Column closure studies are a tool to assess whether in situ and remote measurements of aerosol optical properties on a given aircraft are mutually consistent. In this paper we describe aerosol and water vapor column closure studies on the basis of instrumentation flown aboard the NCAR C-130 aircraft in the ACE-Asia field experiment in March–May 2001. For in situ observations, aerosol particles were sampled through a newly designed low-turbulence inlet (LTI). In 28 profiles extending to altitudes of up to 8 km, the in situ observations of scattering and absorption were compared to measurements with the six-channel NASA Ames Airborne Tracking Sun photometer (AATS-6). The comparison of Sun photometer and in situ-derived layer aerosol optical depth (AOD) at 550 nm showed agreement (closure) within the measurement uncertainties in 25 out of 28 case studies. The average difference in layer AOD derived from the two methods was 0.03, corresponding to an average difference of 11.5%. The uncertainties in AATS-6-derived layer AOD ranged between 5 and 59% (with a mean of 22%), and for the first time included an estimate for the uncertainty in layer AOD caused by possible horizontal variability in AOD encountered in the vertical profile. The average uncertainty in AATS-6-derived layer AOD due to possible horizontal variability alone was 19%. The uncertainties in in situ-derived layer AOD were between 10 and 55% (with a mean of 19%). Stratification of the extinction closure data by ambient relative humidity (RH) revealed that in situ-derived aerosol extinction at low ambient relative humidity (<20% RH) tended to be slightly less than Sun photometer-derived aerosol extinction, while in situ-derived aerosol extinction at higher relative humidity was slightly greater than the Sun photometer-derived values. Stratification of the extinction closure data by the fine mode fraction of scattering indicated a modest enhancement of coarse mode extinction in the combined LTI/plumbing system. Analogous closure studies for layer water vapor and water vapor density showed that AATS-6 measured these quantities with very high accuracy, with correlation coefficients of 0.989 and 0.955 (rms differences of 10% and 33%), respectively.
 The spring 2001 phase of the Asian Pacific Regional Aerosol Characterization Experiment (ACE-Asia), studied aerosol outflow from the Asian continent to the Pacific basin. It was designed to integrate suborbital and satellite measurements and models so as to reduce the uncertainty in calculations of the climate forcing due to aerosols [Huebert et al., 2002]. ACE-Asia included various aircraft, ground-based and ship-based observations in close coordination with satellite overpasses. The close coordination of measurements on the various platforms was intended to yield important insights into the spatial and temporal variability of Asian aerosols as they are transported into the Pacific Basin troposphere. In particular, the vertical distribution of aerosols and hence the vertical distribution of their climatic impact needs to be determined in order to assess aerosol climate interactions [Hansen et al., 1997; Ramanathan et al., 2001].
 To assess whether or not the instrumentation aboard the various participating aircraft measured an adequate representation of the ambient aerosol, extinction and optical depth closure studies need to be carried out. Previous closure studies have advanced our understanding of in situ aerosol measurement methods in field experiments, such as the Tropospheric Aerosol Radiative Forcing Observational Experiment, TARFOX [Hegg et al., 1997; Hartley et al., 2000], the 2nd Aerosol Characterization Experiment, ACE-2 [Collins et al., 2000, Schmid et al., 2000], the Indian Ocean Experiment, INDOEX [Masonis et al., 2002] and the Southern African Regional Science Initiative, SAFARI 2000 [Magi et al., 2003].
 This paper describes closure studies based on instrumentation flown aboard the NCAR C-130 aircraft in research flights from 30 March 2001 to 4 May 2001. The aircraft was based at the Marine Corps Air Station, Iwakuni, Japan (34.144°N, 132.236°E). In particular, we report on the comparison of aerosol extinction determined by differentiation of vertical profiles of aerosol optical depth measured using the six-channel NASA Ames Airborne Tracking Sun photometer, AATS-6, to aerosol extinction measured in situ using a combination of nephelometers to determine aerosol scattering and particle soot absorption photometers (PSAPs) to determine aerosol absorption. Vertical integration of the in situ-derived aerosol extinction profiles yielded layer aerosol optical depth, which was compared directly to the Sun photometer AOD measurements.
 The closure studies described here are a test of both the in situ and Sun photometer measurement methods, as both measurement techniques have strengths and weaknesses. For example, in determining aerosol extinction from the AATS-6 measurements of aerosol optical depth, one needs to be concerned with the possible horizontal inhomogeneity in aerosol properties encountered along the vertical profile, since it may be misinterpreted as a vertical variation in aerosol properties. In addition, the required smoothing of AATS-6 aerosol optical depth profiles makes it impossible for this technique to capture very strong vertical gradients in the aerosol field. The in situ measurements on the other hand, are subject to losses or enhancements of particles in the combined inlet/plumbing system, through which the aerosols are sampled. Further, the aerosol is usually dried out in the in situ sampling process, necessitating the humidification of dry scattering measurements. The in situ aerosol sampling system aboard the NCAR C-130 aircraft used a newly designed low-turbulence inlet (LTI) [Huebert et al., 2003], which was built to reduce inertial impaction losses of large aerosol particles in the inlet itself. Indeed, the closure studies carried out here represent a test of the performance of the aerosol sampling system in accounting for all particles responsible for ambient light extinction, as well as a check of the assumptions and corrections that both measurement methods are subject to. We would like to point out that most of the previous attempts at aerosol column closure studies were confined to a total of 10–12 vertical profiles [e.g., Hegg et al., 1997; Hartley et al., 2000; Schmid et al., 2000; Magi et al., 2003]. In this paper, however, we present a total of 28 profiles, which ultimately allowed the stratification of the data by ambient relative humidity (RH) and aerosol fine mode scattering fraction (defined here as the fraction of dry light scattering due to aerosols smaller than 1 μm in diameter). The amount of data available and hence the stratification by the above quantities permitted further insight into the performance of both measurement techniques.
