In all large atmospheric and global climate researchprograms, our lack of understanding of the role ofwater vapor in atmospheric processes has been rec-ognized. This lack includes both modeling and ob-servations of atmospheric water vapor. Forexample, in the pathway report of the Committee onGlobal Change Research it has been stated that“�a�ny assessment of climate chance . . . must bebased on significant better observations of the watercycle”.1
In connection with mesoscale processes, the firstprospectus development team of the U.S. WeatherResearch Program stated that “�i�mprovement in nu-merical weather prediction, and especially quantita-tive precipitation forecasting, is severely impeded by
poorly resolved and inaccurate measurements of at-mospheric water vapor. High priority must be givento new water-vapor measurement systems . . . ”.2
In connection with boundary layer research, theBoard on Atmospheric Sciences and Climate of theNational Research Council named as one of the mostimportant research challenges is to “�e�xploit newremote sensors to broaden the scope of boundarylayer studies” and called for “Improve�d� observa-tional capabilities in support of studies in atmo-spheric physics”.3
An analysis of the research needs for climate, toweather, to turbulence yields the following results�see, e.g., Refs. 1–14�: Whereas, for climate re-search, measurements with global coverage and highaccuracy �error �5%� are needed, measurements forturbulence research require lower accuracy but veryhigh resolution, of the order of meters and seconds.Furthermore, for research in atmospheric chemistry,quantitative precipitation forecasting, and studies ofthe initiation of convection as well as boundary layerresearch there is a strong need for an instrument thatis capable of observing the three-dimensional distri-bution of water vapor in a range of at least 15 km witha time and a spatial resolution of approximately 10min and hundreds of meters, respectively. For theseresearch areas, clear-air measurement capability isone of the most important features of such an instru-ment.
When this research was performed, the authors were with theAtmospheric Technology Division, National Center for Atmo-spheric Research, Boulder, Colorado 80307. V. Wulfmeyer wasalso with the Environmental Technology Laboratory, NationalOceanic and Atmospheric Administration, Boulder, Colorado80303. He �[email protected]� is now with the Insti-tute for Physics, University of Hohenheim, 70599 Stuttgart, Ger-many.
Received 17 November 2000; revised manuscript received 15May 2001.
It is obvious that the combination of requirementsmentioned above can be fulfilled only by remote-sensing systems. It is also clear that a single instru-ment cannot cover all these measurement needssimultaneously. However, if a measurement tech-nique is available that is capable of making clear-air,range-resolved measurements with simultaneouslyhigh accuracy and resolution under different atmo-spheric conditions, such a technique can make signif-icant contributions to many research areas inatmospheric sciences.
Radiosonde sites are sparse, and their temporalresolution is poor. Their accuracy is still not clearlyspecified, and recent findings show that, even in theboundary layer, errors of as much as 10% can occur.15
Passive remote sensing provides global coverage;however, temporal as well as spatial resolutions �par-ticularly the vertical resolution� are too low for manyapplications. Its error is of the order of 10–20%, andthe bias can depend on atmospheric conditions.Weather radars provide little information about at-mospheric water vapor.
In this paper we show that an available technique,the differential absorption lidar �DIAL� technique,has the potential to provide the basis for powerfulobservation systems. An advanced water-vaporDIAL system is proposed that allows measurementsto be made under different atmospheric conditions inclear air. That the range of clear-air measurementcapability is limited by clouds and rain is not seen asa major drawback, as even in clear air we do not knowmuch about the water-vapor distribution. It is thepreconvective environment that one has to investi-gate to address major areas of weather research, suchas the initiation of convection.
As we want to take advantage of the most impor-tant features of the DIAL technique, namely, its flex-ibility, its accuracy, and its high resolution, thesystem has to be a direct-detection system that oper-ates in the ��� band of water vapor near 940 nm.Such a system can be applied for turbulence, me-soscale, and climate studies from ground-based andairborne platforms up to the lower stratosphere.Measurements can be performed from the arctic tothe tropics. In this paper we derive the basis for thesimulations of its performance by means of a detailederror analysis. The validity of the equation for pre-cision is proved by comparisons with experimentaldata. In the companion paper, simulations of alarge set of different measurement situations are pre-sented.16 The development of this system wasstarted at Atmospheric Technology Division of theNational Center for Atmospheric Research and at theInstitute of Physics, Hohenheim University, Ger-many.
2. Differential Absorption Lidar Technique
The DIAL technique uses the absorption of watervapor to derive information on the water-vapor dis-tribution. This technique was proposed by Schot-land.17 For a detailed introduction to themethodology of water-vapor DIAL, see Refs. 18–20.
Here some important principles are summarized forthe reader.
In a water-vapor DIAL measurement two frequen-cies are emitted alternately. The first frequency�on� is tuned to a water-vapor absorption line, andthe second one �off� is tuned to a nonabsorbed region.Applying the lidar equation twice, taking the loga-rithm of the ratio of the on-line and off-line backscat-ter signals Pon and Poff, and calculating thederivative, we end up with the DIAL equation21
nH2 O�R� �1
2R��� on � �off��ln�Pon�R1� Poff�R2�
Poff�R1� Pon�R2��
� K��par�R1, R2��� , (1)
where nH2Ois the water-vapor number density.
Consequently, water-vapor DIAL is a method formeasuring the dependence of absolute humidity inrange R. �� on is the effective on-line absorption crosssection when the spectral distribution of the laserlight is taken into account. �off is the off-line absorp-tion cross section, which has to be considered if theoff-line absorption is significant. R is the rangeresolution, and R1 and R2 are the centers of two rangecells separated by distance R. K is called theRayleigh–Doppler correction; it depends on the par-ticle backscatter coefficient �par.21,22 In principle, ittakes into account changes in the backscattered spec-trum between the range cells.
Important conclusions can be derived from Eq. �1�:The equation shows no calibration constant, so theDIAL technique has the potential to provide highlyaccurate measurements. A relative systematic er-ror in � translates to the same relative error in ab-solute humidity; therefore, accurate knowledge of theabsorption cross sections is required. These errorscan be measured carefully by spectroscopic measure-ments in the laboratory.
