The focus of this study is to model and validate the performance of intensity-modulated continuous-wave (IM-CW) laser absorption spectrometer (LAS) systems and their column measurements from airborne and satellite platforms. The model accounts for all fundamental physics of the instruments and their related measurement environments, and the modeling results are presented statistically from simulation ensembles that include noise sources and uncertainties related to the LAS instruments and the measurement environments. The characteristics of simulated LAS systems are based on existing technologies and their implementation in existing systems. The modeled instruments are specifically assumed to be IM-CW LAS systems such as the Exelis’ airborne multifunctional fiber laser lidar (MFLL) operating in the 1.57 μm absorption band. Atmospheric effects due to variations in , solar radiation, and thin clouds, are also included in the model. Model results are shown to agree well with LAS atmospheric measurement performance. For example, the relative bias errors of both MFLL simulated and measured differential optical depths were found to agree to within a few tenths of a percent when compared to the in situ observations from the flight of 3 August 2011 over Railroad Valley (RRV), Nevada, during the summer 2011 flight campaign. In addition, the horizontal variations in the model differential optical depths were also found to be consistent with those from MFLL measurements. In general, the modeled and measured signal-to-noise ratios (SNRs) of the column differential optical depths () agreed to within about 30%. Model simulations of a spaceborne IM-CW LAS system in a 390 km dawn/dusk orbit for column measurements showed that with a total of 42 W of transmitted power for one offline and two different sideline channels (placed at different locations on the side of the absorption line), the accuracy of the measurements for surfaces similar to the playa of RRV, Nevada, will be better than 0.1% for 10 s averages. For other types of surfaces such as low-reflectivity snow and ice surfaces, the precision and bias errors will be within 0.23% and 0.1%, respectively. Including thin clouds with optical depths up to 1, the SNR of the measurements with 0.1 s integration period for surfaces similar to the playa of RRV, Nevada, will be greater than 94 and 65 for sideline positions placed and , respectively, from the line center at 1571.112 nm. The column bias errors introduced by the thin clouds are for cloud optical depth , but they could reach for more optically thick clouds with optical depths up to 1. When the cloud and surface altitudes and scattering amplitudes are obtained from matched filter analysis, the cloud bias errors can be further reduced. These results indicate that the IM-CW LAS instrument approach when implemented in a dawn/dusk orbit can make accurate column measurements from space with preferential weighting across the mid to lower troposphere in support of a future ASCENDS mission.
© 2013 Optical Society of America
Atmospheric carbon dioxide () is one of the major greenhouse gases in the Earth’s climate system. The concentration within the atmosphere has been significantly changed over the last 150 years, due mainly to anthropogenic activities. The Intergovernmental Panel on Climate Change (IPCC) estimated that the change of the concentration in the atmosphere produces approximately a global radiative forcing , which is a key factor causing a net radiation imbalance, or heating at the top of atmosphere (TOA), to the climate system [2,3]. The long-term TOA radiation imbalance could lead to a significant global temperature increase . Furthermore, atmospheric is a crucial part of the Earth’s carbon cycle. Currently, there are unacceptably large uncertainties in estimated budgets even for global annual means (50% or more) . Comprehensive measurements of global atmospheric distributions are urgently needed to develop a more complete understanding of sources and sinks. The U.S. National Research Council has recommended a midterm space mission of Active Sensing of Emissions over Nights, Days, and Seasons (ASCENDS) in its decadal survey report for Earth science and applications from space  to address the aforementioned need for global monitoring. The ASCENDS mission calls for global light detection and ranging (lidar) measurements of atmospheric column densities using the integrated path differential absorption (IPDA) technique with preferential column weighting across the mid to lower troposphere. The space implementation will consist of a laser absorption spectrometer (LAS) system capable of column measurements during day and night, over all seasons, and in the presence of thin clouds. To enhance the accuracy of current flux transport models as well as to better quantify the long-term climate effects of increasing anthropogenic emissions, high-accuracy and high-precision column-integrated mixing ratios () are required to be determined to within 1.0 ppm or approximately 0.26%. The first critical step in determination of is the measurement of the column density. Besides the measurements of column densities, a separate means of determining the surface dry air pressure is required to convert column densities to . One solution for obtaining the dry surface pressure is to simultaneously measure the column density and scale it to the equivalent dry surface pressure. The scope of this study focuses on the modeling of column density measurements from airborne and satellite platforms as the first step in the simulations of atmospheric measurements. Modeling of column measurements will be studied later.
In preparing for the ASCENDS mission, Exelis Inc. developed an airborne prototype LAS instrument for column measurements, and NASA Langley Research Center (LaRC) has been assessing the space-based capabilities of the LAS instrumentation, including the accuracy and precision of the and column measurements. Results of the column measurements from aircraft flight campaigns using the Exelis’ prototype LAS instrument have been very encouraging . The column measurements were in excellent agreement with in situ derived columns to within 0.17% or . The signal-to-noise ratio (SNR) for IPDA measurements of optical depths for a 10 s average (horizontal distance of ) was found to be as high as 1300, resulting in a column precision estimate of 0.1% ( equivalent of ). The LAS instrument used in these measurements is an intensity-modulated continuous-wave (IM-CW) multifunctional fiber laser lidar (MFLL) that operates in the 1.6 μm absorption band with one laser line on the absorption line center at 1571.112 nm, and two other laser lines are on either side of the absorption line where the atmospheric absorption is very low . The two offline wavelengths equally spaced on either side of the absorption line are used to (1) demonstrate the feasibility of transmitting multiple laser wavelengths from a single laser transmitter, and (2) evaluate and remove biases from any spectral dependence in the receiver characteristics and atmospheric effects.
