The measured MPL signal is raw data containing returns from molecules (Rayleigh scattering), aerosols, and clouds. The measured MPL signals also contain quantities associated with background noise, and instrument effects. The measured MPL signal PMPL(r) is given by
where PMPL(r) is the lidar signal at range r (m), β(r) is the backscatter coefficient (m sr)−1 at range r, σ(r) is the extinction coefficient (m)−1 at range r, the R subscript denotes a Rayleigh quantity (due to molecular scattering), and the P subscript denotes a particle (aerosols, clouds) quantity. C is the MPL system constant (principally a function of the optics). E is proportional to the pulse output energy, and Nb is background noise due to sunlight at 523 nm. O(r) (overlap function), and A(z) (afterpulse function) are instrument effects and are discussed later in Appendix A.
 All Rayleigh quantities in the MPL signal are considered known because of the accuracy current models have achieved in calculating molecular scattering and absorption. SR is a constant, and βR (r) and σR (r) are constructed using tables of McClatchey et al.  for tropical, midlatitude (winter/summer), and subarctic (winter/summer) atmospheres.
A1. Extinction-Backscatter Ratio
 Extinction and backscatter are related using the extinction-backscatter ratio (units of sr),
where Si is the extinction-backscatter ratio and the i subscript indicates a Rayleigh or particle quantity. The extinction-backscatter ratio can also be related to ωo, the single scatter albedo, and Pi(180), the phase function at 180° (normalized to 4π), by the following equation:
SR is a constant and is equal to 8π/3. Sp, henceforth referred to as the S ratio, is unknown but typically ranges in value from 10 to 100 sr [Spinhirne et al., 1980; Ackermann, 1998; Doherty et al., 1999; Welton et al., 2000; Ansmann et al., 2000; Voss et al., 2001] for aerosols. In this study, the S ratio is treated as constant with respect to range through an aerosol layer. The S ratio of each individual layer will change depending upon the single scatter albedo and phase function of the aerosols and/or clouds in the layer. Errors from using an assumption of range constant S ratios in analysis of MPL data are discussed by Welton  and Welton et al. , and also in section 4.
A2. Signal Corrections
 The raw signal in equation (A1) is not in a mathematical format suitable for use in lidar algorithms. Also, the following instrument-related quantities in the raw signal are not related to returns from molecules, aerosols, or clouds: C, E, O(r), and A(r). These quantities must be removed from the raw MPL signals before analysis can be performed. The first step in the correction process is to subtract Nb, and then to normalize equation (A1) by multiplying by r2 and dividing by E.
 Afterpulse A(r) is detector noise and is caused by turning on the detector prior to triggering the laser pulse. The initial signal spike on the detector causes the release of photoelectrons from the photodiode detector with time. The photoelectrons released during this process are recorded as an apparent signal (afterpulse), which is not associated with the true signal returns from the atmosphere. Afterpulse is determined by measuring the normalized signal when the MPL laser pulses are completely blocked prior to the first range bin. In this arrangement, the signal does not contain any return from the atmosphere and the measured signal is the normalized afterpulse (range corrected and energy normalized). The afterpulse is measured over 20 min and the average is used to correct the field measurements. The standard deviation during this period is used as a measure of the afterpulse error. To perform the afterpulse correction, the normalize afterpulse function is subtracted from the normalized signal.