The principal disadvantage of the DIAL technologyis that a large effort must be expended on the devel-opment of the laser transmitter, the detector system,and the data-acquisition system. For Eq. �1� it isassumed that the position of the laser with respect tothe water-vapor absorption line is exactly known.However, water-vapor absorption lines are spectrallynarrow and have spectral widths of only 3 GHz nearthe ground and 1.2 GHz at the top of the troposphere.It is assumed for Eq. �1� that the laser spectrum is adelta distribution and that its frequency is exactlyknown and stable. Therefore, when one is transmit-ting the on-line frequency, the laser frequency mustbe stable, the bandwidth narrow, and the spectralpurity high to reduce errors to an acceptable limit.A summary of the requirements for the laser source isgiven in Table 1 of Ref. 23. Additionally, as twononlinear operations are applied for calculatingnH2O
�R�, errors caused in signal detection and acqui-sition propagate strongly in Eq. �1�, so a careful de-sign of these parts of the system is necessary.Furthermore, we use two different laser pulses at the
on-line and off-line frequencies to derive Eq. �1�, andthis increases the averaging time. Also, it is as-sumed for Eq. �1� that a decorrelation between theon-line and off-line signals due to fluctuations in thebackscatter coefficient can be neglected. It must beensured that the delay between the off-line and theon-line pulses is short enough to maintain this con-dition.
The maintenance of all these requirements is chal-lenging; however, if the development of a suitableDIAL system is accomplished, the effort is worth-while. DIAL is the only technique to date that pro-vides absolutely calibrated water-vapor data withoutthe need to rely on other instruments. This makesthe DIAL technique currently the most accuratewater-vapor remote-sensing technique. Extendedanalyses of the DIAL methodology have shown that,throughout the troposphere, water-vapor DIAL mea-surements can be performed with a systematic errorof typically 5%.18,20 The recent success of DIALmeasurements caused the DIAL technique to beadopted as a reference standard within the scope ofthe World Climate Research Program. In particu-lar, in the Global Water Vapor Project the develop-ment of ground-based water-vapor reference stationsequipped with DIAL systems for satellite calibrationsis planned.7,8
As the method for analyzing elastic backscattersignals is different the Raman lidar method �see, e.g.,Refs. 24–26�, the resolution and range of DIAL sys-tems are high even during daytime. A comparisonof Raman lidar and DIAL performance is found inRef. 19. It has been shown that the DIAL measure-ments described here resolve turbulent processes inthe daytime boundary layer.27,28 The investigationof mesoscale processes has also been reported.29,30
The time resolution of the DIAL measurements isgood enough that a DIAL system can be deployed onan airplane.18,30,31 The DIAL method makes evenrange-resolved airborne measurements in the strato-sphere possible.32
All these measurements can be performed in clearair because, at the short wavelengths used for lidarmeasurements, the signal is strongly attenuated inoptically thick clouds and rain. However, it has tobe emphasized that lidars yield unique informationfor the investigation of optically thin clouds such ascirrus clouds, which can often be penetrated. Fur-thermore, in all atmospheric research programs,water-vapor observation systems are required thatwill allow measurements to be made in clear air. Inthis connection, weather radar systems yield littleinformation about water-vapor distribution. Atleast a clear-air measurement capability is requiredfor investigating important issues, such as the initi-ation of convection, in atmospheric sciences. Addi-tionally, whereas radar techniques to extractinformation about atmospheric water-vapor distribu-tion are under development,33,34 we demonstrate be-low that these techniques can hardly compete withthe DIAL technique with respect to accuracy, resolu-tion, and flexibility.
The high resolution of DIAL measurements, asdemonstrated with current systems, creates the po-tential for performing three-dimensional scans ofwater-vapor fields with advanced laser transmitters.Another important property is the maintenance of aconstant relative error under different atmosphericconditions. The error propagation of Eq. �1�, whichis derived in relation �27� below, shows that by usingdifferent strong water-vapor absorption lines one canachieve the same relative error for measurements inarctic as well as in tropical regions. The same prop-erty holds for measurements on the ground and in thestratosphere.
3. Current Systems
To date there are only a few systems that fulfill thestringent requirements for accurate water-vaporDIAL measurements. The main reason for thedearth of appropriate instrumentation is the diffi-culty in developing a suitable laser transmitter �see,e.g., Ref. 23�, a hurdle that scientists have only re-cently been able to overcome. State-of-the-artwater-vapor DIAL systems have been developed atthe Max-Planck-Institute for Meteorology �MPI� inHamburg, Germany; the German Aerospace Agencyin Oberpfaffenhofen, Germany; the Serviced’Aeronomie of the Centre National de la RechercheScientifique, France, and the National Aeronauticsand Space Administration �NASA� in Langley, Vir-ginia.
A system that fulfills all the requirements for mea-surements throughout the troposphere (without anycorrection for laser properties) was developed in 1994at the MPI.35,36 The laser transmitter is based on aninjection-seeded unidirectional alexandrite ring la-ser. The average power of the laser transmitter is�0.3 W. In what follows, we define as averagepower the average power at the on-line frequency.The laser emits in the 720–780-nm region. Heresuitable water-vapor absorption lines for measure-ments from the lower troposphere to the ground aswell as from mid-latitudes to the tropics exist.Stronger water-vapor absorption lines for measure-ments in drier environments cannot be reached withan alexandrite laser.
At the Centre National de la Recherche Scienti-fique, an airborne water-vapor DIAL system has beendeveloped that is called Lidar Embarque pour l’etudedes Aerosols et des Nuages, de l’interactionDynamique-Rayonnement et du cycle de l’Eau”�LEANDREII�.31 This system is routinely used forairborne missions. The laser transmitter is alsoconstructed of alexandrite, so it has average power�0.5 W� and tunability similar to those of the MPIDIAL system. The line narrowing that is necessaryfor laser emission with narrow bandwidth is achievedwith intracavity etalons. This technique results in asomewhat higher bandwidth than from the MPI sys-tem, so corrections have to be applied if measure-ments are performed in the upper troposphere.
A routinely applicable and well-characterized sys-tem is NASA’s Lidar Atmospheric Sensing �LASE�
system.37 The LASE system is the first autonomousairborne DIAL system, and its high accuracy hasbeen investigated by use of a large set of intercom-parisons.38 The laser transmitter is based on aninjection-seeded Ti:sapphire laser that operates be-tween 813 and 819 nm.39 The average power is ap-proximately 0.5 W. A special feature is its capabilityof switching the laser frequency in flight from thewater-vapor absorption line center to the wing. Thisallows for an extension of the range to include anaircraft height level from 12 km to ground level.This system is suitable for measurements up to 12km and for operation from the arctic to the tropics.The line strengths of water-vapor lines near 815 nmare too weak for measurements in the lower strato-sphere.