To be able to accurately predict the performance of a future ASCENDS LAS system, an accurate model needs to be developed and validated with LAS observations. This model must be able to incorporate the latest technologies and operational techniques to accurately represent the global performance of the LAS system, including the random and systematic affects that go into determining the global distributions of . This study is targeted at modeling IM-CW LAS systems for column density measurements, verifying the model results with MFLL observations, and projecting the performance of a future spaceborne system for these measurements.
Recently, several studies have reported simulations of IPDA measurements for space applications [7–10]. Both pulsed [8,9] and CW [7,10] systems have been studied. These space simulations were based on LAS instrument technologies and operational modes that are expected to be available for the upcoming ASCENDS mission. The SNR of differential column optical depths and its relationship with LAS transmitter power and measurement uncertainties for spaceborne systems were some of the key areas of these investigations. Other important factors that were studied included the selection of appropriate absorption lines, telescope sizes, and ranging capabilities. These simulations indicated that a space-based LAS could make high-precision column measurements () with several seconds of averaging from a relatively low average power system . As with MFLL, the absorption lines around the 1.6 μm band were chosen because of the availability of commercial telecommunications laser technologies in that wavelength region. However, the specific online positions are slightly different for the spaceborne implementations due to the large optical depth at the line center. To optimize the pressure weighting function to the near surface and also to obtain strong enough received laser power while maintaining sufficient differential absorption optical depth, sidelines slightly off the center of the selected absorption lines (for example, and offset from line center) are being considered for space applications. The choice of two sidelines (at 3 and 10 pm from the line center) can improve vertical weighting of column and flux inversion retrievals . Telescope sizes of diameter are being used in the simulations, as these can readily be accommodated by a medium-sized spacecraft such as that being proposed for the ASCENDS mission. Pulsed systems intrinsically have high-accuracy ranging capabilities, while the proposed IM-CW LAS systems  require the utilization of phase information from the modulated return signals to provide accurate ranging information. These modeling and simulation studies pointed out clear directions for LAS system designs and laid a solid foundation for the formulation of an IM-CW LAS space mission.
Since there is a long history of using CW laser systems in the 1.6 μm band for telecommunications , high-power CW lasers in this region have advantages over their pulsed laser counterparts for satellite observations. Currently, more space-qualified CW laser components are available, and the high-average-power CW lasers required for these space applications are expected to be available in the next 3–5 years . Furthermore, CW LAS systems simultaneously transmit all of the IPDA wavelengths to the surface in the same beam, and thus they have the same sensing volumes and surface footprints for all the different wavelength channels, which significantly reduces the uncertainties in the column retrievals introduced by atmospheric and surface reflection variations. This study is targeted at the modeling and simulation of IM-CW systems for column measurements. Compared to previous work [7–10], this study simulates the column measurements using the current MFLL system architecture and knowledge of system components available for LAS system development. Furthermore, this study considers advanced IM-CW schemes aimed at achieving ranging capabilities similar to those described in [6,12], which overcome the ranging limitations of previously simulated CW LAS space systems . The model that we have developed is a physically based simulation system, and our results are generated from simulation ensembles of at least 100 model runs that are statistically distributed due to the noises and uncertainties related to instruments and environments.
Basic theoretical considerations of highly accurate column measurements, especially the IPDA technique and ranging capability for both the instrumentation and simulation models, are presented in Section 2. Based on these considerations, the LAS instrument design and the simulated LAS systems are discussed in Section 3. Simulation results, compared to airborne data and predicting the performance for space applications, are presented in Section 4, while Section 5 provides a summary of this simulation study.
2. Methodology of Column Measurements
A. IPDA Measurements for Column Retrieval
As mentioned in the introduction, the science requirements for the accuracy of atmospheric column measurements for the ASCENDS mission are very high. These requirements could be achieved through an active IPDA technique (cf., e.g., [6–8,13,14]) that measures the difference of the total gas absorption along the path length between two or more laser wavelengths. The wavelengths of the transmitted lasers need to be very closely spaced (typically less than 100 pm) to eliminate the wavelength dependence of atmospheric scattering and surface reflectance from producing errors in the IPDA measurements, and to minimize speckle effects. For the MFLL airborne system, one laser wavelength is positioned at the center of the absorption line at 1.571112 μm (called the “online”), and two other laser wavelengths are positioned in the distant wing of the absorption line at offsets of (called the “offlines”) . All the IPDA wavelengths were selected to minimize water vapor and other trace gas effects on the differential absorption between the online and offline measurements .
For a nadir viewing remote sensing laser system, the received signal power at wavelength can be considered as an integrated result of the backscattered powers from all atmospheric scatters and the surface; that is,8,10]), the received power at wavelength from a Lambertian surface with albedo and reflectance in the direct backscatter direction can be expressed as 10] 15–17]. Generally, compared to gas absorption, the Rayleigh scattering contribution to the extinction of the laser light in the considered wavelengths is very weak. Also, the wavelength dependence of at the closely spaced IPDA laser wavelengths is negligible.
The backscatter returns from intermediate atmospheric scatterers can be expressed similarly to those from the surface. Corresponding changes in Eqs. (2) and (3) for an intermediate backscatter layer basically include the range, the number of intermediate backscatter layers, the gas absorption optical depths, and the replacement of surface albedo related terms with backscatters as shown in . Because of the capability of range discrimination with an IM-CW LAS system, surface signal returns are mainly considered here. Analysis of the effects of intermediate backscatters and ranging capability will be discussed in the next subsection. When return powers at two closely spaced wavelengths (assuming for online and for offline) are measured and assuming surface albedos at these wavelengths are the same, the grand power ratio of the two received returns becomes4) is reduced to 6) further reduces to 8) would also include the contribution of the differential water vapor optical depths and must be accounted for in retrievals. We also note that the retrieved optical depth exhibits an altitude weighting that depends on the location of the laser lines with respect to the absorption line profile [6–8]. For certain studies such as transports, information regarding the amounts in the boundary layer as well as the free troposphere is important. Thus, more than two laser lines with different altitude weighting functions are needed to address this for space missions.
