8

Differential-Absorption Lidar for Water Vaporand Temperature Profiling

Jens Bösenberg

Max-Planck-Institut für Meteorologie, Bundesstraße 55, D-20146 Hamburg,Germany (boesenberg@dkrz.de)

8.1 Introduction

The importance of water vapor in the atmosphere can hardly beoverestimated. Water vapor is the most important greenhouse gas, muchmore effective than CO2, it governs the atmospheric water cycle whichis the basis for life on earth, and it is a key component in atmosphericchemistry. The frequent occurrence of phase transitions from vapor toliquid water or ice crystals further enhances the importance of atmos-pheric humidity. Cloud formation and the various forms of precipitationcertainly belong to the most important weather phenomena. The strongtemperature dependence of the saturation vapor pressure in combinationwith vertical transport processes causes a large variability of the atmos-pheric humidity which exists on practically all scales from turbulence toglobal distribution.

In view of its importance the observation capabilities for atmosphericwater vapor are clearly insufficient, both for the operational global obser-vation system and for detailed process studies. Most routine observationsare still made using in situ sensors on radiosondes. Apart from the prob-lems caused by the sensor properties it is also the sampling strategy,typically only two instantaneous measurements per day for a relativelysmall number of stations worldwide, which does not permit a charac-terization of the water vapor distribution that comes even close to therequirements. Retrievals from spaceborne passive sensors can provide

214 Jens Bösenberg

some information, but vertical resolution in particular is insufficient inview of the frequent occurrence of strong vertical gradients.

For process studies the vertical structure of the atmosphere is ofgreat importance. Observational possibilities for water vapor profilesthat provide the necessary high resolution and accuracy are very limited.In situ measurements are possible from aircraft or helicopters, free flyingor tethered balloons, and kites, but all of these have serious limita-tions especially for vertical profiling. Therefore remote sensing eitherfrom the ground or from aircraft is a highly appreciated solution of theobservational problem, provided that good accuracy and resolution isattained.

Two lidar techniques can provide the required information on thewater vapor vertical distribution with the necessary vertical and temporalresolution: Raman lidar and differential absorption lidar (DIAL). Ramanlidar is treated in detail in Chapter 9 of this book. DIAL methodology andselected experimental results are presented here to provide an overviewover the principal strengths and weaknesses of the method as well as itspotential for applications in atmospheric research.

8.2 Methodology

The application of the DIAL technique as described in Chapter 7 to watervapor or temperature measurements does not pose any new fundamentalproblem, but there are some details that need to be considered carefully.This comes about mainly for two reasons: the accuracy requirementsfor water vapor and temperature retrievals are quite high, and the useof very narrow absorption lines of the rotational–vibrational spectrumin the near infrared makes the inversions prone to errors resulting evenfrom small changes in the transmitted spectra or absorption spectra.

The primary result of the DIAL technique is the differential absorp-tion coefficient, which is the product of the molecular differentialabsorption cross section and the molecule number density of the gasunder study. From a measurement of the differential absorption coef-ficient, the density can be deduced if the differential absorption crosssection is known, e.g., in water vapor profiling with DIAL. If the mix-ing ratio of a gas is known, e.g., for oxygen, the differential absorptioncross section can be determined. Selecting an absorption line with astrong temperature dependence then allows the temperature profile to beobtained.

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 215

The common basis for water vapor and temperature profiling withDIAL is the use of isolated narrow absorption lines of the vibration–rotation spectrum of the water vapor or oxygen molecule, respectively.Therefore a brief summary of the spectroscopy of these gases is givenbelow, mainly to quantify the pressure, temperature, and wavelengthdependence of the absorption cross section. This helps assess the per-formance requirements for the main lidar components, the laser systemand data acquisition.

8.2.1 Spectroscopy

The absorption coefficient αg of a gas depends on the molecule numberdensity�n of the gas under study, the temperature, the partial pressurespi

of the components of the gas mixture, and the details of the transitionsthat contribute to absorption at the specified wavenumber. A generalexpression for the absorption αg at wavenumber ν of a single absorptionline centered at wavenumber ν0 is given by

αg(ν) = �nS(T , ε)!(ν − ν0, pi, T ) (8.1)

where S(T , ε) is the line strength of the transition at temperature T andinitial-state energy ε, and !(ν − ν0, pi, T ) is the line shape functionfor wavenumber ν, the partial pressures pi of the components of the gasmixture, and temperature T. For water vapor and oxygen, the gases underconsideration here, the dependencies are given as:

S(T , ε) = S0

(T0

T

)l

exp

[− ε

kB

(1

T− 1

T0

)](8.2)

and

!(ν − ν0, p, T ) ≈ !V (ν − ν0, p, T ) = f ′Rw(ξ + ia) (8.3)

where S0 is the absorption line strength under standard conditions,kB is Boltzmann’s constant, and l is a constant that depends on themolecule (l = 1 for O2 and l = 3/2 for H2O). !V is the Voigt absorp-tion line function, which is a sufficiently good approximation to theactual line shape. The parameters for the Voigt function are given byf ′ = b−1

d

√ln 2/π, a = bc · b−1

d · √ln 2, and ξ = (ν − ν0) · b−1

d · √ln 2,

where bc and bd are the halfwidths (HWHM) for collision and Dopplerbroadening, respectively. Rw denotes the real part of the complex errorfunction and i = √−1.