2. Instrumentation and Methodology
2.1. Sun Photometer Measurements of Aerosol Optical Depth
 AATS-6 is designed to operate on a variety of aircraft. Once pointed to a position in the sky within 30 degrees of the Sun, it can track the Sun without input from an operator and record data in a self-contained data system. In addition, it must interface to an aircraft-provided data system, and receive and execute commands from a remote operator station (laptop), and transmit science and instrument-status data to that station. Using aircraft-provided data on latitude, longitude and ambient static pressure, aerosol (or particulate) optical depth τp(λ) and columnar water vapor CWV are computed in real time and displayed at the operator station (along with raw data, instrument status, and aircraft-provided data). In AATS-6, azimuth and elevation motors controlled by differential Sun sensors rotate a tracking head so as to lock on to the solar beam and keep detectors normal to it. The tracking head of the instrument mounts external to the aircraft skin, to minimize blockage by aircraft structures and also to avoid data contamination by aircraft-window effects. Each channel consists of a baffled entrance path, interference filter, photodiode detector, and preamplifier, which are temperature-controlled to avoid thermally induced calibration changes.
2.1.2. Data Reduction
 The most recent deployments of AATS-6 include the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX) in July 1996 [Russell et al., 1999a, 1999b] and the Puerto Rico Dust Experiment in September 2000 [Livingston et al., 2003]. AATS data processing conceptually consists of two steps. First, the determination of a calibration that is consistent with premission and postmission calibration (as well as high altitude AOD spectra measured during the field deployment); and second, the actual data reduction which consists of (1) the application of a cloud-screening algorithm to the measurement signals, (2) the separation of gaseous attenuation and aerosol contributions to the slant-path transmission measurements, and (3) the correction of aerosol optical depth for diffuse light entering the Sun photometer field of view in addition to the direct solar beam. A general description of the methods for AATS data reduction and error analysis can be found in the work of Russell et al. [1993a], Schmid and Wehrli , and Schmid et al. [2003b]. A brief summary is given here.
 Radiometric calibration is generally determined from Langley plots [Schmid and Wehrli, 1995] at high-mountain observatories. Premission and postmission calibration for the ACE-Asia field campaign was determined via Langley plots using data taken at the high-altitude Mauna Loa Observatory (MLO) in March and June of 2001, respectively. For AATS-6, comparison of premission and postmission calibration constants, inspection of high-altitude AOD spectra in addition to in-flight and ground-based comparisons to AATS-14 revealed that premission calibration constants need to be used for flights until 12 April 2001 (NCAR C-130 flight RF07), from which point on postmission calibration should be applied. Because of occasional poor tracking performance of AATS-6, a tracking uncertainty of 2% was added to the uncertainties in the calibration constants.
 The AATS-6 channels are chosen to allow separation of aerosol and water vapor. From the slant-path transmissions we retrieve τp(λ) in 5 narrow (about 5 nm bandwidth) wavelength bands centered at 380.1, 450.9, 525.7, 864.5, and 1021.3 nm and the columnar amounts of water vapor. The 864 nm channel, which was most affected by poor tracking performance of AATS-6, is excluded from consideration in this paper and is excluded from the ACE-Asia archive. It should be noted that the tracking performances of the 6 channels in AATS-6 are completely independent of each other, because each channel has its own specific field of view and hence responds differently to slightly imperfect Sun-tracking of the instrument as a whole. The field of views of the 864 nm channel have been found to be the most prone to imperfect Sun-tracking of the instrument and its data were thus eliminated from the data set. In addition to the corrections for Rayleigh scattering and O3 absorption, some channels require corrections for NO2, H2O and O2-O2 absorption. Cross sections were computed using LBLRTM 6.01 [Clough and Iacono, 1995] with the CKD 2.4.1 continuum model using the HITRAN 2000 (v 11.0) line list [Rothman et al., 2001] (including an update for water vapor from 04/2001; see http://www.hitran.com/hitran/updates.html). NO2 cross sections not included in LBLRTM 6.01 were taken from Harder et al. . NO2 was assumed constant at 2 × 10−15 molecules cm−2. Daily observations of total ozone column content were taken from the Total Ozone Mapping Spectrometer (TOMS) on the Earth Probe satellite, and ranged between 327 and 362 Dobson units during the entire field campaign.
 During ACE-Asia, AATS-6 data were recorded every 4 s consisting of an average and standard deviation of 9 samples taken during the first 3 of the 4 s. The standard deviations were used in our cloud-screening algorithm that is based on clouds exhibiting higher standard deviations than clear sky.
 Because Sun photometers have a nonzero field of view (FOV), they measure some diffuse light in addition to the direct solar beam. As a result, uncorrected Sun photometer measurements can overestimate direct-beam transmission and hence underestimate τp(λ). For most aerosol conditions and Sun photometer FOVs these effects are negligible. For example, Eck et al.  report that for the AERONET Sun/sky radiometers, which have FOV half-angle 0.6°, the diffuse-light correction to apparent τp(λ) is <0.7% of τp(λ), even for desert dust with effective (area-weighted) radius as large as 1.75 μm. The Ames Airborne Tracking Sun photometers, AATS-6 and -14, are designed and built with a relatively large FOV (measured half-angle 1.85°) to help keep the full solar disk in view when Sun-tracking during aircraft maneuvers. This larger FOV makes it necessary to assess quantitatively the diffuse light effects on AATS-derived τp(λ) when large particles are dominant. We have previously done this for postvolcanic stratospheric aerosols [Russell et al., 1993a, 1993b] and for the Saharan dust encountered in the Puerto Rico Dust Experiment (PRIDE) [Livingston et al., 2003].
where τp(λ)′ is apparent (uncorrected) τp(λ). Our calculations used the AATS-6 FOV (half-angle 1.85°) and aerosol scattering phase functions derived both from (1) size distributions and compositions measured on the Twin Otter in ACE-Asia [Wang et al., 2002] and (2) size distributions and complex refractive indices retrieved from Sun and sky radiance measurements by AERONET stations [Holben et al., 1998; Dubovik et al., 2002] in the ACE-Asia region during spring 2001.
 We found that the correction factors were well correlated with Ångström exponent
and that the correlation improved as wavelengths λ1 and λ2 increased. (Evidently this is because longer wavelengths are more sensitive to the larger particles in a distribution, and the larger particles are responsible for the diffuse light effects). Scatterplots of C-1 versus α were well fitted by exponentials of the form
 We also found no systematic differences between the f versus α scatterplots for Asian aerosols and analogous plots for Saharan aerosols (the latter derived from AERONET measurements in the Cape Verde Islands and Puerto Rico [Dubovik et al., 2002]). Therefore we included both Asian and Saharan aerosols in the scatterplots for our final fits, to obtain a robust relationship applicable to both Asian and Saharan aerosols. The f versus α data points for the Twin Otter in situ cases were consistent with the scatter of the AERONET data points; hence including or omitting them had negligible effect on the fitted equations obtained. For our ACE-Asia data set we corrected each individual τp(λ)′ measurement using the α value of the overlying aerosol column (using λ1 = 380 nm and λ2 = 1020 nm) in the fitted equation of the form of equation (3) for that wavelength. These fitted equations yield correction factors f that decrease with increasing wavelength. For the shortest AATS-6 wavelength (380.1 nm), 90% of all τp′ had to be corrected by less than 5.1%, with 40% of all τp′ requiring less than 3% correction. Uncertainties in the diffuse-light correction factors, based on the standard deviations of α-grouped values of C calculated from the AERONET and Twin-Otter data sets, were included in the overall uncertainty of τp(λ) from Russell et al. [1993b, equation (A22a)].