Another airborne DIAL system has been developedby the German Aerospace Agency in Oberpfaffen-hofen, Germany. It is the first airborne system tooperate near 940 nm, thus permitting water-vapormeasurements to be made with high accuracy andresolution in the upper troposphere and the lowerstratosphere.32 The average power is as high as 1W, and the repetition rate is 100 Hz. Reaching thispower level became possible by application of ad-vanced diode-laser-pumped Nd:YAG laser technolo-gy.40
Current water-vapor DIAL systems have reachedpower levels of just 1 W, which is more than an orderof magnitude less than the power of current water-vapor Raman lidar systems.24–26 To push the rangeand resolution of DIAL systems further clearly willrequire that the average power as well as the tele-scope size be increased. Other systems are in thedevelopment stage at the National Oceanic and At-mospheric Administration �NOAA�, EnvironmentalTechnology Laboratory41 �ETL� and at the Universityof Illinois at Urbana–Champaign.42
It is worthwhile to analyze the performance of cur-rent systems to check whether the high expectationswith respect to the accuracy and the precision ofDIAL measurements are fulfilled. The absolute ac-curacy of airborne DIAL measurements has been ex-tensively investigated by intercomparisons with insitu sensors and Raman lidars. A large intercom-parison data set has been collected with the NASALASE system.38 In this study an error in the DIALmeasurements of the order of 5–10% was foundthroughout the troposphere. Note that it was diffi-cult to perform these studies, as temporal and spatialsampling from an airborne platform is considerablydifferent from sampling of ground-based Raman li-dars and in situ sensors, which were used for com-parison. A few studies have been performed withthe German and French airborne systems.43 Again,generally an error of 5–10% was found, even in thelower stratosphere.
From ground-based MPI DIAL, a large set of inter-comparisons with radiosonde data was collected. Inparticular, in the lower troposphere, where spatialand temporal averages are in best agreement, anerror of �5% was found. In the upper troposphere,
a new technique was applied for intercomparison.With a cirrus cloud at a height of 9 km and with theassumption of water-vapor saturation over ice in thecloud, a comparison of the DIAL-derived water vaporand that in the cloud could be performed. Here anagreement of 5% was found, although the absolutehumidity in the cloud was very low, 0.054 g m 3.19
All these measurements confirm a low relative er-ror in water-vapor DIAL measurements, of the orderof 5–10% up to the lower stratosphere. Recently,further comparisons of MPI DIAL with Raman lidarmeasurements were performed.44 Initial resultsshowed a bias of 10% between these instruments.The origin of the bias is under investigation. Today,using active remote sensing, we are able to investi-gate such kinds of bias with an error of the order of5%.
The precision of DIAL measurements has beencharacterized in detail for the NASA LASE system aswell as for the MPI DIAL. To achieve a precision of5–10% in the middle troposphere requires that theLASE data be averaged for 1 min with a range reso-lution of 300 m, resulting in a horizontal resolution ofapproximately 6 km.13 Although these results aretypical, they cannot be generalized, as their precisiondepends on the choice of the strength of the water-vapor absorption line and the atmospheric condi-tions. A more general conclusion about theperformance of DIAL systems can be derived by useof the simulations described in Ref. 16.
The MPI system is one of the highest-resolutionground-based water-vapor remote-sensing systemsduring daytime. Focusing on measurements in theatmospheric boundary layer, measurements can beperformed with a range resolution of 60–240 m andan averaging time of 10–60 s, resulting in a precisionof 0.2 g m 3. In the convective mixed layer, thisresolution allows for the investigation of water-vaporfluctuations even in the inertial subrange.27,28
Thus our analysis of the performance of currentDIAL systems confirms the extraordinary combina-tion of high accuracy and resolution, although the fullpotential of the DIAL technique has not yet beenrealized. Therefore it is logical to consider a futuresystem with higher average power and higher effi-ciency of the detector system to further extend therange and time resolution of DIAL systems and topermit, for the first time, three-dimensional scans ofthe water-vapor field.
4. Proposed System
A. Choice of Wavelength
The most important decision for the development of anew water-vapor DIAL system is the proper choice ofthe operating wavelength of the laser transmitter.This choice is determined by compromises among thefollowing requirements:
The presence of suitable water-vapor absorptionlines within the tuning range of the laser transmitter,
Availability of detectors with high efficiency andlow noise,
Wavelength dependence of the atmospheric back-scatter and extinction coefficients,
Wavelength dependence of the atmospheric back-ground signal, and, as far as possible,
Eye safety of the laser transmitter.
1. Suitable Water-Vapor Absorption LinesThe laser transmitter has to be operated in a wave-length region where suitable water-vapor absorptionlines exist. The absorption lines must be strongenough to permit measurements to be made in thelower stratosphere and the upper troposphere fromairborne platforms. The question as to what suffi-cient strength means within this context can be an-swered by analysis of the error propagation of theDIAL equation (see Subsection 5.A below�. It turnsout that differential optical thickness � in a rangecell must be of the order of 0.03–0.1 to facilitate mea-surements with acceptable resolution and range.19
Figure 1 shows the global climatology of water va-por45 that has been used for the simulations pre-sented in this section as well as in Ref. 16. Taking
� � nH2 O�onR � 0.03–0.1 (2)
and the typical water-vapor number density for acertain atmospheric condition, after inserting an ac-ceptable range resolution into Eq. �2� we get the ap-
propriate water-vapor absorption cross section. Forexample, in the mid-latitude summertime boundarylayer the absolute humidity is �15 g m 3, whichcorresponds to nH2O � 5 � 1017 cm 3. In the bound-ary layer, measurements with high vertical resolu-tion of approximately 60 m are required for resolutionof turbulent fluctuations of water vapor. Hence theneeded water-vapor absorption cross section � shouldbe �1.7 � 10 23 cm2. � is related to the water-vaporabsorption line strength S, which is usually given inspectroscopic databases as
� � SV, (3)
where V is the normalized line form function. Forwater vapor it can be described with good accuracy bya Voigt profile. Near the ground, the Voigt profilecan be approximated by a Lorentzian function, so, inthe line center at center frequency c,
��c� � S�(�bc). (4)
In the boundary layer the collision-broadened line-width is bc � 0.1 cm 1, so S � 5.3 � 10 24 cm. Moredetails on the position and line form functions ofwater-vapor absorption lines are found in Refs. 46and 47.
The other extreme of the measurement range is thelower stratosphere, where it is expected that nH2O �4 � 1013 cm 3. In this region the range resolutioncan be reduced to 500 m, so � � 2.5 � 10 20 cm2. Inthe lower stratosphere the absorption line is mainlyDoppler broadened, so
��c� � �ln�2�
� �1�2 Sbd
. (5)
The Doppler-broadened half-width bd can be calcu-lated according to
bd � c�2 ln�2�kTMH2 OC2
�1�2
, (6)
where k is the Boltzmann constant and MH2O is themass of a water-vapor molecule. Thus bd � 500MHz or 0.017 cm 1, so in this case S � 9 � 10 22 cm.
These line strengths can be searched for in data-bases such as HITRAN.48 Other necessary linestrengths can be determined by application of thisprocedure in various atmospheric conditions.