Equation (8) shows that the differential optical depth , and hence the column number density, can be determined via the combination of an online wavelength located on the absorption line (not necessarily at line center) and an offline wavelength somewhere in the distant wings of the absorption line but within of the online spectral location. Also, obtaining highly accurate measurements of the differential optical depth or grand power ratio is the key for high-precision remote sensing of column amounts. The simulated IPDA remote sensing system that demonstrates the capability to achieve required accurate measurements will be discussed in the following section.
B. Ranging Capability
A significant difference between our current simulation model and those from previous studies [8–10] is that the current work adds a sophisticated ranging capability, such as from the use of swept-frequency and stepped-frequency IM schemes [6,14], into the simulated LAS measurement system. The ranging capability is needed owing to the high-accuracy and high-precision requirements of the differential absorption optical depth measurements and the previously unaccounted for influence of intervening scattering layers on these measurements. Range variations during different data integration periods will cause changes in the optical depth during that period, are a potential error source in the IPDA optical depth estimates, and must be quantified. Also, this capability extends measurements of the LAS system from only those under clear skies to those with thin clouds and/or aerosol-scattering conditions, which effectively increases the remote column measurement rates for gridded data.
Since the range to the backscatter layer for a lidar system is proportional to the time delay of the transmitted laser signal to the backscatter layer, the ranging capability from an IM-CW LAS system can be realized through a time-dependent frequency modulation of the transmitted power amplitude . For example, in the swept modulation case,1) can be expressed as 2) and (3)].
With range encoded signals, such as those expressed in Eqs. (9) and (10), a phase sensitive detection system can clearly discriminate laser powers reflected from the surface against those from other intermediate backscatters [6,12,14,18]. A commonly used technique in the detection system for signal discrimination is a matched filter  that correlates the range encoded modulation waveforms with the recorded signals. Figure 1 illustrates the ranging capability of a swept-frequency IM system. The simulation is for an idealized case of a target at 12 km range with an intermediate backscatter in the middle between the LAS and the target. The plots have arbitrary units, due to the use of normalized power. The laser system simulated here has three channels. The simulated sampling rate, swept-frequency bandwidth of the IM waveform, and UR are 2 MHz, 500 kHz, and 15 km, respectively, which are consistent with the current airborne MFLL LAS system . The sampling rate and UR lead to the inherent range resolution of 75 m and 200 samples per IM frequency sweep. The bandwidth of the IM waveform dictates the sharpness of the main-lobe peaks of the matched filter decomposition of the return signal, which is critical for discriminating several closely spaced scattering targets. The power ratios for the received signals among these three channels are assumed to be . Figure 1(a) shows these simulated laser signals (i.e., neglecting noise) before entering the detector. The detector simultaneously receives the combined signal from the three channels, which is then passed through an electronic bandpass filter to reduce background noises and to avoid spectral aliasing as illustrated in Fig. 1(b). Note that the bandpass filter also removes the DC component of the signal after the detector as shown in Figs. 1(b)–1(d). The beat frequencies among the three channels are clearly shown in the variations of the signal power with the time delay due to the IM scheme used [Fig. 1(b)]. However, the detector would not only detect signals from the target but also those from the intermediate scatterers and background noise sources. A further assumption is that the received signal power from the intermediate scatterer is equal to that of the target, and the noise level is as high as the return signal power from both scatterers. Compared to candidate IM waveforms [cf. Figs. 1(a) and 1(b)], the signature of swept-frequency modulation in the received signal [Fig. 1(c)] seems to be very weak due to three-channel signal mixing, a combination of signals from target and intermediate backscatter with different time delays, and noises. Even in this case, the matched filter technique with a 0.1 s integration period clearly demonstrates the capabilities of detecting weak target signals and minimizing the effects of intermediate scatterers and noises. The outputs of the matched filter show two distinct correlation peaks corresponding the target and intermediate scatterer [Fig. 1(d)]. When the intermediate scatterer is located nearer to the target, the two peaks of the matched filter outputs would be closer to each other. The wider the IM bandwidth, the narrower the peaks and the easier it is to differentiate between two closely spaced scattering objects. Besides the detection of target signals, Fig. 1(d) also illustrates that the target range can be estimated by measuring the time delay of the peak power of the target reflection. Generally, a broader bandwidth, along with a higher sampling rate, would provide a more precise measure of the time delay and enhance the ranging capability of LAS systems.
Although a 2 MHz sampling rate results in a range resolution of 75 m, considerably smaller range errors can be achieved by applying curve fitting techniques to the correlation shape of the matched filter outputs . The initial development in range estimations used a sinc function as the fitting curve, which produced range errors as small as 3 m . This study focuses on the retrievals of integrated differential optical depths, i.e., column estimates.
3. LAS Simulation Model
LAS systems for column measurements generally have a laser transmitter, a receiving telescope, a data acquisition system, and a signal-processing unit. Environmental conditions that affect the column measurements include solar background radiation, atmospheric gas, cloud, aerosol, and surface reflectance. The simulation system for these LAS measurements consists of the initialization, the instrument and measurement modules, the control of the simulation, and the output (Fig. 2). For a modeling case, the parameters of individual components of simulated instrument and environmental and flight conditions are uploaded to the simulation system in the initialization. The number () of simulation runs for a statistical ensemble is also set up in this stage. LAS instrument and column measurements are simulated in the transmitter, environment, receiver, and postprocessing modules by their physical characteristics. Noises related to transmitter and receiver are included in their corresponding modules. The influence of environmental conditions on received radiation such as solar radiation, clouds, surface reflection, speckle, and turbulence is simulated in the environmental module. The postprocessing module simulates matched filter, data processing, and calculations of the peak power, differential optical depth, range, and SNR values of and . When the number of iterations for the single modeling case reaches the value defined in the initialization, the ensemble of simulated results is calculated at the end of this simulation system.