 Vertical differentiation of the AOD and CWV data in suitable flight patterns yields vertical profiles of aerosol extinction and water vapor concentration, respectively. The general procedure for deriving aerosol extinction profiles involves fitting the vertical AOD profiles with smoothed cubic spline functions, which are then differentiated with respect to altitude.
Figure 1 shows the location of 28 profiles flown by the NCAR C-130, which have been determined to be suitable for a comparison of the AATS-6-derived aerosol optical depth and extinction to in situ measured values of the same variables (the in situ-derived layer aerosol optical depth is determined by vertical integration of the in situ measured extinction profiles, cf. next section). In determining the suitability of these profiles for a closure study, we observed the quality of in situ and Sun photometer data in these profiles and sought to minimize the obscuration of AATS-6 by clouds. In fact, for all profiles that were considered suitable from the AATS-6 perspective, in situ data were readily available.
Figure 2 shows the vertical profiles of τp(λ) at four wavelengths (380.1, 450.9, 525.7, and 1021.3 nm), while Figure 3 shows the derived vertical profiles of aerosol extinction, σep(λ), at the same wavelengths. To derive aerosol extinction at 550 nm for an easy comparison to in situ-derived aerosol extinction at 550 nm, the aerosol optical depth spectra at each altitude were first fit with an Ångström law to derive a profile of τp(550 nm). In a second step, the profile of τp(550 nm) was fit with a smoothed cubic spline curve which was then differentiated to yield the vertical profile of σep(550 nm).
2.1.3. Uncertainty in Sun Photometer Retrievals
 The total uncertainty of the retrieved τp(λ), due to uncertainties in calibration, tracking performance, signal measurement, air mass computation, diffuse light correction, and corrections of molecular scattering and absorption, was computed following the procedures given by Russell et al. [1993a]. The uncertainty in CWV was computed following Schmid et al. .
 The main sources of uncertainty in the AATS-6-derived extinction are due to (1) potential misinterpretation of cloud optical depth as aerosol optical depth, (2) horizontal inhomogeneity along the measurements that comprise a vertical profile (i.e., when the location of two AOD measurements along the profile are horizontally separated) and (3) the constraints of fitting smoothed curves through the profiles of aerosol optical depth. Out of these sources of uncertainty (1) is minimized by our general cloud screening technique, which filters consecutive AATS-6 τp(λ) measurements with standard deviations above a certain threshold level as clouds, assuming that clouds generally exhibit larger spatial variability. In cases of doubt, the Ångström exponent, which is close to zero for clouds, was considered. The uncertainty caused by (3) will affect the AATS-6-derived extinction only at altitudes where there is a strong vertical gradient in aerosol light extinction.
 Of biggest concern, because not directly measurable, is the potential uncertainty in AATS-6-derived aerosol extinction due to horizontal inhomogeneity in the aerosol field during the vertical profile measurements. Because the AATS-6 extinctions are computed from the increase in aerosol optical depth with decreasing altitude, there is the possibility that an aerosol plume suddenly enters the Sun photometer-to-Sun path at a higher altitude and the increase in τp(λ) is interpreted as aerosol extinction at the altitude of the airplane. However, depending on flight track, wind conditions and inhomogeneity in the aerosol field, such an aerosol plume must not have necessarily been measured by the in situ instrumentation on the same aircraft. To illustrate the effect of horizontal inhomogeneity on AATS-6-derived layer AOD, assume that the aircraft traverses a horizontal gradient, g, in aerosol optical depth while flying a vertical profile. If the aircraft carrying AATS traveled a horizontal distance, Δx, while making the profile measurements of τp, the uncertainty in layer AOD due to a horizontal aerosol gradient would be given by:
where is the mean AOD measured in the layer. For example, for an arbitrary gradient in AOD of 10% per 100 km, a horizontal distance of 50 km traveled during a vertical profile and a mean AOD of 0.2 in a given layer, the gradient uncertainty computed using equation (4) is 0.01. Here we chose to compute the relative horizontal gradient, g, as the ratio of standard deviation and mean of aerosol optical depth during a low-level flight leg, divided by the length of that leg in kilometers. g(525 nm) thus computed during low-level legs on 11 flights ranged from 1 to 14% at 525 nm, with a mean of 6% per 100 km. A publication on the topic of AOD variability in ACE-Asia is forthcoming.
 In analogy to equation (4), the uncertainty due to a horizontal gradient in AATS-6-derived extinction from two measurements of τ, separated by a small vertical distance Δz can be written as:
where τtop, is the aerosol optical depth at the higher altitude of the two AOD measurements. The sign in equations (4) and (5) depends on the orientation of the aerosol gradient denoted by g. Generally, the uncertainty in the difference of two measurements of τp(λ) at different altitudes, due to uncertainties in calibration, signal measurement, air mass computation, and corrections of molecular scattering and absorption would be negligible due to the fact that these uncertainties represent merely a bias in the measurements. However, AATS-6 frequently exhibited poor tracking performance and it cannot be assumed that uncertainties in tracking are equal at the top and the bottom of a profile. From observations of AOD irregularities in select channels, we concluded that in general, the tracking performance uncertainties were less than 0.02 at air masses around 1. Because the dominating source of uncertainty, i.e., the calibration uncertainty, was of equal magnitude, we decided to use the root-square-sum of half of the total AOD uncertainties (instrumental plus tracking), δτ, at the top and the bottom of a given profile as an additional term in the uncertainty in layer AOD, viz.:
 Finally, the total error in layer AOD from AATS-6 is the root-square-sum of the two terms given in equations (4) and (6).