The other constraint on the applicability of an ab-sorption line is the ground-state energy of the tran-sition. The ground-state energy should be lowerthan 300 cm 1 to reduce systematic errors in DIALmeasurements to �0.4% K 1 caused by a cross sen-sitivity to the atmospheric temperature.20
After taking these boundary conditions into ac-count we performed an analysis of the water-vaporspectroscopy. Emphasis was laid on wavelength re-gions where water-vapor absorption lines exist thatallow boundary layer as well as lower stratosphericmeasurements to be made �see above�. This analy-sis showed that only absorption bands in the 945-,
Fig. 1. Global climatology of water-vapor, pressure, and temper-ature profiles.
1400-, and 1900-nm regions can cover the desiredrange of atmospheric conditions. Figures 2–6 showthe locations of suitable absorption lines and theirground-state energies. Water-vapor absorptionbands that are used for the MPI DIAL system andLEANDREII near 725 nm as well as the wavelengthregion near 820 nm used for the LASE and the NOAADIAL system are also shown. These absorptionbands are too weak for measurements in the uppertroposphere.
2. Availability of DetectorsThe availability of detectors places an important con-straint on the choice of wavelength. To get a highsignal-to-noise ratio �SNR� of the return signal, oneneeds a product of quantum efficiency and gain of thedetector of at least 100 to be able to discriminateefficiently between the atmospheric signal and thedark current background. Furthermore, the detec-tor noise current should be as low as possible. Theresponse of the detector must be linear over a dy-namic range of 108. Research shows that only pho-tomultipliers and avalanche photodiodes �APDs� areapplicable for observations in the near IR up to 1000nm. InGaAs P–I–N diode detectors are applicable inthe IR.
The best performance is achieved by APDs, as theyhave both high quantum efficiencies of more than50% up to a wavelength of 1000 nm and a gain of the
order of 100. APDs are less prone than photomulti-pliers to ringing after saturation of the detector.This is an important issue in a lidar system, as back-scatter signals from clouds often cause saturation ofthe detector. If a ringing of the detector occurs, sig-nals can be contaminated for a certain time after thecloud disappears. InGaAs detectors are commonlyused at wavelengths longer than 1000 nm. How-ever, although they have a high quantum efficiency,the gain is only of the order of 1, so typically coherentdetection is applied for lidar systems in this wave-length region.
The research that we performed points to the con-clusion that only operation at wavelengths shorterthan 1000 nm leads to a DIAL system with highresolution and long range. As it is difficult enoughto reach laser transmitter power levels of 10 W at1000 nm, it is extremely unlikely that a way will befound to develop a laser transmitter at a longer wave-length that will compensate for the loss of detectorefficiency by a further increase in average power by afactor of 50.
3. Wavelength Dependence of the AtmosphericBackscatter and Extinction CoefficientsThere is another effect that reduces the efficiency of alidar system at longer wavelengths. The atmo-spheric backscatter signal of molecules and particlesdecreases with increasing wavelength. The molecu-
Fig. 2. Water-vapor absorption lines in the region from 740.7 to714.3 nm.
Fig. 3. Water-vapor absorption lines in the region from 833.3 to806.5 nm.
lar backscatter decreases proportionally to 1��4, andthe particle backscatter coefficient decreases accord-ing to �1��. Simulations of the molecular and theparticle backscatter coefficients at 940 and 1400 nmare presented in Figs. 7 and 8. The data were ex-tracted from Ref. 49.
These atmospheric profiles have also been used inthe simulations reported in Ref. 16. The figures showthat an increase of the operating wavelength from940 to 1400 nm causes an order-of-magnitude reduc-tion of the molecular backscatter signal. The parti-cle backscatter coefficient does not decrease thatsignificantly. However, for the system under con-sideration, often measurement conditions will bepresent in which only molecular scattering occurs�e.g., in the upper troposphere and the lower strato-sphere�. Consequently, from the point of view ofbackscatter efficiency the operating wavelengthshould be as short as possible.
4. Wavelength Dependence of the AtmosphericBackground SignalTo a wavelength of 2000 nm the daylight backgroundis determined mainly by scattering of sunlight. Asthe Sun’s spectral power decreases with longer wave-length, this effect is favorable for operating at longerwavelengths. Using the MODTRAN database,50 wesimulated the daylight background at a Sun zenithangle of 40°. Figure 9 demonstrates that the back-
ground decreases by a factor of 4 from 940 to 1400nm. A lower background, however, has only a pos-itive influence during daytime in the far range. Inthe near range, the daylight background hardly de-creases the resolution of the DIAL measurements�see the simulations in Ref. 16�.
5. Eye SafetyEye safety is an important issue, as additional safetymeasures have to be taken for a general application ofthe DIAL system if the laser transmitter is not eyesafe. A technique for circumventing this problem issimultaneous measurement with a safety radar.51
A simulation of the dependence of eye-safety limitson wavelength is presented in Fig. 10. We used theANSI standard52 for these calculations. It is obviousthat a high-average-power laser transmitter can beeye safe under all experimental conditions only if thewavelength is longer than 1450 nm. Reducing thepulse energy and increasing the repetition rate at 940nm results in a beam radius of 50 cm at the single-shot limit and of 160 cm at a repetition rate of 2 kHz.Such a system can be made eye safe only in adownward-looking mode from an aircraft.
6. DecisionCurrently, operation of a high-power DIAL system inthe eye-safe wavelength region cannot be recom-mended, as the loss in precision that is due to low
Fig. 4. Water-vapor absorption lines in the region from 980.4 to892.9 nm.
Fig. 5. Water-vapor absorption lines in the region from 1492.5 to1298.7 nm.
quantum efficiency and low gain of the available de-tectors as well as the strongly decreasing atmo-spheric molecular backscatter signal is notacceptable. This loss accounts for a precision that isan order of magnitude less than for operation at 940nm at the same power of the laser transmitter andretrieval parameters. This effect is not compen-sated for by a slight reduction in the daylight back-ground. At even shorter wavelengths, no strongabsorption lines are available for measurements inthe upper troposphere and the lower stratosphere.These considerations demonstrate that a future high-average-power DIAL system must operate near 940nm. This conclusion will need to be reconsidered ifnew detectors at 1400 nm become available.
B. Choice of Signal-Detection Method
Two techniques can be applied to detection of thebackscatter signal. In direct detection the backscat-ter signal is just focused on a detector that works asa rectifier of the electric field. As the electric field issquared, which partly cancels the spatial variation ofthe phase over the detector area, the effect of specklesis low. However, it can still be significant �see Ref.16�. The downside of such a system is the largedynamic range of the backscatter signal. The 1�R2
dependence of the squared received signal contrib-utes significantly to the dynamic range. Techniquesfor dynamic range reduction have to be applied and
have already been developed.53 The setup for adirect-detection lidar system is straightforward.54,55
The optical path of such a system is easy to align andhighly stable even in a hostile environment. An-other important advantage is that the bandwidth ofthe receiver channel is large enough for molecularbackscattering to be detected. Consequently, mea-surements are possible in clear air without any aero-sol particles, which is particularly important in thefree troposphere and the lower stratosphere.