216 Jens Bösenberg

Two effects must be considered in the pressure dependence of theabsorption cross section: collision broadening of the absorption line andshift of the line center with pressure. Pressure broadening is described bythe collision broadening coefficient bc in theVoigt function, it is differentfor each component of the gas mixture. Usually a single coefficient isgiven for air broadening which accounts for pressure broadening bynitrogen and oxygen. This is sufficient for a large altitude range wherethe mixing ratio remains constant. For tropospheric measurements watervapor pressure must also be considered, contributions from all othergases are negligible. It should be noted here that the self-broadeningcoefficient of water vapor is about 5 times higher than air broadening,so it is important even though its partial pressure is much smaller thanthe total pressure.

The pressure and temperature dependence of collision broadening bya single component of the mixture with partial pressure pi is

bc,i(pi, T ) = bc,i(p0, T0)pi

p0

(T0

T

)ηc,i

(8.4)

where bc,i(p0, T0) is the collision broadening coefficient at standardconditions. The effective collision-broadened width in a gas mixture is

bc =√∑

i

b2c,i(pi). (8.5)

The pressure shift of line center frequency with air pressure isdescribed by a linear relation, the shift coefficient is temperature-dependent:

ν0(pair, T ) − ν0(p = 0, T0) = dpairpair

p0

(T0

T

)ηdp

(8.6)

The pressure shift induced by water vapor is different from that causedby air pressure, but is neglibly small under all atmospheric conditions.

The temperature dependence of the absorption cross section is ofparticular interest: for water vapor retrievals this dependence shouldbe small to avoid errors due to insufficient knowledge of the tempera-ture profile, and for temperature profiling this dependence should be aslarge as possible to increase the sensitivity of the method. CombiningEqs. (8.1)–(8.3) we derive

dα

α= dT

T

[ε

kBT− l − 3

2+ "(!)

]. (8.7)

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 217

Here " is a value that depends on the actual line shape and assumesvalues between 0 in the limit of pure Doppler broadening and 1 forpure collision broadening. It follows immediately that high temperaturesensitivity is obtained for lines with a high initial-state energy ε. Lowtemperature dependence for water vapor measurements is achieved forε/kBT = 2 when collision broadening prevails, and ε/kBT = 3 whenDoppler broadening is dominant.

For temperature profiling a tradeoff has to be made between linestrength and temperature dependence, since with increasing initial stateenergy the lines become weaker, so that the measurable differentialabsorption becomes smaller. Lines that are useful for atmospheric meas-urements have temperature sensitivities of about 1.4% K−1 (e.g., lineP P27,27) to 2.4% K−1 (e.g., P P31,31). Obviously very accurate meas-urements of the differential absorption coefficient are required for anaccuracy of better than 1 K in temperature retrieval. This can only beachieved if all details of the spectral distribution that affect the effectiveabsorption coefficient are considered very carefully.

To be complete we note that small deviations from theVoigt line shapehave been observed [1]. According to [2] the effect of these deviations ontemperature retrievals is not very large, and it is even smaller for watervapor. Modified line shape functions have been developed which maybe used if necessary.

In summary, the following parameters are needed for the calculationof the absorption cross section at wavenumber ν for H2O or O2 in anisolated absorption line at air pressure pair, water vapor partial pressurepH2O, and temperature T:

ν0 absorption line center under standard conditionsS0 absorption line strength under standard conditionsl temperature exponent of the absorption line strengthε initial-state energy of the transitionbc,air,0 collision broadening coefficient for air at standard

conditionsbc,H2O,0 collision broadening coefficient for H2O at standard

conditionsηc,air temperature exponent of collision broadening for airηc,H2O temperature exponent of collision broadening for

water vapordpair pressure shift coefficient for airηdp temperature coefficient of the pressure shift.

218 Jens Bösenberg

These parameters have been measured with high precision for a num-ber of suitable lines, notably [1, 3–5]. Standard spectroscopy databases,e.g., HITRAN [6] or ESA [7], do not include all of these parameters, sothe missing ones remain to be determined whenever a new absorptionline is to be used for high precision DIAL measurements.