2.2. In Situ Measurements of Aerosol Scattering and Absorption
2.2.1. Instrument Description
 Aboard the NCAR C-130, a suite of instruments was used to carry out in situ measurements of aerosol light scattering and absorption. Two integrating nephelometers (TSI Inc., Model 3563) measured integrated total scatter at 450, 550, and 700 nm wavelengths [Anderson et al., 1996; Anderson and Ogren, 1998]. One nephelometer always measured all aerosol, while the second nephelometer usually measured only aerosol of dry aerodynamic diameter D < 1 μm. Two Radiance Research, Inc. particle soot absorption photometers were used to measure light absorption by aerosols at 550 nm [Bond et al., 1999]. For the C-130 research flights 6–19, one PSAP measured the total aerosol and the other measured only aerosol of dry aerodynamic diameter D < 1 μm. All of the measurements described so far were made at low (nearly always <45%) relative humidity and are described in more detail by Anderson et al. . A separate measurement of the increase in 540 nm integrated light scattering with relative humidity was made using two model M903 Radiance Research nephelometers. One of the Radiance nephelometers was run at low (<45%) RH and the other at 85% ± 2% RH. By assuming an exponential fit (see below) to the increase in light scattering with RH [Kasten, 1969], f(RH), we were able to use this two-point data to determine f(RH) and thus predict light scattering at ambient relative humidity. This is important in the context of this closure study because the Sun photometer measures light extinction by aerosols under ambient conditions.
2.2.2. In Situ Data Reduction
 Light scattering at 550 nm and ambient RH was calculated from the dry TSI nephelometer-derived scattering at 550 nm using the following formulation:
The parameter γ in equation (5) is derived using scattering values from the Radiance Research nephelometers as:
Because the effect of humidification on light absorption was not measured, light absorption data are not adjusted to ambient RH. In addition, the only currently available modeling studies by Redemann et al.  suggest that absorption humidification factors for a range of atmospheric conditions are likely negligible (i.e., at most favorable conditions, absorption humidification factors for an increase in RH from 30 to 80% were between 7 and 15%). At the time of completion of this manuscript, we were unaware of any experimental studies geared toward absorption humidification.
 The data reported here have been averaged to 10-s resolution. In order to improve the signal-to-noise ratio, the light absorption data have additionally been smoothed over a 30-s shifting window. Similarly, the humidified scattering measurements by the Radiance Research nephelometers are filtered through a smoothing function with an approximately 20-s response time. Data from the TSI integrating nephelometers were processed using eight span gas (air and CO2) calibrations to determine corrections to the gain and offset calibration coefficients. Calibration corrections were applied on a flight-by-flight basis. Angular truncation correction factors were applied as recommended by Anderson and Ogren . Data from the Radiance Research nephelometers were also adjusted for calibration changes using span gas measurements. Additionally, in-flight filtered air measurements were used to adjust the Radiance nephelometers' calibration on the first two flights to account for changes in calibration that occurred between span gas calibrations. Note that the angular sensitivity function for the Radiance Research nephelometers has not yet been carefully quantified and issues in understanding the absolute value of the Radiance nephelometer scattering measurement for the coarse mode remain unresolved. Hence angular correction factors have not been applied to these data. However, based on a preliminary assessment of the Radiance nephelometers' angular truncation range done in the UW lab and measurements of the RH dependence of the Ångström exponent during ACE-Asia [Carrico et al., 2003], we feel confident that errors in the derived values of γ, and hence f(RH), should be small because there should not be a significant difference in the angular truncation corrections between the wet and the dry nephelometer measurements. For submicron aerosol, this is because the angular truncation correction factor is always small (∼5–10% of σsp maximum). Observations of the change in Ångström with RH for the ACE-Asia submicron aerosol indicate that there should be at most a 3% difference between the angular correction factors at 40% and 85% RH [Carrico et al., 2003, Figure 6; Anderson and Ogren, 1998]. For coarse mode aerosol, the fraction of light scattered into the near-forward direction does not change much with aerosol size so neither does the angular truncation correction factor. Additionally, the coarse mode aerosol measured from the C-130 during ACE-Asia was dominated by dust, which was not very hygroscopic (f(RH)∼1.1; Anderson et al. ) so its size did not change much with RH.
 Data from the Radiance Research particle soot absorption photometers (PSAPs) were corrected for spot size, flow rate, artifact response to scattering, and error in the manufacturer's calibration, all given by Bond et al. . Light absorption, reported at standard temperature and pressure, were adjusted to ambient air density.
 The sum of total aerosol 550 nm scattering adjusted to ambient RH, and aerosol 550 nm absorption yields ambient aerosol extinction at 550 nm. Integration of vertical profiles of aerosol extinction with respect to altitude yields the layer aerosol optical depth at 550 nm. This in situ-derived layer aerosol optical depth can then be compared to the AATS-6-derived layer aerosol optical depth to determine the degree of closure between the in situ and Sun photometer measurements. In an additional closure test we compare the AATS-6-derived aerosol extinction at 550 nm to the in situ-derived extinction. We make both comparisons because extinction is more directly measured by the in situ instruments, while optical depth is more directly measured by the Sun photometer. Also presented herein are values of the Ångström exponent derived from the TSI nephelometer data using an equation analogous to equation (2), where τp is replaced by σsp as measured at low RH.
2.2.3. Uncertainty in In Situ Data
 The uncertainties in the in situ-derived ambient extinction are due to instrumental uncertainties, uncertainties in the determination of f(RH), and due to the uncertainty in losses of particles in the LTI (low turbulence inlet) or plumbing system through which the aerosols are sampled. For this study, the instrumental uncertainties are taken from Anderson et al.  and are described briefly below. We made no attempt to include the uncertainty due to the potentially imperfect transmission efficiency of the combined plumbing and inlet system. Initial laboratory measurements of the plumbing efficiency and theoretical calculations of the LTI performance suggest that the enhancement of large particles in the LTI system are largely compensated for by plumbing losses [Anderson et al., 2003], such that only a ∼10% enhancement in scattering is expected when coarse mode aerosol dominate scattering. Indeed, the closure studies carried out here are a partial test for the validity of such an assumption.