The other technique is applied in coherent Dopplerlidar systems and is called coherent detection.57,58
Here the electric field of the backscatter signal ismixed with the field of a local oscillator �LO�. In thecase of a coherent lidar system this LO is anotherfrequency-stable cw laser �analogous to the stable LOin a radar system�. The advantage is that coherentdetection provides a lower dynamic range of the back-scatter signal. A simplified explanation is that theelectric field of the backscatter signal is detected thathas a dynamic range of only 1�R. Coherent water-vapor DIAL measurements have been published inthe literature59–62; however, they have never reachedthe reliability and resolution of direct-detection DIALmeasurements. This is so because they have thefollowing disadvantages, which appear to forbid ap-plication of coherent detection for the DIAL systemunder consideration:
Fig. 6. Water-vapor absorption lines in the region from 2000 to1754.4 nm.
Fig. 7. Molecular backscatter, extinction, and optical thicknessprofiles for 940 and 1400 nm.
�1� The overlap function between the backscattersignal and the LO is range dependent, as it is diffrac-tion limited by the transmitted pulse as well as by theLO. It is shown in Ref. 19 that this usually un-known dependence is a source of severe systematicerrors.
�2� A coherent lidar system has a limited receiverbandwidth, which makes processing of the largeamount of data possible. Typical bandwidths are ofthe order of �25 MHz,63–65 so basically the molecularbackscatter signal is cut off. Therefore, present co-herent lidar systems can make measurements with
high SNRs only when a sufficient number of aerosolbackscatter particles is present. The reduction ofthe SNR in the free troposphere is usually so severethat DIAL measurements are no longer possible.Even measurements with a 1-J coherent laser trans-mitter operating at 10 �m often did not yield a suf-ficient SNR for backscatter measurements in the freetroposphere.66
�3� The SNR of a power measurement in a singleindependent range bin cannot be larger than 1, be-cause of speckle effects. The speckle noise is uncor-related between the on-line and the off-line shots ifthese shots are not sent out simultaneously. If this isthe case in current coherent Doppler lidars, the SNRcan be increased only by spatial and time averaging.The resultant error in a DIAL measurement can beexpressed as57,62
�n
nH2 O�
12� � 2
L Tm1�2��1 �1
CNRon2
� �1 �1
CNRoff2�1�2
, (7)
where �n is the rms error in the measurement ofnH2O
, L is the on-line or off-line laser repetition rate,T is the averaging time, m is the number of indepen-dent range bins, and CNR is the carrier-to-noise ratioof the backscatter signal. The most important fea-ture of relation �7� is that the laser pulse energy aswell as the aperture of the receiver influences onlythe CNR. If the pulse energy and the efficiencywithin certain range gates are large enough, relation�7� can be approximated by
�n
nH2 O�
1�
1�L Tm�1�2 , (8)
which is the upper performance limit for the precisionof a coherent DIAL system if the on-line and off-linespeckle noise is uncorrelated. The maximum perfor-mance without range ambiguity can be achieved with
Fig. 8. Atmospheric aerosol model at 940 and 1400 nm.
Fig. 9. Dependence of wavelength on daylight background.
Fig. 10. Dependence of the radius of an eye-safe laser beam onwavelength.
a repetition rate of 3 kHz. However, under this con-dition it is still difficult to make high-resolution DIALmeasurements even in the boundary layer, let alonein the free troposphere. In contrast, in a direct-detection system the laser pulse energy and the re-ceiver aperture appear directly in the equation forprecision �see, e.g., Ref. 29�, so one can increase theprecision more significantly by improving the laseraverage power as well as the size of the receivingtelescope. Consequently, we do not consider a co-herent water-vapor DIAL system flexible enough forthe measurement situations under consideration inthis study �see Section 1�.
5. Precision
A. Theory
In what follows, we consider a direct-detection DIALsystem. The precision of the water-vapor measure-ment can be estimated by the propagation of inde-pendent errors in the DIAL approximation. TheDIAL approximation �Eq. �1�� is used without theRayleigh–Doppler correction K.
The total photon number Nt produced at the detec-tor of a direct-detection lidar system is
Nt � Ns � Nb � Ndc, (9)
where Ns is the photon number that is due to thebackscatter signal, Nb is due to daylight background,and Ndc is due to dark current. Nb is estimated withthe equations given in Ref. 16.
Ns is calculated by use of prescribed backscatterand humidity profiles as well as other system param-eters from the single-scattering lidar equation55
Ns�R� �E0
h0
ct2
�las,0�rec,0O�R���R�AR2
� exp� 2�0
R
��r�dr� , (10)
where R is range, E0 is the laser pulse energy, h isPlanck’s constant, 0 is the laser frequency, c is thespeed of light, and t is the duration of the laser pulse�approximated by a rectangular pulse�. The mini-mum range resolution Rmin can be approximated bythe range interval ct�2. �las,0 and �rec,0 are theoverall transmission of the laser steering and thereceiver optics, respectively. O�R� is the normalizedoverlap function. At full overlap between the field ofview �FOV� and the laser transmitter, O�R� is nor-malized to unity. � is the atmospheric backscattercoefficient, which is the sum of particle and molecularbackscatter. In the derivation of Eq. �10� it was as-sumed that � does not change considerably withinRmin. A is the aperture of the receiving telescope,and � is the atmospheric extinction coefficient that isdue to molecular and particle extinction as well as toeventual absorption by a gas.
The total photo current PHt of an APD reads as
PHt � �Ns � Nb � Ndc� Be�, (11)
where B is the output bandwidth of the receiver, e isthe electron charge, and � is the quantum efficiency.In what follows, we assume that the receiver low-passfilter with bandwidth B is matched to the laser pulseduration such that B � 1�t. We consider all rangebins with length 1�B to be statistically independent.This assumption corresponds to a lidar range resolu-tion Rmin � ct�2 of statistically independent sam-ples.
The total current It measured after amplificationreads as
It � �Ns � Nb � Ndc� Be�G � Idc,0 (12)
�: Is � Ib � Idc � Idc,0 (13)
�: Is � Itb, (14)
where G is the gain of the APD and
Idc,0 � Be�Ndc,0. (15)
Idc,0 and Ndc,0 are the unamplified dark current anddark photon number, respectively, which have to betaken into account in an APD. Is and Itb are thesignal and the total background currents, respec-tively.