We note that the line strengths of water vapor are still under dis-cussion. Significant changes for the HITRAN database have beenintroduced, and there are large differences between HITRAN and ESA,up to 30%. Since the sources for these differences have not yet been iden-tified, a major uncertainty remains, although it is much smaller for thelines that are in use for DIAL work, because for these high-resolutionstudies based on tunable laser spectroscopy have been made as citedabove, which presently appear to be the most reliable sources for theline parameters considered here.

Water vapor absorption lines are present in many regions of theinfrared spectrum. For DIAL work the most suitable wavelengths arearound 730, 820, and 930 nm, where interference with other gases isminimal, suitable laser sources and sensitive detectors are available, anda wide range of line strengths is covered. Figure 8.1 shows the absorp-tion coefficient of water vapor in the 700 to 1200 nm region, for standardpressure and temperature and 80% relative humidity.

.00001

.0001

.001

.01

.1

1

10

100

wavelength, nm

mk/1,tneiciffeocnoitprosba

700 750 800 850 900 950 1000 1050 1100 1150 1200

Fig. 8.1. Absorption coefficient of water vapor from 700 to 1200 nm. Standard pressureand temperature, 80% humidity.

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 219

8.2.2 Detailed DIAL Methodology

The use of the DIAL technique for narrow absorption lines requiresdetailed consideration of the spectral shapes of the transmitted andthe backscattered radiation. While modern laser technologies can beused to generate extremely narrow lines with high spectral purity, thebackscatter originating from molecular scattering always shows consid-erable Doppler broadening. Typical H2O and O2 linewidths are plottedin Fig. 8.2 as a function of altitude in a standard atmosphere and com-pared with the widths of the Rayleigh line. It is obvious that the spectralshape of the Rayleigh-scattered light needs to be considered explicitly.For a full description of the problem the reader is referred to [8], a briefsummary of the main results is presented here.

The General Lidar Equation

The monochromatic form of the lidar equation reads [9]

P(ν, R) = ELc

2

A

R2η(ν, R) · β(ν, R) · e−2

∫ R0 α(ν,r)dr (8.8)

0

2000

4000

6000

8000

10000

0 0.02 0.04 0.06 0.08 0.1

alti

tude

, m

linewidth, cm–1

Rayleigh lineoxygen absorption

water vapor absorption

Fig. 8.2. Widths (HWHM) of the Rayleigh scattered line, the oxygen absorption lineP P27,27 at ν0 = 13010.81 cm−1, and the H2O absorption line at ν0 = 13718.58 cm−1.

220 Jens Bösenberg

where P(ν, R) is the signal power received from distance R, ν thewavenumber of the transmitted light, R the distance of the scatteringvolume from the transmitter/receiver, EL the transmitted pulse energy,A the active area of the receiver telescope, η(ν, R) the total system effi-ciency, β(ν, R) the total backscatter coefficient at distance R, andα(ν, R)

the total atmospheric extinction coefficient including gaseous absorp-tion and molecular as well as particle scattering. We note explicitly thatEq. (8.8) is derived assuming instantaneous, incoherent, elastic singlescattering. For specific applications the validity of these assumptionsshould be verified.

For a transmitter with an arbitrary spectral distribution lt(ν), assumedto be nonzero in the interval ν ∈ �ν, and normalized to

∫�ν

lt(ν) dν = 1,Eq. (8.8) is integrated over the spectral distribution [10]:

P(R) = P0

R2

∫�ν

lt(ν) · η(ν, R) · β(ν, R) · τ(ν, R)2 dν (8.9)

where we make use of a lumped system constant and the atmospherictransmittance:

P0 = EL · c · A2

and τ(ν, R) = e− ∫ R0 α(ν,r)dr (8.10)

Generally the spectral distribution may change during the scatteringprocess, e.g., by inelastic scattering or by Doppler broadening of theRayleigh backscatter. This can be treated in analogy to the treatment ofthe nonvanishing laser bandwidth by introducing a normalized spectraldistribution after scattering, ls(ν − ν ′, R), where monochromatic excita-tion at ν is assumed. Then the most general lidar equation (still assumingthe case of incoherent, instantaneous, single scattering only) reads

P(R) = P0

R2

∫�ν

∫�ν′

lt(ν) · η(ν ′, R) · τ(ν, R) · β(ν, R)

× ls(ν − ν ′, R) · τ(ν ′, R) dν ′dν. (8.11)

This equation is very general and is capable of handling complex laseremission as well as the full range of scattering processes with only therestrictions mentioned above. While Eq. (8.11) appears formally simple,the double integration can cause substantial problems, in particular whenthe equation is used for the inversion of measured lidar signals rather thanfor forward calculations.