 The 95% confidence interval uncertainties in the mean values were calculated for the scattering and absorption parameters, except for those derived from the Radiance Research nephelometers. Because the sources of measurement uncertainty for the Radiance Research nephelometers have not been quantified, we have fixed the uncertainty in γ at 0.2 and we calculate the uncertainty in f(RH) and ambient-RH light scattering accordingly. Calculation of total uncertainty from multiple sources was made using standard propagation of errors under the assumptions that (1) each source of error is independent of the others such that they can be added in a sum-square sense and (2) noise uncertainty decreases with the square-root of averaging time while all other sources of uncertainty do not change with averaging time. For the TSI integrating nephelometers, the following sources of uncertainty were considered: (1) instrument accuracy [Anderson et al., 1996], (2) instrument calibration uncertainty [Anderson and Ogren, 1998], (3) uncertainty in the angular truncation correction factors [Anderson and Ogren, 1998], (4) uncertainty due to instrumental noise [Anderson and Ogren, 1998], (5) for total scattering at ambient RH, uncertainty in the adjustment from low to ambient RH, calculated using the assigned uncertainty in γ of 0.2. For the particle soot absorption photometers, the sources of uncertainty included were (1) instrument accuracy, (2) instrument precision, (3) uncertainty due to instrumental noise, and (4) uncertainty in the applied scattering correction [Bond et al., 1999].
2.3. Measurements of Columnar Water Vapor With the NASA Ames Airborne Tracking Sun Photometer, AATS-6, and Derivation of Water Vapor Density
 From the slant-path transmission in the AATS-6 wavelength band centered at 941.9 nm we retrieve the amount of columnar water vapor, after the contributions of ozone absorption, Rayleigh scattering and aerosol attenuation have been removed. Cross sections were computed using LBLRTM 6.01 [Clough and Iacono, 1995] with the CKD 2.4.1 continuum model using the HITRAN 2000 (v 11.0) line list [Rothman et al., 2001] (including an update for water vapor from 04/2001; see http://www.hitran.com/hitran/updates.html). Differentiation of CWV data obtained in vertical profiles allows derivation of water vapor density ρw as a function of altitude.
2.4. In Situ Measurements of Ambient Absolute Humidity
 There were a number of redundant measurements of water vapor density aboard the NCAR C-130 in ACE-Asia. Humidity measurements were made using two collocated thermoelectric dew point sensors, two Lyman-alpha fast-response hygrometers and an experimental TDL laser hygrometer. As is typically the case, the two dew point sensors were set up differently to provide the best coverage under the widest range of ambient conditions. The first dew point sensor was set up for fast response, but its dynamic range was limited. The second dew point sensor had a slower response but had the capability of measuring greater dew point depressions. A comparison of the data sets from these two sensors yielded generally good correlation in instrument signatures. However, some problems with water ingestion occurred which resulted in sensor drift. Each flight was evaluated on a case-by-case basis to see which dew point sensor was functioning the best on that particular flight. The selection of a reference humidity sensor for use in calculating all of the derived measurements was varied accordingly. When neither of the dew point sensors was considered to be working properly, the reference ambient humidity archived by the NCAR Research Aviation Facility (RAF) was derived from one of the two Lyman-alpha fast-response hygrometers. Effectively, the RAF reference humidity used in this paper was derived from a dew point sensor in flights RF01–03, 07, 09, 12, 14, 15, and 17–19, while the RAF reference humidity in flights RF04–06, 08, 10, 11, 13 and 16 was measured by one of the Lyman-alpha hygrometers. In analogy to the integration of in situ-derived aerosol extinction profiles to yield layer aerosol optical depth, the in situ measured water vapor density can be integrated to yield layer water vapor, facilitating the comparison to AATS-6-derived layer water vapor.
3.1. Comparison of Aerosol Extinction and Layer Aerosol Optical Depth at 550 nm
 Examining the AATS-6-derived aerosol extinction profiles in Figure 3, there are two types of profiles distinguishable. First, there are profiles which have a considerable amount of τp above an altitude of 2 km, usually caused by large dust particles (e.g., Figures 3j–3t), as supported by in situ observations and small Ångström law exponents (cf. Figure 4). Secondly, there are profiles, in which the total column aerosol optical depth is dominated by a strong contribution by mostly small particles in the boundary layer (e.g., Figures 3a–3h). The vertical stratification of these two aerosol types is more clearly seen in profiles of the Ångström law exponent, α, shown in Figure 4. The Sun photometer-derived values, αext, are fitted at each altitude to the AATS-6-derived extinction spectrum (black dots in Figure 4) where the in situ values, αscat, are derived using the low-RH scattering values at 450 nm and 700 nm (gray dots in Figure 4; See below for a discussion and quantitative comparison).
Figure 5 shows the comparison of AATS-6-derived profiles of aerosol extinction at 550 nm (black lines and markers) to the in situ-derived aerosol extinction at the same wavelength (gray lines and markers). As described in section 2, the AATS-6-derived extinction was determined by first fitting an Ångström law to τp(λ, z) at each altitude, computing a profile of τp(550 nm,z), cubic spline fitting this profile and finally differentiating the resulting smoothed spline fit. The in situ-derived extinction is determined by humidifying the total dry scattering measurements at 550 nm using equations (7)–(9), then adding the PSAP absorption measurements at 550 nm.
 The large suite of profiles shown in Figure 5 allows us to look for both systematic and intermittent sources of error in the measurements. The largest potential error sources for the in situ measurements (i.e., inlet/plumbing efficiencies not equal to one and over- or under-humidification of light scattering from dry to ambient RH) are more likely to lead to systematic biases, whereas the largest potential sources of error in the AATS-6 measurements (i.e., the inability to capture strong vertical gradients and the misinterpretation of horizontal gradients in the aerosol field as vertical gradients) are more likely to lead to errors that are only present some of the time and will not always be in one direction. The latter type of error is demonstrated in Figure 5t, where the in situ instrumentation exhibits large vertical variation. It can be seen that the AATS-6-derived extinction cannot follow such a complex vertical profile. However, neglecting all other effects, the AATS-6-derived extinction should, over a broader vertical average, yield the true ambient value as illustrated by the fact that in Figure 5t the in situ-derived extinction profile merely oscillates around the AATS-6-derived extinction profile. Similarly, in Figure 5e the Sun photometer-derived extinction oscillates about zero in the 4–5 km altitude range; this could be due to a horizontal gradient in the aerosol viewed overhead as the aircraft ascended. Such intermittent errors are clearly seen in direct comparison profiles as given in Figure 5, but systematic biases and their potential sources will best be revealed by correlations between the two data sets.