The propagation of uncorrelated errors in the DIALapproximation results in a rms error �n of the water-vapor number density nH2O:
�n2 �
1�2�R�2 � 1
�mk�2 �i�1
m
�j�1
k �Is,on, j�R1,i�
Is,on, j�R1,i��2
�1
�mk�2 �i�1
m
�j�1
k �Is,on, j�R2,i�
Is,on, j�R2,i��2
�1
�mk�2 �i�1
m
�j�1
k �Is,off, j�R1,i�
Is,off, j�R1,i��2
�1
�mk�2 �i�1
m
�j�1
k �Is,off, j�R2,i�
Is,off, j�R2,i��2� . (16)
The subscript i indicates averaging over m range binsin an environment of R1 or R2, whereas the subscriptj indicates averaging of k samples in time. Is is theoverall error that is due to uncorrelated and indepen-dent noise in the measurement of return signal Is.The contributors to Is are discussed below.
We replace the sample value Is, j�R1,2,i� by its mean,Is�R1,2�, and use the approximation Is�R� :� �Is�R1� �
Is�R2���2 � Is�R1� � Is�R2�. Furthermore, we replacethe sums over �Is, j�Ri��
Hence the relative error that is due to uncorrelatednoise reads as
�n
nH2 O� � 2
mk1�2 1
2� ���Is,on
Is,on
�R��2
���Is,off
Is,off
�R��2�1�2
.
(18)
Before we proceed, we have to consider that we needto perform three measurements to get Is. These arethe measurements of the total backscatter signal It,the electronic background with a shutter in front ofthe laser output, and the daylight background. Ibhas to be determined with the same time resolutionas the backscatter signal, as this background can behighly variable, for example, as a result of the pres-ence of clouds. Typically, one measures Ib by aver-aging the far-range signal, in which the backscattersignal is no longer present. Here a coarser spatialaveraging than the range resolution of the backscat-ter signal can be used. Although the electronicbackground is usually determined with a longer timeaverage than the daylight background, in what fol-lows we assume that the electronic background ismeasured by use of the same spatial and time aver-ages as for the daylight background. This procedurecan only lead to a safe underestimation of the preci-sion. The error terms that have been taken intoaccount are due to backscatter signal photon statis-tics, background noise from the atmosphere or reflec-tion from the Earth’s surface, detector as well asamplifier noise, speckles, laser intensity fluctuations,fluctuations of the atmospheric backscatter coeffi-cient, and digitization.
We do not take into account errors that are due toincomplete overlap between laser transmitter andtelescope, as we are starting our analysis in the re-gion of full overlap. We approximate all the corre-sponding noise distributions by a normaldistribution. We neglect errors due to fluctuationsin the atmospheric transmission, as these are consid-erably lower than backscatter fluctuations within theusable measurement range.
Is � It Itb, so the propagation of independenterrors yields
�Is
2 � �It
2 � �Ib
2 � �Idet
2 � �Iamp
2 (19)
� �Is,pois
2 � �Is,speck
2 � 2*�Ib,pois
2 � 2*�Ib,speck
2 � �Is,E
2
� �Is,�
2 � 2*BIdet2 � 2*BIamp
2 � �dig2 , (20)
where �Is,pois
2 and �Ib,pois
2 are the variances in the mea-surement of It that are due to Poisson photon statis-tics, �Is,speck
2 and �Ib,speck
2 are the variances in the currentthat are due to speckles in the signal and the back-ground and �Is,E
2 and �Is,�
2 are the variances induced bylaser pulse energy and backscatter fluctuations, re-spectively. Here we assume that the variance in thebackground signal is due mainly to photon statistics.Idet and Iamp are the noise currents �A��Hz� inducedby the detector and by a transimpedance amplifier.The two last-named values were chosen such thatthey also include noise that is due to dark current.
The factor 2* appears if the error has to be taken intoaccount in both It and Itb. We have not seen thisfactor considered in the literature. Factor 2* de-pends on the ratio between the number of indepen-dent range bins for determining the backscattersignal Is and the background. For example, if therange resolution in the measurement of Ib is a factorof 2 less, then 2* � 1.5; if it is a factor of 4 less, then2* � 1.25.
When we include the errors that are due to photonstatistics,
�Is
2 � �BeG�2�Ns � �Is,speck
2
� 2*�BeG�2�Nb � 2*�Ib,speck
2
� �Is,E
2 � �Is,�
2
� 2*B�Idet2 � Iamp
2 � � �dig2 . (21)
In a further discussion of precision we have to con-sider the dynamic range of the return signal and thedigitization error. We focus on the range interval�Rmin, Rmax�. The dynamic range of the return sig-nal is Ns,off�Rmin��Ns,on�Rmax�. If the range is ex-tended beyond those to existing systems, which is oneimportant goal of this project, we have to deal with adynamic range of the order of 108. It is clear thatthis range cannot be captured by a single digitizer, sotechniques for dynamic range reduction will have tobe considered.
Digitization error can be considered in the follow-ing way: The current of the detector is transformedto a voltage by a transimpedance amplifier. The re-sultant voltage signal is digitized with a transientrecorder and stored in a computer. The resolution ofthe transient recorder is 2bit, and the minimum res-olution is 1 least-significant bit �LSB�. We have todistinguish between two cases:
�1� The signal rms error is larger than 1 LSB. Be-cause of dithering effects the digitizing error is in thiscase 1��12 LSB.56 This is considerably less thanthe signal rms fluctuations and leads to a mere 10%increase in the absolute value of the precision. Asthe uncertainty in the simulations is significantlyhigher as a result of atmospheric effects �see Ref. 16�,we neglect the digitizing error here.
�2� The signal reaches a rms error of less than 1LSB at a certain range. In this case averaging doesnot help to reduce the measurement error, so theerror remains 1 LSB. It is clear that this situationmust be avoided, as this effect will limit the measure-ment range to this distance.
In what follows, we neglect the digitizing error andconsider a system in which, in the range interval�Rmin, Rmax�, the rms noise always exceeds 1 LSB.Nevertheless, we bear in mind that this error is animportant problem that has to be solved by dynamicrange reduction of Is. In what follows, we includethe function D�R�, which describes a range-dependent attenuation of the backscatter signal.
There are two ways to reduce the dynamic range ofthe signal: electronically �described by the functionDel� or optically �described by the function Dopt�. Incontrast to optical range reduction, electronic rangereduction may be the more elegant solution, as thefunction Del does not influence the Poisson errorterms. However, electronic range reduction can in-troduce additional noise through the use of a loga-rithmic amplifier, by the presence of additionalsystematic errors, or both; see Ref. 19�. Thereforethese possibilities have to be investigated carefully.