It can be seen that the main program of this simulation system features the transmitter, environment, receiver, and postprocessing modules that represent LAS instruments and environmental conditions for differential absorption optical depth measurements. Details in the simulation of individual instrument components and environmental conditions within these modules will be discussed in following subsections. Here we provide a brief overview of these simulation modules. Figure 3 illustrates the basic elements within these simulation modules. The simulated LAS system has a similar design structure to the current airborne MFLL instrument that has demonstrated the capability of highly accurate measurements of the column . Since detailed information about the instrument can be found in , this paper only provides a brief description of the simulated LAS system. It is emphasized that MFLL is a demonstration unit and not a fully optimized system, as it is mostly composed of commercially available components. Individual elements in the figure were simulated by their functions, characteristics, or signal waveforms, which are important for IPDA measurements. Noises associated with these elements were also incorporated into the simulations. One of the key attributes of this simulation model is that signals were simulated through each stage of the IM-CW LAS system, including signal generation, detection, and processing. Because of the noises within the instrument and uncertainties related to environmental conditions, the output of modeled results was obtained from statistical calculations of the multiple simulation runs even though the entire simulation was based on a physics-based model of the instrument and the optical depth measurements.
A. Transmitter Model
Seed signals are simulated for individual online and offline channels of the LAS system based on characteristics of the distributed feedback (DFB) lasers and fed into their corresponding modulators. The modulator signals are modeled according to their modulation schemes provided by the modulation generator (i.e., local oscillator simulator, Fig. 3). Although various modulation schemes can be generated from the local oscillator, instrument operations and our simulations at any given time only use one modulation scheme. The modulated online and offline signals are amplified to simulate the amplification using an erbium-doped fiber amplifier (EDFA) and sent to the environment module as single laser beam to model the transmission of the signals to the atmosphere. A tiny fraction of the amplified laser signals is used in a reference detector representing fiber tapping of the amplified laser signals to a reference detector as a reference signal for transmitted laser power calibration, which is needed to achieve accurate grand-power-ratio estimations, as seen in Eq. (4). These processes can be expressed in a similar way to those in Eq. (10), except noise is included. Thus,
B. Environmental Conditions
Environmental conditions are important to specify for measurement simulations. Gas absorption cross sections are mainly determined by atmospheric temperature, pressure, and moisture profiles. Surface reflectance and its variability play a critical role in determining the magnitude of the laser reflected signal from the surface. Solar radiation adds background light and associated shot noise at LAS laser wavelengths. The impact of the detected background light and associated noise is minimized by the matched filter because they are uncorrelated to the IM waveforms of the transmitted laser signals. Thin clouds and aerosol layers not only introduce their power returns at different time delays from those of surfaces but also reduce the signal power from surfaces. Furthermore, speckle and atmospheric turbulence increase the uncertainty in the measurements.
For this study, gas absorption coefficients at individual laser wavelengths were calculated using the HITRAN 2008 database . To achieve high accuracy in the calculation of the absorption cross sections, the line absorption parameters from recent measurements  were included and the Voigt approximation for the absorption profile was used. The absorption from neighboring lines was also included. The atmospheric profiles of temperature, pressure, and moisture were taken from either climatological atmospheric profiles  or in situ measurements. Variations in the surface type can produce huge variability in the surface reflectance. Surface types can vary from white deserts with albedos as high as 0.55 to water bodies with albedos less than 0.09 under high wind conditions [23,24]. Even within the same type of surface, the variability in the surface reflection can be significant . Many factors, such as surface roughness, moisture, topography, etc., can introduce large variations in the reflectance. Although the IM-CW approach being considered in this work minimizes the surface reflectance effect due to the simultaneous transmission of all wavelengths, this effect was included in the simulation because of this importance for remote sensing. Solar radiation within the bandwidth of the receiver optical filter at TOA is estimated through blackbody emission of the sun. The absorption and scattering of solar radiation was treated in the same way as the LAS laser light except the downward radiation was dependent on solar zenith angle and gas absorption from TOA to surface. For airborne systems, the gas absorption of the laser beams is only for the path length from the aircraft, not from TOA, to the surface.
For thin clouds, a uniformly distributed cloud vertical profile is assumed where physical thickness is arbitrary and normally set to be 300 m, similar to previous studies [25–27]. The reflectance of thin clouds with optical depth can be expressed as 16,28]. is assumed to be 1 and 0.5 for airborne and spaceborne cases, respectively, based on previous lidar measurements and data analyses [15,16,28,29]. Similar to clouds, aerosol-scattering characteristics were initially modeled by a uniformly distributed profile. This profile can be easily adapted to other aerosol vertical distributions to meet observation and modeling needs. Values of and 50 sr were used for the backscatter coefficient and extinction-to-backscatter ratio , respectively, for the aerosols .
The number of statistically independent cells generated during the integration period and within receiving aperture of the LAS system determines the impact of speckle noises on the received signals. The noise level of speckles is inversely proportional to the product of and . The calculation of and is straightforward and can be found in [8,10]. Because of the relatively long integration period and large telescope size (or big and numbers), the effect of speckle on signal measurements is usually small. For the effects of atmospheric turbulence on laser light intensity, the turbulent strength is considered. A common indication of the strength is the parameter of atmospheric structure constant [30–32]. This structure constant determines the variance of the turbulence fields , which further generates uncertainties in the laser intensity as log-normal distributed noise sources. For this study, a value of is used. This value corresponds to very weak turbulence cases [30,32]. Since most of the IPDA measurements considered in this study are under either clear sky or thin cirrus conditions, the atmosphere is generally stable in meteorologically spatiotemporal scales. Thick or convective clouds are normally associated with much stronger turbulences and are beyond the scope of current simulation and the studied IPDA LAS remote sensing. Remote sensing of column amounts above clouds is one of the key areas for future studies.