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 221

For the applications considered here, i.e., humidity and temperatureprofiling, a few simplifications can be made. For these purposes lasersources with a very narrow transmitted spectrum should be used in anycase. Then we may assume η(ν) and β(ν) to be constant for all ν in thetransmitted spectrum. Of the total extinction coefficient, which is thesum of extinction due to molecular scattering αm, particle scattering αp,and gaseous absorption αg, only gaseous absorption shows rapid spectralvariations.

The spectral distribution function generally is a function of range Rand differs for upward and downward propagation. For each spectraldistribution an effective gaseous absorption coefficient can be defined as

αeff(R) =∫�ν

α(ν, R)l∗(ν) dν. (8.12)

Introducing the effective absorption coefficients for upward anddownward propagation, αu,eff and αd,eff , which are generally differentbecause of potentially different spectral distributions, and the correctionterm G which accounts for changes in the transmission of the back-scattered light on its way down from distance R due to a change in thespectral distribution, we can derive a lidar equation in differential formwith direct physical interpretation:

d

dRln(P · R2) = d

dRln η + d

dRln β − 2αp − 2αm

− αu,eff − αd,eff + G. (8.13)

The main difference compared to the standard lidar equation is theseparation into upward and downward propagation, the introduction ofeffective extinction coefficients, and the correction term G.

DIAL

The DIAL equation is obtained by combining the lidar equations forthe two wavelengths used. Let us denote them by the index on for thewavelength at the center of an absorption line, called online, and the indexoff for the offline wavelength away from the line center. Let us furtherassume that we have chosen the offline wavelength sufficiently far fromany other absorption line, but close enough to the online wavelength thatthe aerosol properties, backscatter and extinction, can be assumed thesame, and in a region with slowly variable absorption coefficient such

222 Jens Bösenberg

that the details of the spectral distribution need not be considered. Underthese conditions the resulting DIAL equation is relatively simple:

d

dRln

Pon(R)

Poff(R)= αu,eff,on + αd,eff,on − 2αoff + Gon. (8.14)

The term ddR ln ηon

ηoff, which describes the difference in the detection

system sensitivity for the on- and offline wavelengths, has been omittedbecause this is considered as too specific for each individual system.A word of warning, however, appears appropriate: the narrow-bandfilters often used in DIAL receivers may in fact have different and range-dependent transmission for the two wavelengths. This results from theangular dependence of the filter transmission and the range dependenceof the angular distribution of the collimated beam; for a detailed treat-ment see [11]. Although this effect can be corrected for, it is certainlypreferable to avoid the problem by proper system design.

Equation (8.14) is the basis for water vapor retrievals as well as fortemperature profiling. With modern laser techniques it is possible tomake the transmitted spectrum sufficiently narrow so that αu,eff,on isgiven directly by the product of the absorption cross section and thenumber density:

αu,eff,on = σon�n. (8.15)

This is also true for αoff , which should be small anyway. For the calcula-tion of αd,eff,on it is necessary to know the spectrum of the backscatteredradiation and the absorption line shape as a function of altitude. Fortemperature-independent lines, which should be chosen for water vaporretrievals, this is straightforward using standard information for the esti-mation of the temperature and pressure profiles. The full treatment ofGon is beyond the scope of this chapter; for more details, the reader isreferred to [8]. It may suffice to note that for its calculation the changein the backscatter spectrum must be known, which requires informationabout the scattering ratio profile. Gon is significant only in regions ofsteep gradients in aerosol backscatter, and is largest when molecular andparticle scattering have about the same magnitude.

For temperature profiling the calculation of αd,eff,on is more complexbecause temperature affects both absorption line shape and line strength.However, an iterative solution with a standard starting profile convergesvery rapidly. Because of the higher accuracy requirements the prob-lem of spectral broadening by molecular scattering is much more severe

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 223

for temperature retrievals. This is even more serious because regionsof special interest such as layers of temperature inversion are typicallyassociated with strong gradients in particle backscatter. Since this is acrucial issue for the applicability of temperature profiling with DIAL, itwill be treated in more detail in Section 8.5.

When Eq. (8.14) is used to derive the water vapor density from mea-surements of Pon(R) and Poff(R), it is necessary to know the parametersdetermining the absorption cross section, as listed in Section 8.2, andthe spectral distribution of the transmitted and the backscattered light. Ifthe transmitted spectrum is not much narrower than the absorption lineunder consideration, it must be specified very carefully.