The errors caused by fluctuations in laser pulseenergy and the atmospheric backscatter coefficientare not equal to their variances because covarianceterms have to be included. Fluctuations in pulseenergy are 100% correlated between the ranges R1and R2 for the off-line and the on-line signals, respec-tively. Therefore the error is considerably less thantypical laser rms fluctuations, which are of the orderof 2%, so we neglect this error in what follows. Fluc-tuations in the backscatter coefficient are nearly100% correlated between the on-line and the off-linesignals if the laser transmitter is well designed.Therefore we also neglect this term. The remainingeffects of these fluctuations are mainly systematic;they were discussed in Refs. 19 and 20.
Including a noise figure Fdet � 1 for the detectorand using relation �21� the error formula for Is yields
��Is
Is2
�Fdet
�DNs� ��Is,speck
Is2
�2*FdetNb
��DNs�2 � 2*��Ib,speck
Is2
� 2*B�Idet
2 � Iamp2 �
�BeG�DNs�2 , (22)
where D � 1 in the Poisson error term if no dynamicor electronic range reduction is used and D � Dopt ifoptical range reduction is applied.
According to Rye,57 the error that is due to specklesin a light pulse with a Fourier-transform-limitedbandwidth is
�Nspeck
2 � N2�l, (23)
where l is the speckle count and N is the number ofphotons that reach the telescope of the receiver. Inthe derivation of Eq. �23�, which is calculated by useof a random walk in the phasor diagram over thedetector area, speckles are treated as if they haveequal sizes and phases, and they are considered tohave a uniform distribution.67,68 This assumption isvalid for a large speckle count l.
To deal with real laser pulses of length t as well asthe daylight background integrated over duration t,we introduce the Fourier-transform-limited band-width FT � 0.44�t and assume that the specklevariance can be decreased according to
�Nspeck
2 �N2
lFT
. (24)
For daylight, the background speckle variable is ex-pressed with use of � f. f is the spectralwidth of an interference filter used in the detectorsystem. For signal, the speckles are � L,where L is the real laser spectral bandwidth, whichdoes not necessarily have to be Fourier-transformlimited. We get the interesting result that a degra-dation of the laser spectrum above the Fourier-transform limit helps to decrease errors caused byspeckles. To our knowledge this effect was not pre-viously considered in direct-detection water-vaporDIAL systems.
Using the Van Cittert–Zernicke theorem,69 we canapproximate the radius of a speckle at the telescopeaperture by the radius of an Airy disk, Rairy � �R�RL.RL is the radius of the laser beam at range R; l is theratio of the receiver area divided by the speckle area,
l �RL
2Rt2
R2�2 , (25)
where Rt is the radius of the telescope. The rangedependence of the radius of the laser beam can beexpressed as
RL � RL,0 � F�
�
�RL,0R � RL,0 � F��R, (26)
where RL,0 is the beam waist located at range R � 0and � � ����RL,0� is the diffraction-limited diver-gence of the laser beam. F� can be interpreted as adivergence-excess factor, which describes an increasein the diffraction-limited divergence of the laser beamby, for example, multitransversal mode operation ofthe laser. It is related to the M2 factor, a similarmeasure of this effect, which is often used in laserengineering. It is typical that a laser beam diver-gence somewhat exceeds the diffraction limit.Again, this helps to reduce errors caused by speckles.
Taking into account that Ns,on � Ns,off exp� 2�� andusing expressions �18�, �22�, and �23�, we end up withthe basic equation for the following error analysis:
�n
nH2 O� [ 1
���2
12mk ( Fdet
�DNs,off
�exp�2�� � 1�
�Fdet
�DNs,off
2*Nb
Ns,off
�exp�4�� � 1�
�2*B�Idet
2 � Iamp2 �
�BeG�DNs,off�2 �exp�4�� � 1�
�1l �2FT
L�
2*Nb2
Ns,off2
FT
f�exp�4�� � 1��)]1/ 2
(27)
in the range interval �Rmin, Rmax�. The first term inboldface parentheses is due to Poisson statistics ofthe backscatter signal, the second term is due to day-light background, the third term is due to noise cur-rent in the detector and the amplifier, and the fourthterm is due to speckles. We call these terms Pois-son, background, amplification, and speckle terms,respectively.
The Poisson term was always considered in previ-ous publications on direct-detection water-vaporDIAL systems. Its influence depends strongly onthe efficiency and noise characteristics of the detec-tor, Fdet and �. In the far range the backgroundterm becomes important, and its influence also de-pends on the setup of the detector system, as carefuldesign can significantly suppress daylight back-ground level Nb. The contribution of Idet in the thirdterm of relation �27� sets a lower limit on the back-ground that is usually exceeded by amplifier noise.It is one of the tasks in detector system design to comeas close as possible to this limit. The speckle term isincluded in all simulations, as its role in the DIALsystem design must be assessed.
In previous studies, the speckle term was neglectedin relation �27�, and it would be worthwhile to doublecheck whether the amplification and backgroundterms were underestimated by omission of the 2*factor.70–73 Neglecting speckles and amplificationreduces expression �27� to the relation
�n
nH2 O� ( 1
���2
12mk � Fdet
�Ns,off
�exp�2�� � 1�
�2*FdetNb
�Ns,off2 �exp�4�� � 1��)1/2
�1
�
1�2mk�Ns,off�
1�2 �Fdet�exp�2�� � 1�
� Fdet
2*Nb
Ns,off
�exp�4�� � 1��1�2
, (28)
which yields �after insertion of Eq. �10� for Noff�
�nH2 O
n�
1�
R exp��0
R
��r�dr��2R�
E0
hL T��R� A�las,0�rec,0�1�2
� �Fdet �exp�2�� � 1�
� Fdet
2*Nb
Ns,off
�exp�4�� � 1��1�2
. (29)
In the derivation of Eq. �29�, O�R� � 1, R � mct�2,and LT � k, where L is the on-line or off-line rep-etition rate of the laser transmitter and T is the av-eraging time. As expected, Eq. �29� gives thereasonable result that the error is independent of thebandwidth of the receiver and of the laser pulse du-ration. The error can be reduced further by a de-crease of the range resolution, which also increasesthe differential optical thickness, as well as by anincrease of the averaging time.
The second term in Eq. �29� indicates that, whilethe laser average power P � E0L is maintained atthe same level, it is more beneficial to operate at lowrepetition rates and higher pulse energies to discrim-
inate between signal and background terms. How-ever, this procedure will be valid only if the speckleterm is neglected. To decrease the speckle effect,operation with a higher repetition rate is beneficial�relation �27��. These trade-offs were investigated indetail in Ref. 16.
An important application of the system under con-sideration will be the investigation of three-dimensional fields of water vapor by scanningtechniques. Therefore it is interesting to modify re-lation �27� to answer the following question: What,after a single round trip of the scanner, is the depen-dence of the width of a square �e.g., from polar planeindicator scanning� on a range within which the num-ber of photons collected is sufficient for a precision ofthe measurement of better than X%?