C. Receiver Modeling
One key part of the receiver is the detector and amplifier subsystem. At the detector, model-calculated received laser radiation at the online and offline wavelengths, along with solar background radiation, is converted to detector currents simultaneously, which can be expressed as7,8,10]. Specifically, their noise spectral densities can be expressed as
A transimpendence amplifier (TIA) is simulated to convert the current signal out of the detector to a voltage signal and amplifies the signal voltage proportional to the TIA feedback resistance . Besides the thermal noise like that of the detector, the TIA also introduces extra preamplifier noise from its electronic input noise current and voltage. The noise spectral density can be expressed as
The voltage signal from the detector-TIA subsystem, along with all of the external and internal noises, is fed into a Butterworth bandpass filter to avoid aliasing and to further limit noise bandwidth before converting them into digital forms. In the simulation of the digitizer, quantization noises based on a uniform distribution of half of the digital step size are generated in the simulated signal series. It is emphasized that for the receiver of the LAS system, reference channel signals used in internal calibration are basically treated the same as those of the science channels. Thus, their simulation is similar except without influences from solar background, atmosphere, and surface.
The key element for postprocessing of recorded data from the digitizer is the matched filter that convolves its impulse response function with the recorded data. Within the matched filter, each channel has its own distinct impulse response function that depends on the IM modulation waveform for that channel. This process can be expressed as2.B. The peak magnitudes of individual channels are proportional to the powers received for their corresponding channels and are used in the retrievals of column amounts. Thus, they lead to the estimates of differential optical depth, while the location of the peaks and shape of the entire correlation functions are used to estimate the range. Since the postprocessing for simulated signals is the same as that for actual instrument measurements, the postprocessing details can be found in a previous report .
The simulation model developed for remote sensing by this study is designed for broad applications. It has many components, including instrument characteristics, environments, signal processing, and data analysis. For this kind of complex simulation model, certain tests and validations of the model are needed. For this purpose, the model and simulated results were evaluated using various techniques including basic lidar equation calculations, model predictions of lidar power returns against the data acquired in test-range experiments involving hard targets, and comparisons with aircraft flight campaign data. Based on the confidence from these evaluations, simulations of column measurements from space were conducted.
As an initial test, comparisons of simulated power returns from the model with those using the analytical form of the lidar equation found that the two calculations yielded almost the same results when all noises in the simulation model of the LAS system were turned off. These comparisons provide critical theoretical assessments for some of the fundamental elements of the current modeling system. To further evaluate the simulation model, the predicted model results were compared with ground-based measurements where the measurement environment was closely monitored and controlled. The ground measurements were conducted using the MFLL instrument in a horizontal viewing mode in an 860 m long test range at LaRC during July–August 2012. Only essential issues related to this study from this test-range experiment are discussed here. Tested surface targets were calibrated with the standard diffuse reflectance products of LabSphere, Inc. (http://www.labsphere.com/products/reflectance-standards-and-targets/spectralon-reflectance-standards/default.aspx). These targets covered a wide range of reflection from various types of products including bright, white, light gray, dark gray, and black, with albedos of 0.78, 0.45, 0.30, 0.14, and 0.04, respectively. The albedo values of various global surface types are generally within the albedo range of these targets. For example, high reflectance of the desert of RRV, Nevada, is close to that of the white target. Weak or very weak reflections of water bodies and snow and ice surfaces are within those of dark gray and black targets based on previous estimations . Figure 4 shows a comparison of the model-predicted LAS returned powers with those measured by the MFLL at the test range. The measurements were conducted during nighttime, which reduced the influence of solar background noises. Corresponding to the measurement condition, solar radiation was turned off in the model for these simulations. There is a very good agreement between model predictions and MFLL measurements for the tested albedo range, which verifies certain fundamentals of the laser beam power propagation in the current LAS model. As expected, linear relationships of lidar return power with target albedo were obtained from both simulated results and MFLL measurements because the return power is proportional to the albedo as shown in the lidar equation [cf. Eq. (2)]. The only outlier was the measured return power from the light gray target (albedo 0.30). The exact reason for the deviation of the return power of this target from a linear relationship is unclear. It is likely that the target does not perfectly obey the Lambertian assumption. The instrument operated on a absorption line that is normally avoided by target calibrations. Also, the specified reflectance of this target could differ from its actual value at the instrument wavelengths. Because of this uncertainty in the quality of the light gray target, the data analysis from the range testing avoided using the target results in the instrument and algorithm comparisons. As mentioned before, details for the range test will be reported in a separate paper, currently in preparation, as these details are not needed in the discussion of the work presented here.
Comparisons were made between the column amount estimates from the model and observations from the DC-8 flight campaign conducted in the summer of 2011 , which provided longer ranges and higher optical depths than the test range. Because the key factors in evaluation of both simulated results and measurements for accurate column remote sensing are the values of the grand power ratio and differential optical depth [cf. Eq. (8)], hereafter this study focuses on the these crucial values, along with their SNR, bias, and relative accuracy. The cases simulated are for the flight over the RRV playa on 3 August 2011. The playa is located at an elevation of more than 1 km over sea level and is generally dry even during the summer time. This site was selected because it currently serves as a satellite radiometric calibration location for the Japanese Greenhouse Gases Observing Satellite (GOSAT) . Ground-based investigations of this surface site have been made for its albedo and reflectance properties . The MFLL column measurements were made at three different altitudes above the playa: 6.1, 7.6, and 9.1 km. (Note: pressure altitudes of these flight legs were controlled at 20, 25, and 30 kft ASL, respectively.) Table 1 lists the basic parameters of the MFLL instrument that were used in the simulations. The three channels of the instrument listed in the table are represented as On, Off-1, and Off-2, respectively. The atmospheric profiles, especially for contents, were obtained from airborne in situ measurements. More details on the instrument and the flight campaign can be found in a previous paper .