 The overlap function O(r) is a multiplicative instrument effect and is due to the difference between the field of view of the transmit and receive paths in the MPL. Overlap causes a reduction in signal strength within the overlap range (typically ∼4 to 5 km) because the MPL cannot accurately image the incoming signals. The overlap problem must be corrected in order to analyze boundary layer aerosols using a lidar system. Our overlap correction is similar to work presented by Sasano et al. . Using vertically oriented lidar data, they assume that the atmosphere is constant through their overlap region (300 m), and then divide the affected signals by the signal at 300 m to calculate an overlap function. Our overlap range is much further than 300 m, and an assumption of atmospheric homogeneity in the vertical is not possible. It is much more likely to have the required homogeneity along a horizontal line of sight. Therefore our overlap correction process involves acquiring MPL data while the instrument is oriented horizontally. When plotting the natural logarithm of the normalized and afterpulse corrected MPL signal versus range, one should obtain a linear relationship at distances greater than the overlap range (where O(r) is = 1). The overlap function will be less than 1 for distances less than the overlap range, and the signal strengths are decreased. O(r) is determined by first performing a linear fit to in the region where the overlap is 1 (r > overlap range). O(r) is calculated by forcing the measured data to equal the fit line in the region r < overlap range, because the fit line represents what the measured data should be in the near range (assuming horizontal homogeneity). The error in the calculated overlap is a function of the standard deviation of the measured signals, the afterpulse error, and error in the linear fit. The overlap error equation is not shown here for brevity. Finally, to correct the measured signals for overlap problems, the normalized and afterpulse corrected signal is divided by O(r).
 The signal resulting from the correction process is referred to as normalized relative backscatter, PNRB(r), also known as NRB, is given by
PNRB(r) is proportional to the total backscatter coefficient at range r and is attenuated by the squared transmission (exponential terms combined) from 0 to range r. The term relative is used because an instrument parameter C is the proportion constant. Error in the NRB signals is a function of both the afterpulse and overlap errors (the equation is not shown here for brevity).
 Calibration involves determination of the lidar system constant C and should be performed routinely during a measurement campaign. C is determined during situations where all aerosols are contained within the boundary layer and where there is also a cloud-free section of air well above the top of the boundary layer. This region is termed the calibration zone.
 A 1 km deep calibration zone is identified using the following criteria. The NRB signal throughout the calibration zone must have a good signal-to-noise ratio. It is not possible to determine C accurately if the NRB signal errors in the calibration zone are large. Also, the NRB signals must decrease with range throughout the calibration zone in the same manner as expected for a Rayleigh-only NRB signal (calculated using modeled Rayleigh terms). If these conditions are met, then the calibration zone is assumed to have βp(r) = 0 at all ranges in the zone.
 C is calculated directly from the lidar signals in the calibration zone after determining the transmission. The transmission is a function of the Rayleigh optical depth (known) and the aerosol optical depth (AOD) from the MPL altitude to the calibration altitude. The AOD is input from an independent measurement using a Sun photometer. C is calculated at each range bin in the calibration zone using the following equation,
where C(r) is the calculated calibration constant at each range bin in the calibration zone, r1 is the bottom of the calibration zone, r2 is the top of the calibration zone, τA is the independent AOD measurement, and PNRB(r) is typically about a 10 min signal average. The values of C(r) are averaged to produce a final value for C. Periodic calibrations must be made during cloud-free periods of an experiment and a linear interpolation is used to generate values of C for any time during the experiment. The NRB signals are calibrated by dividing them by C.
 The error in C is termed ΔC and is calculated using the following equation:
where ΔPNRB is the combined NRB error and deviation in the measured signals during the calibration time period, ΔβR is the error in the Rayleigh backscatter value, ΔTR2 is the error in the Rayleigh transmission-squared term (first exponential in equation (A4)), and ΔTA2 is the error in the aerosol transmission-squared term (second exponential in equation (A4)). The maximum error for both Rayleigh terms was estimated by using a comparison of the two extreme Standard Atmosphere models. The tropical and subarctic winter atmospheres were averaged to produce a model Rayleigh profile. The deviation between the average model and the two extreme atmospheres was used to determine the maximum error for both ΔβR and ΔTR2. The results are considered the maximum expected errors since in reality the correct atmospheric model model is obtained far more accurately then our model assumed. The results (unpublished data) showed that the maximum error due to both Rayleigh terms combined was less then 2% at typical MPL calibration altitudes (approximately 6 to 8 km). The error in the ΔTA2 term is calculated using error bars on the measured AOD. The final ΔC for both MPL systems during INDOEX 1999 was calculated to be ±5% using the NRB error during the calibration measurements, the measured AOD error bars, an assumed total Rayleigh induced error of 1%, and an additional small error from the linear fit function used to determine C.