To address this question we rewrite relation �27� as
X �100� � Y
2mk1�2
(30)
and define the round-trip time of the scanner as TR.The angular resolution of each double shot is
� �360°L TR
, (31)
so the horizontal length S of a sector at range R is
S � 2�R�
360°�
2�RL TR
. (32)
If R is defined simultaneously as the horizontal andthe range resolutions that we want to achieve, thenumber of independent shots k within this slice willread as
R � kS � k2�RL TR
.
Hence,
k �L TRR
2�R. (33)
Using Rmin � ct�2 and R � mRmin leads to
X �100
nH2 O�mRmin� Rmin
mRmin
�RL TRR
Y1�2
�100
nH2 O��R�2 ��RRminYL TR
1�2
, (34)
so we achieve the condition that
R � � 100nH2 O�X ��RRminY
L TR1�2�1�2
. (35)
As expected, all terms other than the speckle term inthe product RminY are independent of the laserpulse duration and receiver bandwidth B.
B. Comparison of Relation �27� with Experimental Data
We investigate the validity of relation �27� by com-paring it with system noise profiles achieved with theMPI system.19 This is, to our knowledge, the firstcomparison of theoretical and experimental systemnoise of an existing DIAL system. The system noisewas measured by use of either a spectral or an auto-covariance analysis of a water-vapor time series at acertain height. These techniques are described indetail in Refs. 27 and 74. The theoretical profile isachieved with relation �27�. We fitted it to the ex-perimental data by varying the amplifier noise andthe signal strength. The latter variation was neces-sary because the lidar system was not calibrated andtherefore there was an uncertainty of the order of100% in the calibration of the backscatter signal pro-file.
Figures 11–13 present the results of the compari-sons. Details of the system parameters and the at-mospheric conditions during these measurementscan be found in Refs. 19 and 75. In all these figuresthe near-range deviations are due to overlap. In thesimulations, an overlap function of 1 was assumedover the entire range, whereas, in the experimentaldata, full overlap was reached only at heights of 600–1000 m. We were able to fit the profiles up to the farrange by assuming a fairly large amplifier noise,which limits the range in all cases. This noise was
considerably higher than can be achieved with state-of-the-art data-acquisition systems, a result that mayindicate that additional noise was coupled into thedata cables by inadequate shielding. Speckle noiseis not a part of this additional noise, as the lasertransmitter was running on two laser modes with abandwidth considerably larger than the Fourier-transform-limited bandwidth. In these measure-ments, the Poisson noise is also significantly lessthan the amplifier noise.
Figure 11 shows that matching the amplifier noisewith a value of 25 pA�Hz0.5 results in good agreementbetween the profiles over the entire range. With thesame value we found a similarly good agreement fora measurement 2 years later at a different site �Fig.12�. Also, a comparison over an extended rangewith coarser resolution yielded good agreement,within a few percent, over the entire range �Fig. 13�.As we are able to predict the error profile over theentire range up to the height where the amplifiernoise limits the measurement range, these resultsconfirm that we can use relation �27� to predict theperformance of future systems.
6. Summary
In this study an advanced active remote-sensing sys-tem was proposed for significantly improvedmeasurements of the two-to-three-dimensional dis-tribution of atmospheric water vapor. For all re-
Fig. 11. Comparison of theoretical and experimental systemnoise measured on 12 December 1994 at 19:13 UT in Hamburg,Germany.
Fig. 12. Comparison of theoretical and experimental systemnoise measured on 29 April 1996 at 20:55 UT in Lindenberg,Germany.
search areas, the capability to make clear-airmeasurements would be one of the most importantfeatures of the system.
We have demonstrated that DIAL has a high poten-tial to enhance our knowledge of the water-vapor fieldover a large range of scales. This potential has threecauses: First, the DIAL technique is flexible and hasthe unique property that it can be applied for measure-ments in the boundary layer as well as in the lowerstratosphere and from tropical to arctic regions. Thesame low relative error in a water-vapor measurementcan be maintained by choice of different strengths ofwater-vapor absorption lines under different atmo-spheric conditions. Second, the DIAL technique iscurrently the most accurate remote-sensing technique.That this is so is due to its intrinsic self-calibratingmeasurement method. Unknown system constantscancel out in the measurement of the water-vapor pro-file, as the derivative of the ratio of two signals, theon-line and the off-line signals, is calculated. Typi-cally, a systematic error of 5% in water-vapor profilesfrom the ground to the lower stratosphere can be ex-pected. Third, a DIAL system can perform measure-ments during either daytime or nighttime withoutstanding resolution under clear-air conditions be-cause this system measures elastic backscatter sig-nals, which provide high signal-to-noise ratios. Totake full advantage of the properties of the DIAL tech-nique requires that the system be a direct-detection
system that operates in the ��� band of water vapornear 940-nm wavelength.
From an analysis of existing water-vapor DIAL sys-tems we realize that the full potential of the DIALtechnique has not been explored yet. In particular,error propagation shows that a considerable increaseof the laser average power as well as of the efficiency ofthe detector system will result in significant improve-ments in DIAL measurements. The dependence ofprecision on time as well as on range resolution andrange includes all kinds of known error, such as errorsthat are due to Poisson statistics, daylight background,amplifier noise, and speckles. So far, speckle errorshave not been considered, and we have shown by usingcertain configurations of the DIAL system that theseerrors can be important.16 Also, digitization noisewas discussed, and it was assumed that one can ne-glect this error by applying an advanced detector sys-tem with a high dynamic range as well as optical orelectronic dynamic range reduction or both.
For the first time to our knowledge, an equation forthe expected resolution of a ground-based scanningDIAL system has been derived. Simulations of theexpected performance of an advanced ground-basedscanning and airborne water-vapor DIAL system arepresented in Ref. 16, based on the equations derived inthis paper.16
This study was supported by the U.S. Weather Re-search Program and was performed at the Atmo-spheric Technology Division of the National Centerfor Atmospheric Research. We thank the lidargroup of the Max-Planck-Institute for Meteorology inHamburg, Germany, headed by J. Bosenberg, for thecollaboration during the field campaigns and forproving programs for the water-vapor retrievals.We are grateful to the German Weather Service�DWD�, particularly to H. Steinhagen of the DWDobservatory in Lindenberg, Germany, for organizingthe field campaign LINEX 96�1. We thank J. Ma-chol of NOAA�ETL for providing a program to calcu-late eye-safety limits. B. Rye and R. M. Hardesty ofNOAA�ETL provided valuable comments on the er-ror analysis. D. N. Whiteman of Goddard SpaceFlight Center was so kind as to provide data on thedaylight background.
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