The model was used to simulate the MFLL measurements at all three altitudes above the playa. The number density profile and absorption cross-section profiles for each of the individual channels were calculated based on the in situ measurements and assumed spectroscopic considerations discussed in . A playa surface albedo of 0.553 at 1.57 μm was assumed based on an independent Lambertian albedo estimate of 0.45  with an additional laser backscatter enhancement of 23% on average . The albedo variation for 2 MHz LAS samples within an integration period (0.1 s) over the playa is set to be 10%. However, the difference in surface types dominates the observed large-scale differences in average reflectance . There are significant spatiotemporal scale dependences in the variability of surface reflections. For example, with a 2 MHz sampling rate, which represents 0.1 mm horizontal distance at aircraft speeds of , the LAS FOV would essentially have no changes between samples; that is, the reflectance variations for laser beams at very fine scales would be negligible. Meanwhile, at a few tens of meters spatial scales, the variability can be very large, as demonstrated in . At larger spatial scales (of order 100 m), the averaging processes would begin to smooth out large variations in surface reflectance that occur on the smaller spatial scales. At even larger scales (), the reflectance variability would depend on large-scale surface type, moisture, and topography changes. A moderate number (10%) of the variability in reflectance is used in the model due to the instrument’s moderate integration period and quick sampling rate for individual laser samples. Clearly thorough studies on the scale dependence of surface reflections are needed, but this is beyond the scope of the current study.
Figure 5 shows comparisons of model simulations and aircraft measurements. Because of the importance of both Off-1 and Off-2 channels in assessment of the instrument technology development and simulation performance, the results of the grand power ratios [Figs. 5(a) and 5(b)] and differential optical depths [Figs. 5(c) and 5(d)] from Off-1 and Off-2 are given in the figure. It is emphasized that the Off-1 channel has a transmitted power 50% higher than that of the Off-2 channel, and, thus, it has been used in the retrievals of column amounts. It can be seen that the variations for both simulated results and observed data are very small: relative changes in the and values using a 0.1 s integration period are within about 0.5% and 1%, respectively. For example, the simulated grand power ratios of the On and Off-1 channels for the highest altitude of 9.1 km flight case [Fig. 5(a)] are generally very stable with a value around 0.627. Small random changes on the order of a few thousandths can be observed. This variation in the values is a combined result of the noises from the transmitter, detector-TIA, and environment, such as solar background radiation. This consistency is also found for other cases and other online and offline combinations such as that shown in Fig. 5(b) for On and Off-2 channels of the 7.6 km altitude case. Because the simulated and measured grand ratios generally agree, the simulated differential optical depth values are also very close to the measured values for different altitudes and online/offline combinations [cf. Figs 5(c) and 5(d)].
Table 2 summarizes the results of the simulations and provides a quantitative assessment of the model for the key parameters in MFLL column measurements. It can be seen that SNR values are generally much smaller than their corresponding SNR values since the SNR of is the product of the SNR of and as shown in the table. As expected (also cf. Fig. 5), the simulated SNRs of and are within 20% of the instrument measurements at the mid and upper altitudes, but are overestimated by about 65% at the lower altitude. The averaged SNR differences are about 30%. Small differences in the modeled performance of various LAS system components could account for the observed differences between model and measurement results. For example, the model does not include a detailed spectral response function for the entire MFLL electronic subsystem. Although the characteristics of individual components may be simulated very well, the simulation of the entire measurement system could still have small differences owing to lack of some secondary details of MFLL. Potentially unknown issues within the instrument could be another factor for the differences in the simulation, particularly at lower altitudes where detector and beam overlap issues become more critical. Slightly better performance is seen in the combination of On and Off-1 channels than that of On and Off-2 channels in both simulations and observations. This is a direct result of the fact that the Off-1 channel transmits and receives stronger powers than the Off-2 channel does. Both the model-simulated retrievals and the instrument measurements of are very close to the in situ derived values, which only includes . The relative bias errors of both simulated and measured differential optical depths are within a few tenths of percent of the in situ observations. The high precision and accuracy of the IPDA measurements of the MFLL instrument have been demonstrated in previous studies . We note that the simulations and measurements are being compared on a 0.1 s (or 10 Hz) temporal scale, and longer time averages would increase SNR values even further.
The simulation for spaceborne column measurements is based on expected advancements in the capabilities from current airborne systems. A sun-synchronous, dawn/dusk orbit as suggested by [8,9] with a simulated spacecraft altitude of 390 km is assumed in this analysis. Changes in the specifications of the space system compared to current airborne systems include having two online wavelengths with (called Side-1) and (called Side-2) offset from the absorption line center, respectively, increasing the total transmitted laser output power to 42 W with a power split of among the three wavelengths and telescope diameter to 1.5 m, and reducing the optical bandpass filter bandwidth to 0.5 nm FWHM and laser half-angle divergence to 50 μrad. The corresponding receiver’s FOV is set to 33% larger than that of laser divergence. The optical throughput of the space system is increased from 0.085 to 0.65 due to direct imaging of the received light onto the detector instead of using a fiber coupling approach similar to that used in the airborne system. Additional change is to use an improved detection subsystem  in current space simulation. The sideline wavelengths are selected to avoid excessive absorption of the entire atmospheric column at the line center for the space case and to have more weighting of the measurement across the mid to lower troposphere, where most of the flux exchanges with ecosystems and transports within the atmosphere take place . The basic information of the subsystem is listed in Table 3. The 42 W output power specification is consistent with the technology development plan of the IM-CW LAS approach for the ASCENDS mission and other studies , although it may be much higher than some suggested low-power transmitter systems . The high-output power could help ensure a sufficient carrier-to-noise ratio in the detector–TIA subsystem and maintain high measurement accuracy even for weak reflection surfaces or in moderately attenuating atmospheres.