 In order to facilitate such a quantitative comparison, we first interpolated the AATS-6 extinctions to the altitudes at which the in situ measurements were reported. This procedure should not introduce additional uncertainty, given the fact that the AATS-6-derived extinction profiles were generally averaged and smoothed at altitude intervals larger than the interpolation distances. The 28 profiles shown in Figure 5 yielded a total of 3555 extinction data pairs. In a least squares regression, we then sought to compare the two sets of data. The availability of ambient RH data, as well as the measurement of the fine mode scattering fraction allowed stratification of the extinction measurement comparisons by these quantities. Figure 6 shows the comparison of the two sets of extinction data stratified by ambient RH. The data were stratified in increments of 20% RH. Because neither method is error-free, we chose to apply not just a simple X on Y regression (model I), but we rather report the “least squares bisector”-line, calculated as the bisector of the minor angle between the two model I regressions: Y on X and X on Y, respectively. The results of the model II regression analysis are given in Table 1. It can be seen that the extinction comparison for all RH (black solid line) is very close to the 1:1 line (black dashed line). The extinction comparison for ambient relative humidity between 0 and 20% seemed to exhibit larger extinction values determined by AATS-6 than by the in situ method, while the in situ method indicated more extinction than derived by AATS-6 for RH between 40 and 60% and for RH between 80 and 100%. However, since about 55% of the data were taken at RH below 20%, the overall agreement between the two methods is reasonable. It is noteworthy however, that the data below 20% RH exhibited the weakest correlation as indicated by the low r square value of 0.467. In part, this scatter is caused by profile Figure 5s, which was apparently affected by large horizontal inhomogeneity. Leaving out the profile shown in Figure 5s resulted in a least squares bisector fit-line with a slope of 0.87 and increased the r square value to about 0.65 (not shown here). Hence the general finding of lower in situ extinctions than AATS-6-derived extinctions would still hold true for RH between 0 and 20%.
Table 1. Comparison of 550 nm Aerosol Extinction as Derived From the AATS-6 and in Situ Method (cf. Figure 6), Stratified by Ambient Relative Humidity (RH)a
RH Range, %
Number of Data Points in RH Range
Model II line fit parameters for least squares bisectors are given in the form y = mx + b. The least squares bisector method uses the bisector of the minor angle between the two model I linear least squares regression fits, x on y and y on x. σm and σb are the standard deviations of the slope and intercept, respectively, calculated as the symmetrical limits for a model I regression, using formulations from Bevington and Robinson [1992, pp. 108–109].
Figure 7 shows stratification of the extinction comparison by the fine mode fraction of scattering, FFscat (here defined as the fraction of dry scattering due to aerosols smaller than 1 μm in diameter). Here we follow the stratification proposed by Anderson et al. , namely to divide the extinction data into three classes with FFscat below 30% (“coarse-dominated”), FFscat between 30 and 60% (“mixed”) and FFscat between 60 and 100% (“fine-dominated”). Anderson et al.  found that such a FFscat classification scheme tended to minimize the variability of most aerosol intensive properties. The total number of data points is less than that shown in Figure 6, because at very low aerosol concentrations, FFscat cannot be determined accurately. The r square values of the extinction comparisons shown in Figure 7 indicate that the correlation between in situ and AATS-6-derived extinction improves as FFscat increases. The regression of fine mode-dominated extinctions (FFscat between 60 and 100%) is not just the best correlated of the three classes, it also shows a regression line with minimal offset (−0.004) and a slope closest to 1 (see Table 2). This result suggests that it is most probable for the in situ instrumentation to measure an ambient extinction that is close to the Sun photometer-derived values when the ambient aerosol is fine mode dominated, and the result further indicates that there may be a bias toward over-sampling of large particles by the low turbulence inlet.
Table 2. Comparison of 550 nm Aerosol Extinction as Derived From the AATS-6 and in Situ Method (cf. Figure 7), Stratified by Fine Mode Scattering Fraction, FFscata
FFscat Range, %
Number of Data Points in FFscat Range
Defined here as the fraction of dry light scattering due to aerosols smaller than 1μm in diameter. Model II line fit parameters were determined as described in captions of Table 1.
 Integration of the in situ-derived profiles of ambient aerosol extinction at 550 nm over vertical layers yields layer aerosol optical depth, τl,is, at that wavelength. The differencing of two AATS-6-derived aerosol optical depths at the bottom and at the top of the same profiles yields AATS-6-derived layer aerosol optical depth, τl,sp. Figure 8 shows the comparison of τl,is and τl,sp for the 28 profiles that comprise this closure study. The average difference in layer AOD derived from the two methods was 0.03, corresponding to an average difference of 11.5%. Owing to the potentially more systematic nature of the uncertainties in the in situ-derived extinctions, the uncertainties in τl,is shown in Figure 8 were calculated as the vertical integral of the extinction errors. The uncertainties were between 10 and 55% (with a mean of 19%).
 The error bars in AATS-6-derived layer optical depths are calculated using the root-square-sums of the instrumental uncertainty (cf. equation (4)) and the “potential” gradient uncertainty (cf. equation (6)). “Potential” in this context is supposed to denote that we did not have independent measurements on horizontal AOD variability during these flight profiles and that the uncertainty in AATS-derived layer AOD was estimated using the horizontal variability measured during low-level flight legs in close temporal and spatial proximity to the actual profiles. Hence the estimated uncertainties only exist if the exact variability seen during the low-level legs was also present during the vertical profiles. For illustration, the separate uncertainties from the instrumental and the gradient term are shown in Figure 8 as green and red error bars, respectively. It is apparent that in the cases with large total uncertainties in τl,sp, the uncertainty is dominated by the gradient uncertainty (red). It turns out that this gradient uncertainty is not caused by large variability measured during the low-level flight leg to determine g in equation (4), but due to the large horizontal distance Δx traveled during the vertical profile. The total uncertainties in AATS-6-derived layer AOD ranged between 5 and 59% (with a mean of 22%). The average uncertainty in AATS-6-derived layer AOD due to possible horizontal variability alone was 19%.
 The model II least squares bisector regression line for the layer aerosol optical depth comparison yields a fit line of y = 0.94(±0.098)x + 0.005(±0.026), with an r square of 0.741 (solid blue line). Also shown for orientation are the 1:1 line (black dashed line) and model I (X on Y) regression result for a line without offset (blue dashed line). It is noteworthy that the model I, no-offset model yields a fit very similar to the least bisector result given above. We conclude that within the fit uncertainties, the layer aerosol optical depth comparison yields the same regression as the extinction comparison for all data points considered in Figure 7 (solid black line) and note that neither the layer AOD nor the extinction regression produces a significant offset in the fit models.