A4. Cloud Screening
 The calibrated signals, referred to as attenuated backscatter, were then cloud-screened by removing any signals with values greater than 0.8 (km sr)1 below the calibration zone. The cloud screen limit was chosen using the following procedure. True cloud lidar signal returns were identified a number of times throughout the cruise by comparing the lidar signals with images from a colocated upward viewing time-lapse camera (roughly bore-sighted to the MPL view angle). The average signal return from the clouds was used as the cloud screen limit given above.
A5. MPL Data Products
 The cloud-screened attenuated backscatter signals were averaged over 30 min periods on the ship, and 10 min periods at KCO, and then used to determine the final data products. The following MPL data products specific to this study include the following: top of the marine boundary layer (MBL top), units in km; top of the highest aerosol layer detected (top height), units in km; aerosol optical depth (AOD) at 523 nm (from 0 km to the top height); aerosol extinction-to-backscatter ratio (S ratio) at 523 nm, units in sr; profiles of aerosol extinction (σ) at 523 nm, units in km−1. Error bars are produced for each data product using ΔC, and signal noise determined by the standard deviation of the signal time average. Signal noise is due to a combination of fluctuations in the aerosol properties during the time average, and the signal-to-noise ratio which is dependent upon the background sunlight level and laser energy output.
 Throughout the experiment, the AOD of each cloud-screened signal average was calculated directly from signals in a particle-free layer of air above the lower troposphere. The layer was identified in the same fashion as used to pick the calibration zone. The AOD is calculated from the signals in the new zone by simply inverting equation (A5) to solve for the AOD.
 Aerosol layer heights were then determined. The layer detection algorithm is based on comparisons between the measured signal strength and the value of a calculated Rayleigh lidar signal that has been attenuated by the measured AOD. The top height is found be searching downward, one altitude bin at a time, from the calibration zone until a point when the measured signal strength is greater than the Rayleigh signal by a predetermined threshold setting. This altitude bin is identified as a possible top height. The signal average over the next 500 m is then compared to the Rayleigh signal in order to avoid false determinations caused by signal noise. If the comparison passes, then the initial altitude bin is termed the top height. The MBL top is found by searching upward from the surface, and computing the percent difference between the measured signal and the Rayleigh signal. If this value changes by more than a predetermined threshold between successive altitude bins, then the lower bin is identified as a possible MBL top. A similar signal average is conducted over the next 500 m (upward this time) to avoid false identification of the MBL top due to signal noise. If the comparison passes, then the initial altitude bin is termed the MBL top. During INDOEX a 5% threshold setting was used for detecting the top height and a threshold setting of 50% was used to detect the MBL top. The thresholds were obtained based on prior experience during an earlier cruise [Voss et al., 2001].
 The extinction profile and the S ratio are determined last using the inversion procedure discussed by Welton et al. . The predetermined AOD is used to constrain the inversion and is used to calculate the S ratio and then the backscatter profile. After determining the backscatter profile, the extinction profile is generated by multiplying the backscatter values by the S ratio. For situations containing both a MBL and aerosol above, the two layers can only be treated separately if there is an aerosol-free layer of air at least 1 km long between the two layers. The latter did not occur during INDOEX, and therefore the extinction profile for both the MBL and above had to be calculated together by assuming that the S ratio is constant with altitude from the surface to the top height. Errors induced using a constant S ratio are discussed further by Welton et al.  and in section 4.
 Baseline errors for the data products were estimated using only ΔC and error propagation of each term through the algorithm process. The estimated baseline error for the AOD was ±0.02 for the MPL systems, and the baseline error in determining aerosol layer heights is estimated at ±0.075 km. The baseline error for extinction values in a profile is estimated to be ±0.005 km−1, and ±5 sr for the S ratio. The actual error bars on individual measurements may be larger than the baseline errors due to signal noise.