To provide both quantitative and qualitative evaluation of simulated results of space column measurements, the simulation results must be compared to ASCENDS mission measurement requirements. For ASCENDS, the top-level accuracy and precision requirements are stated in terms of those for column mixing ratio measurements at a spatial scale of about 70 km (or in 10 s temporal interval) over the areas with the surface reflectance similar to that of the RRV playa under clear conditions. For the column amount measurements, thus, the required accuracy and precision must be higher than those for the mixing ratio since some of the error budget must be allocated to the (or dry air pressure) measurements and all other uncertainties, such as satellite pointing geometry uncertainties and uncertainties in calculated absorption coefficients caused by uncertainties in the atmospheric profiles of temperature, pressure, and humidity. Considering a required total error budget for column mixing ratio measurements of 1.0 ppm or 0.3% and assuming the variance error in column measurements could be assigned one third of the total error of the column mixing ratio measurements, the required accuracy and precision of column measurements, thus, would be equivalent to or 0.15%. The corresponding SNR requirement on column differential optical depth measurements is approximately 670. At a 700 m spatial scale (or 0.1 s temporal scale), the SNR requirement would be about 67. For surfaces with reflectance values other than that of RRV, the return power of LAS signals of these surfaces would be proportional to the change in surface reflectance. Thus, the SNR requirements should be rescaled to be consistent with those of RRV. For example, for a dark surface of snow and ice with reflectance, the SNR requirement of 10 s integration time would be scaled down from 670 to 61. These are very stringent measurement requirements. The following evaluation of the simulated satellite column measurements will be mainly aimed at them.
The simulated results for the different surface reflectances ranging from to under clear sky conditions are shown in Fig. 6. These reflectance values represent various surface reflectance conditions from very dark (such as snow and ice) to bright (such as RRV playa) surfaces. The simulated results show that the satellite measurements will be more accurate from the measurements with the Side-1/Off combination than from those of the Side-2/Off combination, and this is due to the values being larger for Side-1/Off than Side-2/Off. Assuming that the returned signal powers of the three channels are similar, a larger would generally result in smaller relative errors. For both combinations, high SNR (or precision) and absolute accuracy measurements of differential optical depth from space could be made. SNR values [Fig. 6(a)] generally vary from about 200 to 66 and 130 to 44 for Side-1/Off and Side-2/Off, respectively. While the precision for the Side-1/Off combination is higher than for the Side-2/Off combination, as discussed earlier the Side-2/Off has higher weighting near the surface than Side-1/Off, and a combination of the two improves vertical flux inversions . Thus, the precisions of 10 s measurements will be better than 0.1% and 0.23% for bright and dark surfaces, respectively. The relative reduction in SNR values is slower than the decrease rate of surface reflectance because the noise level, especially shot noise, is lower when the received signal and background power is weaker. The relative bias errors [Fig. 6(b)] are small and all within 0.1%. The bias errors for Side-2/Off retrievals, which are more important for lower tropospheric measurements, are even smaller and below .
We note that the accuracy and precision requirements of 1.0 ppm for the column mixing ratio and 0.58 ppm for the column density measurements for the ASCENDS mission are basically the same as for the RRV area under clear conditions. For regions with lower surface reflectance or attenuating atmospheric conditions, the measurement requirements would be scaled down from RRV and clear conditions to corresponding lower signal return conditions (e.g., integration time would increase or measurement requirements would be relaxed). We also note that the high-accuracy and high-precision measurements in differential optical depth projected by this study would provide certain tolerant spaces to allocate the overall error budget for the errors in calculating absorption coefficients due to absorption line uncertainties (e.g., line shifting and broadening) as well as in column amounts or surface pressure measurements for column mixing ratio retrievals. Thus, the estimates in current simulated cases for spaceborne application would meet the assumed uncertainty requirements of ASCENDS.