3.2. Comparison of Sun Photometer and in Situ-Derived Ångström Exponents
 AATS-6-derived Ångström exponents were determined from least squares fits of the Ångström law to the four-wavelength aerosol extinction spectrum at each altitude as presented in Figure 3. At the same altitudes, the three-wavelength TSI nephelometer measurements of dry aerosol light scattering were fitted with the Ångström law to derive an in situ dry scattering Ångström exponent. Figure 9 shows the comparison of the two sets of data thus derived. Because both methods have considerable difficulty in determining Ångström exponents at very low aerosol loadings, we restricted the comparison to those altitudes where total aerosol extinction at 550 nm was above 0.01 km−1 (=10 Mm−1), effectively reducing the total number of data points shown in Table 1 from 3555 to 2490. It can be seen in Figure 9 that there is considerable scatter in the Ångström exponent comparison (r2 = 0.62). We attribute this fact to the fundamentally different techniques used to determine the two sets of Ångström exponents and the very different sources of error involved in the two techniques. The fit model however, indicates line fit parameters as shown in Table 3. It is evident that there is an offset of ∼0.1 but a slope of nearly 1 to the model fit for all data points. Stratification of the data by low RH (<40%, green lines) and high RH (>40%, blue line) reveals the intuitive results that the offset is largely driven by data points with high RH. This result is consistent with our understanding of the effects of humidification on particles size and Ångström exponent, because the in situ values of the Ångström exponent are derived from low-RH scattering and the humidification of the dry scattering would generally tend to produce smaller values of αscat (i.e., larger, more humidified particles yield smaller Ångström exponents). Also, in general (i.e., for dry scattering Ångström exponents greater than zero), the addition of wavelength-independent aerosol absorption (an assumption just for illustration) to the three-wavelength scattering measurements would tend to produce extinction spectra that would yield smaller Ångström exponents. However, the addition of wavelength-dependent absorption may not produce any change in the Ångström exponent at all. The fact that the offset is in the direction that can be expected when comparing dry scattering-derived Ångström exponents to ambient AATS-6-derived values, in conjunction with the fact that there is no considerable slope in the regression of the two data sets indicates again that there is no obvious size-dependent sampling bias in the in situ-derived representation of aerosol scattering properties.
Table 3. Comparison of Ångström Exponents Derived From AATS-6 Extinction Spectra and in Situ Measured Dry Scattering Between 450 and 700 nm (cf. Figure 9), Stratified by Ambient Relative Humidity (RH)a
RH Range, %
Number of Data Points in RH Range
Model II line fit parameters were determined as described in captions of Table 1.
3.3. Comparison of Layer Water Vapor and Absolute Humidity
 Columnar water vapor data from the AATS-6 941 nm channel transmission measurements was collected for the same 28 profiles as for the AOD measurements shown in Figure 2. Vertical differentiation yielded water vapor density, which was compared directly to the reference humidity measurements archived by the NCAR RAF (Research Aviation Facility). Figure 10 shows the comparison of vertical profiles of water vapor density from the Sun photometer (blue lines) to the in situ measurements (green lines). Because AATS measurements of columnar water vapor are possible through thin, homogeneous clouds, the number of CWV data points along a profile is generally higher than the number of AOD measurements along the same profiles. This fact explains the generally more structured appearance of the AATS-6 water vapor density profiles in Figure 10 by comparison to the AATS-6 extinction profiles in Figures 3 and 5.
 It can be seen that both methods indicate water vapor density above 12 gm−3 for only two profiles (u and v), taken within 2 hours of each other on the same flight (RF16, 30 April 2001). All other profiles indicate relatively dry conditions with water vapor density below 12 gm−3, in agreement with the low humidity measurements taken aboard the CIRPAS Twin-Otter aircraft [Schmid et al., 2003a].
Figure 11 shows the scatterplot comparisons between in situ-derived layer water vapor and AATS-6-derived layer water vapor, while Figure 12 shows the same for the water vapor density along the profiles shown in Figure 10. We chose the in situ measurements as the independent variable for both plots, because we ascertain that in situ observations of humidity are a much more direct measurement and hence the standard against which the remote method is to be tested. For the same reason, we chose to use a standard model I least squares linear regression of X on Y (which minimizes the squares of the distances in the y direction only) of the form y = mx + b (black solid lines in Figures 11 and 12). For comparison, Figures 11 and 12 also show the fit lines for linear models without offset (gray lines). In Figure 11, the no-offset fit line coincides with the 1:1 line and in Figure 12 the no-offset fit line coincides with the regular fit line.
 The regression of layer water vapor for the 28 profiles (cf. Figure 11) indicates a regression line of y = 0.95(±0.020)x + 0.087(±0.028), with a very high correlation coefficient r square of 0.989. Both the fit parameters as well as the correlation coefficient are heavily influenced by the two high data points, which indicate slightly greater in situ-derived layer water vapor measurements than the AATS-6-derived values. The comparison of water vapor density (6334 data points) shows a fit line with y = 1.02(±0.003)x + 0.018(±0.010), with a slightly smaller correlation coefficient of 0.955. The agreement found here is well below the precision limit of measuring water vapor using solar transmittance measurements in the 940 nm region [Schmid et al., 1996] and hence must be considered, at least in part, to be fortuitous.
4. Summary and Conclusions
 In this paper, we present 28 vertical profiles of aerosol optical depth and extinction at four wavelengths (380.1, 450.9, 525.7, 1021.3 nm), as well as profiles of columnar water vapor (CWV) and water vapor density measured by the NASA Ames Airborne Tracking Sun photometer, AATS-6, aboard the NCAR C-130 in ACE-Asia.
 In an aerosol column closure study, AATS-6 data collected in these 28 profiles were compared to aerosol extinction derived in situ from a combination of nephelometer aerosol scattering and PSAP aerosol absorption measurements. In analogy, the AATS-6 water vapor measurements were compared to the in situ humidity sensors aboard the same aircraft. A companion paper describing the same efforts for data collected aboard the CIRPAS Twin-Otter aircraft is presented by Schmid et al. [2003a].