A common problem for lasers with a broad tuning range is spectralimpurity caused by amplified spontaneous emission, a broadbandemission with typically very low spectral density which is hard to meas-ure directly with standard spectroscopic techniques. We define spectralimpurity as that fraction Pb of the total transmitted energy that is out-side a well-defined laser line. Since this portion of the transmitted lightwill pass the atmosphere with practically no absorption, its contributionto the backscatter for the online wavelength will increase with opticaltickness τ0. The relative error in the retrieved absorption coefficient isthen

�α

α= Pb

Pb + (1 − Pb)e−τ0. (8.16)

Only very small levels of spectral impurity can be tolerated when highaccuracy is required. Another crucial point is that the laser must betuned very precisely to the center of the absorption line. For small valuesof detuning the relative error in the effective absorption coefficient isgiven by

�α

α= 1 − b2

eff

b2eff + �ν2

. (8.17)

The requirements regarding laser properties for use with water vaporor temperature profiling are summarized in Table 8.1, as far as they canbe derived from the spectroscopy of the absorption lines that are used.Specifications are such that individual errors remain<3% for water vaporand <0.6 K for temperature for worst-case conditions throughout thetroposphere.

224 Jens Bösenberg

Table 8.1. Required laser performance for water vaporand temperature retrievals with individual errors of<3% for water vapor and <0.6 K for temperature.

RequirementParameter H2O T

Laser linewidth, cm−1 <0.013 <0.0042Frequency stability, 1σ, cm−1 <0.007 <0.0025Spectral purity >0.995 >0.999

8.3 Specific Solutions for Water Vapor DIAL Systems

Since the first application of the DIAL technique in 1966 [12], anumber of systems for water vapor profiling have been described byseveral groups; for an overview over the developments before 1991 see[13]. The applicability of most systems before 1996 was severely limitedby imperfections of the laser systems. Lack of wavelength stability andinsufficient spectral purity were the most common problems. With theapplication of the injection seeding technique both problems could beovercome. In this technique a low-power stabilized cw laser providesthe necessary spectral properties and is used to seed a power oscillatorthat provides the required pulse energy. This scheme is used successfullyin different variants: Chyba [14] used a diode laser as a well-controlledcw source to seed a laser-pumped linear titanium:sapphire (Ti:Sa) poweroscillator. Wulfmeyer [15] employed a laser-pumped Ti:Sa master oscil-lator and a flashlamp-pumpedAlexandrite ring laser as a power oscillator.Ehret [16] reported the properties of an optical parametric oscillator,based on a Nd:YAG-laser and KTP as a nonlinear crystal. While all thesedevelopments have shown good performance in short-term missions,there is still need for further development. Operation requires too mucheffort for adjustment and maintenance, and long-term unattended oper-ation has not yet been demonstrated. However, with the availability ofreliable and affordable pump lasers (either diode- or flashlamp-pumped),with simplified resonator designs, ultra-stable mechanical setups for theresonator and the coupling of the subsystems, and automated systemcontrol, it appears feasible to overcome these problems in the next fewyears.

The second subsystem of a water vapor DIAL which has to meet verydemanding specifications is the data acquisition chain from the detectorto the analog-to-digital converter. No signal distortions �0.3% can betolerated, and a large dynamic range is required. The latter is different

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 225

for airborne or spaceborne systems looking downward and for ground-based systems looking upward. Figure 8.3 shows simulated lidar signalsfor a standard atmosphere [17] assuming constant relative humidity of80% for all heights. For the aerosol backscatter an approximation to theaverage summer profile over Hamburg [18] is used, and an absorptionline is chosen such that the optical depth of the troposphere due to watervapor absorption is 1. Plotted are online signals for a spaceborne lidar at450 km altitude, a downward-looking airborne system at 12 km altitude,and a ground-based system looking upward. All signals are calculatedfor a nominal transmitted energy of 0.1 J, a telescope diameter of 0.5 m,and an overall system efficiency of 0.22. Nighttime conditions with nobackground light are assumed just to show the effect of the viewinggeometry rather than to provide a complete performance simulation. Thedynamic range the ground-based instrument must cover is enormous: sixorders of magnitude. It is in particular the range below 2 or 3 km thatcauses substantial trouble, but that is also the region of special interest.For the downward-looking systems the situation is much easier. The air-borne system needs to cover less than two orders of magnitude. Thesame holds for the spaceborne lidar, but the signal is very small for theparameters assumed here.

2000

0

4000

6000

8000

10000

12000

m,ed

utitla

received power, W

airborne, offlineairborne, online

spaceborne, offlinespaceborne, online

Fig. 8.3. Simulated lidar signals, online and offline, for a ground-based system, anairborne system flying at 12 km altitude, and a spaceborne system flying at 150 kmaltitude, all with the same technical specifications.