The simulated results for thin cirrus clouds are plotted in Fig. 7. A cloud optical depth up to 1 is considered, which represents not only subvisual cirrus  but also certain visible clouds. These clouds are assumed to be at 9 km altitude, which is typical for cirrus clouds all over the globe, especially in the tropics and summer midlatitudes [37–39]. The surface reflection is assigned to be the same as that of RRV. It can be seen that when clouds are subvisual or very thin (), there are no significant reductions in SNR values of [Fig. 7(a)]. With some very thin clouds, the SNR values can actually be higher than those under clear sky conditions, as can be seen in Fig. 7(a), due to the larger attenuation of the solar background through the very thin cirrus at large tangent angles at dawn/dusk time compared to the signal attenuation in the nadir. Also, for LAS laser returns, the levels of some noises, such as shot noises from laser returns and solar radiation, are related to the light power received by the detector, and others, such as dark current and thermal noises of the detector–TIA component of the LAS system, are independent of the laser signals. Variations in the total noise for different atmospheric and surface conditions may generate nonlinear relationships of SNR (or precision) with the surface returned power received by the instrument as indicated in Fig. 7(a). A previous study  also showed nonlinear error features in scenes with tenuous clouds. Based on the simulated SNR range (94–260 and 65–170 of 0.1 s integration for Side-1/Off and Side-2/Off, respectively) for cloud optical depth , a precision of or better can be achieved when average measurement times of 10 s are used. The lower precision for the estimates from Side-2/Off channels is essentially the result of a smaller value. The relative bias errors of are within about 0.5%, and may also be reasonably small considering cloudy conditions. As mentioned before, the accuracy and precision requirements of a 1.0 ppm mixing ratio or 0.3% for the ASCENDS mission are assumed for an area with surface reflectance similar to that of the RRV area under clear skies. Under cloudy conditions, the accuracy and precision requirements will have corresponding changes due to power loss to the surface and interference caused by clouds. However, it is important to realize that any contamination from clouds renders passive measurements essentially unusable, and even with the reduced precision of the active measurements under these conditions, there is a significant advantage from the active measurement. For cloud optical depth less than 0.4, the systematic bias errors for the simulated spaceborne LAS system could be maintained to within 0.1%, which is expected to be within the ASCENDS science requirements (yet to be fully defined), particularly when the dependence of the total budget requirements for column mixing ratio measurements on cloudy conditions is considered. Furthermore, when clouds are present, certain peak power outputs for the clouds from the matched filter will exist within the UR of analyzed data (cf. Fig. 1). The systematic errors introduced by thin clouds could be further corrected based on the height and optical depth of the thin clouds retrieved from LAS backscatter measurements, especially those of the Off channel. For a simple example, the simulation shows that the systematic bias errors for Side-1/Off and Side-2/Off channels in these cloudy sky cases are generally positive and negative, respectively. When the received signal powers of Side-2 and Off channels are about equal at TOA and both are higher than that of the strong absorption Side-1 channel, the signal power of the Side-2 channel at cloud layers would be stronger than that of the Off channel. On the other hand, this signal power of the Off channel would be higher than that of Side-1. Thus, the grand power ratios of Side-1/Off would be underestimated under the influence of cirrus clouds, while the values for Side-2/Off would be overestimated, which causes the positive and negative biases, respectively, in retrievals. Combining the results of Side-1/Off and Side-2/Off would decrease the systematic errors, especially when cloud OD is estimated from the outputs of the matched filter. In addition, more advanced retrieval techniques are being developed to further remove residual cloud contamination effects on the derived optical depths to the surface due to the sidelobes of the matched filter output being infinite in extent. The simulated accuracy and precision in the measurements indicate that the assumed space LAS system could leave needed margins for the total error budget for column mixing ratio retrievals. Furthermore, the required accuracy and precision of mixing ratio measurements under cloudy conditions may not be as high as those for clear skies, but are still a significant improvement over current passive capabilities. Based on this work, the satellite LAS system simulated here, the IM-CW approach, is capable of achieving the column measurements needed for the ASCENDS mission.
This study focuses on the modeling of LAS instruments and simulations of their column measurements. The modeled LAS systems are assumed to operate in the 1.6 μm absorption band with the IM-CW approach. The characteristics of the simulated systems are based on both a general LAS system design that is similar to the architecture of an existing airborne instrument and the understanding of the considered instruments for spaceborne applications and their components. To simulate the measurements of atmospheric columns, environmental conditions related to surface reflectance; atmospheric , temperature, pressure, and humidity profiles; solar radiation; thin clouds; and aerosol layers were introduced into the model. With these considerations, the signals and noise sources related to the LAS column measurements, including all of the physical effects of the transmitter, atmosphere, surface, receiver, matched filter, and other signal postprocessors, were numerically calculated, based on the physics of individual components and processes. However, the results are presented statistically due to the noises and uncertainties of the instruments and environments, respectively.
The developed simulation model has been tested by different techniques. The lidar returned powers were validated through not only theoretical considerations but also the MFLL measurements operating over a horizontal ground test range during the summer of 2012. The SNRs of the simulated laser signals and estimates of the differential optical depths of the atmospheric column were directly evaluated using MFLL observations from a flight campaign conducted during the summer of 2011. The model inputs of atmospheric profiles, including absorption optical depths, for the flight campaign cases were obtained from in situ measurements. All tests show very good agreements between the simulated results and those from other independent measurements and estimations when the demonstration nature of MFLL is considered. MFLL was developed using commercially available parts, and the differences between model results and MFLL measurements are attributed to a combination of uncertainties in the MFLL parameters that are affected by MFLL environmental factors, system integration, and slight degradation with time.
The simulations for spaceborne measurements show that the assumed space LAS system will be capable of making accurate column estimates over various types of surfaces when implemented in a 390 km dawn/dusk orbit with 42 W transmitted powers. In the presence of thin clouds, the column measurements will be able to meet the accuracy and precision requirements of the ASCENDS mission for surfaces similar to those of RRV, Nevada, which is currently the defining case for ASCENDS requirements.
Although significant progress has been made in instrument development and modeling studies, there are certain critical areas that require further improvements. For example, one of the main limitations on the high transmitted powers is detector noise. Improvement in detector sensitivity and lowering the subsystem noises will directly increase the carrier-to-noise ratio and reduce the required transmitted power. The UR for current instrument configuration and model studies is 15 km. Since certain amounts of thin cirrus clouds and polar stratospheric clouds exist in the upper troposphere and/or low stratosphere, the UR will be increased to 30 km. Advanced fitting algorithms are expected to further reduce the impact of clouds and aerosols on IM-CW LAS column measurements. Also, to reduce the burden of curve fitting for the correlation functions of matched filter outputs in ranging estimations , a higher sampling rate and wider electronic bandwidth are needed. Currently, LaRC and Exelis are working together to demonstrate approaches to address these critical areas. The results of these advancements will be presented as these capabilities are demonstrated.
The authors express their appreciation to C. Hostetler, W. Edwards, M. Dijoseph, B. Meadows, J. Campbell, S. Chen, M. Vanek, Z. Liu, J. Dempsey, Y. Hu, W. Sun, and J. LaPan for their valuable comments and encouragement, and to D. McGregor, N. Blume, G. Mathew, and the entire LaRC/Exelis team for their strong support in instrument evaluation and data collection. This research was supported by the NASA ASCENDS Mission Study and NASA Langley Research Center.
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