 The AATS-6 measurements in ACE-Asia indicated generally dry conditions with the majority (26) of the profile studies indicating layer water vapor contents of less than 2 gcm−2. The aerosol measurements showed two situations. First, a vertical distribution with pollution-dominated aerosols confined to the lower two kilometers and secondly, the scenario in which mineral dust particles produced significant midvisible aerosol extinction at altitudes between 4 and 8 km. The notable advantage of the present study is the fact that the NCAR C-130 was able to penetrate into and frequently traverse the high-altitude mineral dust aerosol layers, enabling extinction comparisons within the dust.
 The main goals of the aerosol column closure study were to check the mutual consistency between the Sun photometer and the in situ-derived ambient aerosol extinction and layer optical depth. It should be noted that each method has its own advantages and that the combination of the two data sets will likely further our understanding of Asian aerosol beyond the capabilities of either method on its own. Among the advantages of the in situ method of determining aerosol extinction (layer optical depth) are a generally better vertical resolution, better sensitivity at low concentration, and a frequently more robust measure of the wavelength dependence than AATS-6 was able to achieve in ACE-Asia. It should be noted that the latter two effects would have been less notable with an improved tracking performance of AATS-6 or the deployment of the newer AATS-14. This fact was evident in comparisons of the performance of AATS-6 and AATS-14 when the two instruments were deployed in close geographical proximity to each other. Among the notable advantages of AATS-6 in determining ambient aerosol extinction is the fact that the aerosol does not need to be taken into the aircraft. Hence there are no alterations of the ambient aerosol similar to the potential losses of particles in the in situ inlet/plumbing system, which required substantial theoretical corrections in previous closure studies. Hence an aerosol column closure study is among other things a test of the potential deficiencies of the two techniques involved. For the NCAR C-130 in ACE-Asia it was also a test of the newly designed low turbulence inlet (LTI) system.
 The comparison of in situ and Sun photometer-derived layer aerosol optical depths at 550 nm yielded agreement within the measurement uncertainties (closure) for 25 of the 28 profiles. The uncertainties in AATS-6-derived layer AOD ranged from 5 to 59% (with a mean of 22%). It should be noted that the AATS-6 uncertainties due to the gradient uncertainties alone averaged ∼19%. The uncertainties in in situ-derived layer AOD were between 10 and 55% (with a mean of 19%). We attribute the lack of closure in the remaining three cases in part to spatial inhomogeneity beyond the level captured by the gradient uncertainty expression.
 Comparison of the corresponding aerosol extinction values showed equally good agreement across the suite of profiles. Stratification of the extinction data by ambient RH revealed that the in situ-derived aerosol extinctions were generally less than the AATS-6-derived values for RH between 0 and 20%, an RH range which accounted for about 55% of all data samples. The in situ-derived extinctions generally exceeded the Sun photometer-derived values in the RH ranges of 40 to 60% and 80 to 100%. These comparisons may indicate that the humidification corrections applied to the dry scattering measurements at low RH could be slightly low, but, even with this large suite of 28 profiles, the regression is not statistically robust enough to state this with high confidence.
 Stratification of the extinction comparison by the fine mode fraction of dry scattering, FFscat, showed that the best agreement between the two methods, both in terms of correlation coefficient and in terms of the fit line being closest to the 1:1 line, was achieved for the fine mode dominated cases and that the in situ values were somewhat higher in coarse mode dominated cases. This result supports the general conception that aerosol closure studies are most successfully performed when dealing with small, spherical particles which pose the least challenges for either measurement technique [Magi et al., 2003]. Again, the statistics are not robust enough to conclude definitively that there is a bias in the measurements. However, these results do indicate that the low turbulence inlet may have lead to an over-sampling of the coarse mode aerosol extinction by the in situ instruments that is consistent with theoretical calculations (i.e., ∼10%).
 A comparison of Ångström exponents calculated from AATS-6 extinction spectra and nephelometer-derived spectra of dry light scattering show generally good agreement, with an offset that can be explained by the fact that dry, in situ scattering spectra were used. The lack of a slope notably different from 1 in the general comparison of Ångström exponents thus derived also indicates that the two measurements techniques generally agreed on the size of particles responsible for the optical measurements. Hence we conclude that AATS-6 and in situ observations of aerosol extinction aboard the NCAR C-130 are mutually consistent and that, on average, the in situ observation system, including its sampling component, can account for essentially all ambient aerosol extinction measured by AATS-6.
 From the better agreement and tighter correlation in the comparison between AATS-6-derived water vapor to the in situ-derived humidity measurements, we conclude that spatial inhomogeneity can only account for a small fraction of the scatter in the aerosol extinction and optical depth comparisons though. This conclusion assumes that the spatial variability in aerosol extinction and water vapor density are comparable. For future field experiments that are focused on column closure studies, we recommend the use of an inlet system equally capable of capturing aerosol extinction due to large particles as the LTI flown aboard the NCAR C-130 in ACE-Asia. We further suggest that flight patterns for closure studies either minimize the horizontal distance traveled during a vertical profile or include a low-level horizontal leg in close succession with the vertical profile, to accommodate the assessment of the horizontal variability in aerosol optical properties.
 We would like to thank S. Howell and C. McNaughton (University of Hawaii) for their help in the acquisition of scattering humidification data. We are indebted to S. Ramirez (BAERI, Sonoma, CA) for help in preparing some of the figures in this manuscript. We would like to thank Edward T. Peltzer (Monterey Bay Aquarium Research Institute, CA) for making available MATLAB shell scripts for linear regression analysis (www.mbari.org/~etp3/regressindex.htm), and the National Center for Atmospheric Research Research Aviation Facility (NCAR-RAF), for their support in the field on the C-130 aircraft and for providing their water vapor data for this analysis. We gratefully acknowledge funding provided to the NASA Ames Sun photometer group by NASA's Earth Observing System Inter-Disciplinary Science (EOS-IDS) Program, by the NASA's Radiation Sciences Program, and by the Office of Naval Research. Funding to the UW, Department of Atmospheric Sciences, was provided by the National Science Foundation (grants ATM-0002198 and ATM-0138250) and by the National Oceanic and Atmospheric Administration (JISAO agreement NA37RJ0198); this publication is JISAO contribution 980. This research is a contribution to the International Global Atmospheric Chemistry (IGAC) Core Project of the International Geosphere Biosphere Program (IGBP) and is part of the IGAC Aerosol Characterization Experiments (ACE).