226 Jens Bösenberg

It must also be noted that the altitude range that can be coveredby ground-based systems is limited to roughly 5 km, depending on thedetails of the meteorological situation. This is because most of thewater vapor is located in the lowest 1–2 km, and the absolute humid-ity decreases by about three orders of magnitude between the top ofthe boundary layer and the tropopause. If a stronger line is chosen, theonline signal becomes extremely weak because of water vapor absorp-tion in the lower layers, and for a weak line extremely small differentialabsorption remains in the upper troposphere. Again the situation is muchmore favorable for downward-looking systems.

8.4 Applications of Water Vapor Profiling

8.4.1 Assessment of Accuracy

The key properties of water vapor profiling lidars for applications inatmospheric research and monitoring are accuracy, availability, range,and resolution. The areas of highest potential of water vapor profilingwith DIAL are high-resolution studies of turbulent processes during day-time, ground-based monitoring of the lower troposphere during daytime,a variety of process studies using airborne systems, and, in the future,possibly spaceborne global monitoring. For turbulence studies high tem-poral and vertical resolution in combination with good relative accuracyare the essential features. For monitoring, absolute accuracy in com-bination with good availability and range are most important, and forairborne systems it depends on the specific application, but probably acombination of all properties is required.

The main properties for turbulence studies can be derived even with-out intercomparison to other systems using only sufficiently long periodsof continuous lidar measurements. This is illustrated by an exampledescribed in [19]. The measurements were made in 1999 during an inter-comparison with the Raman lidar at the Clouds and Radiation Testbed(CART) of the Atmospheric Radiation Measurement Program of the USDepartment of Energy (ARM) in Oklahoma. At that time this system(CARL) was one of the most advanced Raman lidar systems for routinehumidity profiling [20]. To demonstrate the method of error assessment,Fig. 8.4 shows a variance spectrum of DIAL water vapor retrievals takenon October 9, 1999, 17:15 to 18:45 UT, at the ARM/CART site. It is adaytime measurement under clear-air convective conditions, altitude is

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 227

frequency, Hz

f −5/3

zH

mg,ytis

nedlartce

p s1

−2

−2

10000

100

0.0010.0001 0.10.01

10

1000

Fig. 8.4. Variance spectrum of the water vapor time series measured with DIAL duringdaytime. Roll-off according to f−5/3 (dotted line) and estimated noise level (dashedline) are indicated.

580 m above ground, temporal resolution 10 s, vertical resolution 75 m.The spectrum shows maximum values at low frequencies and a markeddecrease toward higher frequencies. This decrease is proportional tof −5/3 over a substantial part of the spectrum as expected for the inertialsubrange. The spectrum of random errors in the measurements shouldbe white, i.e., constant over the whole frequency range. This is clearlyvisible in Fig. 8.4 for frequencies beyond 0.005 Hz. Even if the spectrado not show this typical pattern, an upper limit for the noise level canbe estimated from the lowest statistically significant spectral density.Figure 8.5 shows two examples of noise levels determined in this wayfor MPI-DIAL and CARL, one during daytime and one during nighttime.For these cases resolution was chosen as 1 minute temporally and 90 mvertically. For the DIAL the estimated noise level is 3–7% during bothday and night, increasing with height. During nighttime the Raman lidarshows about the same level in the near range and significantly less noisebeyond 1 km. During daytime the Raman lidar performance is reducedconsiderably, noise level is at about 15%. Better performance of DIALhas been achieved on other occasions; nevertheless, this example demon-strates that high resolution in combination with good relative accuracycan be achieved during both day and night in the lower troposphere whereturbulent processes are most important.

228 Jens Bösenberg

1400

1200

1000

800

600

400

200

020 10 15 20 250 5 10 15 25 0 5

heig

ht a

bove

gro

und,

m

Fig. 8.5. Relative error of high resolution water vapor measurements for DIAL (solid)and Raman lidar (dashed) during daytime (left) and nighttime (right).

During the same campaign an attempt was made to compare theabsolute accuracies of the MPI-DIAL, CARL, and radiosondes. We notehere that Raman lidar does not provide absolute humidity measurements.The calibration of CARL relies on matching the total integrated watervapor to the results of a microwave radiometer operated at the same site.As an example Fig. 8.6 shows coincident profiles from a radiosounding,CARL, and MPI-DIAL measured during nighttime on October 10, 1999.Obviously there is very close agreement between all three systems up toabout 8 km height, a height range in which water vapor density varies bytwo decades. Some deviations occur at layer boundaries, in particular incomparison of the two lidars with the radiosoundings. This illuminatesone of the problems of intercomparisons, specifically with in situ sensors:mostly the sampled volume is not the same, and natural variability in thehumidity distribution sets limits for this kind of intercomparison. Theestimated errors for the two lidar soundings, presented in the right panel,clearly show that Raman lidars perform much better at night than in thedaytime.

