude range from 11.2 to 11.3 km as it settled in, giving some indication of the bound on this gradient. Also, the features in the ER-2 water measurements around 66.3° DC-8 latitude do not exactly match up with the corresponding feature in JLH DC-8, indicating the limits of our ability to compensate for the temporal separation of the two aircraft.
Figure 6 demonstrates the high sensitivity of the DLH instrument and the level of agreement of the retrieved water vapor volume mixing ratios with a suite of other water vapor instruments. DLH seems to compare well with the JLH ER-2 and the HW for at least the first half of the intercomparison period. In the later portion the agreement is fair, due, at least in part, to the imperfect temporal and spatial matching of the aircraft. The JLH DC-8 and DLH seem to track each other well but have a fairly constant offset between them of 2.0 ppmv throughout the intercomparison region. The source of this offset is currently being investigated by both instrument groups. An error analysis for DLH during this flight period, combining uncertainties in line strength (2.8%), 2f offset correction (2.3%), pressure (0.4%), and temperature (0.6%) gives a 1σ error estimate of 3.7%. A conservative 2σ error bar for the DLH data shown in Figure 6 would be ±0.75 ppmv, which spans all of the JPL ER-2 and Harvard ER-2 data during the first portion of the intercomparison.
 The DLH instrument provided high-quality water vapor volume mixing ratio data at both 1-Hz and 20-Hz rates from the NASA DC-8 over 0-12 km altitude during the TRACE-P campaign. Using well-characterized NIR absorption lines near 1.4 μ, the instrument is calibrated in the laboratory using a NIST traceable dew point hygrometer at dew points above and below 0°C. The algorithms to reduce the DLH data have been explained, and a comparison with other water instruments on both the DC-8 and ER-2 during the SOLVE campaign under dry conditions has been presented. Work is currently underway to improve the accuracy of the instrument in anticipation of future Global Tropospheric Experiment (GTE) projects.
 The response of a second harmonic laser spectrometer to an isolated Voigt profile absorption line is presented by Reid and Labrie . Here we expand on their results to include finite absorption conditions and the equation for the DC signal amplitude (H0V) as well as for the 2f signal amplitude (H2V). The equations are
where ν is the laser frequency, ν0 is the center frequency of the absorption line, a is the amplitude of the sinusoidal laser frequency modulation, I0(ν) is the laser intensity before passing through the absorbing medium as a function of laser frequency, γD is the Doppler half width at half maximum (HWHM), and γL is the Lorentz HWHM, to account for pressure broadening. The absorption of the Voigt profile line is
where S is the line strength, N is the absorber number density, and L is the absorption path length. The Voigt line-shape function (K(x,y)) is given by
 The laser frequency modulation (a) is the product of the tuning rate (TR) and the modulation drive voltage used in flight (125.5 mV):
The line strength used is the product of the line strength of Toth  and the strength scaling factor determined from the calibration runs:
where the temperature dependence of the Toth strength is derived from a combination of the partition function parameterization and the lower-state energy for the given transition from HITRAN 96.
 The authors wish to thank Thomas Slate of Swales Aerospace for his invaluable contribution to this work. Also, George Tucker of The Sage Colleges provided keen insight and operational support during several measurement missions. This work was supported by the GTE program of NASA headquarters.