To come to a more generalized view of the differences between thesystems, we compare the total water vapor content iwv integrated over aheight range in which both systems operate reliably. Figure 8.7 shows thisfor the MPI-DIAL and CARL for 12-hour periods on 5 days, based on

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 229he

ight

abo

ve g

roun

d, m

0.01 0.1 1 10 0.01 0.1

7000

6000

5000

4000

3000

2000

1000

water vapour density, g/m³ σ, g/m³

8000

Fig. 8.6. Water vapour profiles (left) and estimated standard deviation (right) fromradiosonde (dotted), Raman lidar (dashed) and DIAL (solid). October 10, 1999, 04:30UT (nighttime).

nighttime

October 4/5October 7/8

October 9/10October 12/13October 13/14

daytime

24222018161412100.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

LAI

D/na

maR

Fig. 8.7. Ratio of integrated water vapor measured by Raman lidar and DIAL for five12-hour periods during the 1999 intercomparison campaign.

230 Jens Bösenberg

10-minute averages. During daytime the integration range extends from1 to 3 km, during nighttime from 1 to 6 km. The ratio iwvCARL/iwvDIAL

shows agreement to better than 10% with only few exceptions. On theaverage the iwv is higher for the DIAL retrievals during daytime andlower during nighttime. There is considerable scatter mainly in the after-noon, and an abrupt change at 17 hours local time when CARL isswitched from daytime to nighttime mode. During nighttime the dif-ference appears to be either zero or around 7%. For the DIAL resultsoccasionally a jump of a few percent occurs when the system is switchedto a different absorption line.

The intercomparison results demonstrate that DIAL is favorable forhigh-resolution measurements in the lower troposphere during daytime,and that presently the relative uncertainty in absolute water vapor contentis a few percent. Different calibration approaches and uncertainties inthe absorption line parameters appear to contribute to the possible errors.These conclusions are also supported by other intercomparisons [21, 22].

8.4.2 Turbulence Studies in the Atmospheric Boundary Layer

Studies of the turbulent boundary layer require daytime measurements ofthe humidity distribution with high accuracy and resolution. An exampleis presented here to demonstrate the capabilities of DIAL for this purpose[23].

Figure 8.8 shows the time–height distribution of the water vapordensity measured on September 13, 1996, 07:00 to 08:15 UT. Measure-ments were made with the MPI-DIAL at the SE shore of the island ofGotland. The distribution shows mainly two different height regions, onewith relatively high water vapor density around 6.5 g/m3 up to about600 m height, and a much drier region above where the water vapordensity is smaller than 4.5 g/m3. The boundary between these two layerschanges rapidly, updrafts of humid air are observed as well as downdraftsof dry air, both with varying dimensions. The mixing zone extends fromabout 300 to more than 700 m height. The pattern shows clearly thatrather strong turbulence occurred during this time period, and that thestrong wind of 12 m/s advected the eddy structures rapidly. It is thehigh-temporal resolution of the DIAL, 10 s in this case, that enables usto resolve these structures.

Figure 8.9 shows humidity variance spectra at selected heights forthe case shown in Fig. 8.8. At lower heights, 270–510 m, the spectrashow a weak maximum at about 0.001 Hz corresponding to a period of

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 231

Fig. 8.8. Time-height cross section of the water vapor density. Temporal resolution is10 s, vertical resolution is 60 m. Gotland, September 13, 1996. From [23].

2.24

0.71

0.22

0.07

ρρ

870 m750 m510 m270 m

f^(−5/3)

0.10.010.001

0.1

1

10

100

s ) mg( ,

3−

2

mg ,veds3

−

S

Fig. 8.9. Humidity variance spectra at selected heights. Gotland, September 13, 1996.From [23].

232 Jens Bösenberg

17 minutes, and then roll off approximately proportional to f −5/3 upto the Nyquist frequency of 0.05 Hz. This is as expected and consistentwith the assumption that for frequencies>0.005 Hz the inertial subrangeis reached in which turbulence energy is mainly transported from largeto small eddies. At the high-frequency end these spectra still show arolloff proportional to f −5/3, there is no indication of noise. Apparentlynoise is <0.07 g/m3 rms at these height levels. At an altitude of 750 mthe variance spectral density is up to a factor of 4 larger, in particular atfrequencies beyond 0.004 Hz, but the same rolloff withf −5/3 is observed,again with no indication of noise. At 870 m the variance is quite similarin the low-frequency range, but the decrease with frequency is muchweaker. This can be explained by an increased noise contribution tothe variance, about 0.4 g/m3 rms. A strong increase in system noise isexpected for height levels beyond the top of the boundary layer becauseof reduced aerosol backscatter.

It is interesting to inspect the probability distribution functions forwater vapor density as shown in Fig. 8.10 at selected heights for the caseunder study. At lower heights the distribution exhibits a rather sharppeak at 6–6.5 g/m3. When the lower end of the entrainment zone isreached, e.g., at 510 m, the distribution shows additional broadening atlower humidity values. In the middle of the entrainment zone, at 630 m,

87.576.565.554.543.530

10

20

30

40

50

60

70

80

90

870 m

630 m

num

ber

of o

ccur

ance

270 m510 m

750 m

Fig. 8.10. Probability distribution functions for water vapor density at selected heightlevels. Gotland, September 13, 1996. From [23].

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 233

the distribution is characteristic for a mixture between a distributioncentered at about 6 g/m3 and another one centered at about 5.3 g/m3.At greater heights the distributions get more localized again at lowerhumidity values before they spread out because of noise contributions.This example clearly demonstrates that profiles of distribution functionsare well suited to characterize the mixing processes in the boundarylayer. DIAL measurements can provide this information.

The combination of high-resolution profiling for humidity and thevertical wind component allows one to determine profiles of the latentheat flux using the eddy-correlation technique [24]. In this technique,which is widely used for in situ flux measurements, the flux F� is deter-mined directly as the product of the water vapor density � and the verticalvelocity w:

F� = � · w. (8.18)

By definition the product is the instantaneous local flux, but averaging intime and/or space is necessary to provide a value that is representativefor a certain period and area. This averaging is indicated by the overbarin Eq. (8.18). This method of direct flux measurement has the advantagethat it does not depend on any assumption about the turbulence structure.However, some care needs to be taken in the estimation of representa-tiveness. Only if a sufficiently large number of eddies has passed over thesystem can F� be assumed representative for a larger area, otherwise theresult may be rather random with even its sign depending on the actuallyobserved part of the eddies.

So far the method has been used only occasionally, mainly with acombination of DIAL for the density measurements of water vapor orozone and a Radio Acoustic Sounding System (RASS) for the verticalwind measurements [24, 25]. Combination of DIAL with a Dopplerlidar has also been reported [26], which promises much better match ofthe sampling volumes and much better height coverage. Attempts arepresently made to explore the possibility of measuring both quantitieswith the same system, a Doppler lidar with DIAL capability [27, 28].

The use of the eddy correlation method with remote sensing instru-ments will find broader application only if the system complexity andthe effort needed for combined system operation is reduced considerably.The attempt is worth being made because it is a unique way to measureflux profiles in the boundary layer over rather long periods (as comparedto, e.g., aircraft measurements).

234 Jens Bösenberg

8.4.3 Airborne Water Vapor Profiling

The possibility of building water vapor DIAL systems that can be oper-ated on board an aircraft has attracted atmospheric scientists from thebeginning. In fact more laboratories were involved in the development ofairborne DIAL than in ground-based systems [29–31]. The main advan-tages of airborne over ground-based systems certainly are the flexibilityin choosing the geographical region for experiments, in particular regionswhich would otherwise be hard if not impossible to access, and to coverlarge areas or to follow an object of interest. It also allows us to lookdown on the lower troposphere while simultaneously looking up to theupper troposphere/lower stratosphere without being obstructed by thedense layer of water vapor near the ground. A series of experiments thatexploited these possibilities to a large extent was organized by NASAin the frame of the Convection And Moisture EXperiment (CAMEX)to investigate the distribution of water vapor, aerosols, clouds, and pre-cipitation around hurricanes. During these experiments an advanced,fully engineered, automated water vapor DIAL, the Laser AtmosphericSensing Experiment (LASE) [29], was operated on board a DC-8 air-craft. It is based on a Ti:sapphire laser, which is injection seeded with adiode laser frequency-locked to a strong water vapor line in the 815-nmband. A special feature of the laser transmitter is that the seeder can betuned electronically to any spectral position on the absorption line tochoose the optimal absorption cross section for the scene to be investi-gated. Fast switching between different positions is possible, permittingthe use of different absorption cross sections in a rapid sequence. Thisallows one to cover the wide range of several decades of water vapordensity that is found in a single column, in particular because the systemis both looking downward into the lower troposphere and upward intothe upper troposphere/lower stratosphere.

Figure 8.11 shows a GOES-8 image of hurricane “Bonnie” closebefore landfall on August 26, 1998, with the flight track of the DC-8 carrying LASE superimposed. It is obvious that such an extendedand fast-developing weather system can only be investigated with anairborne instrument in such a way that all important parts of the systemare observed in about the same status of development.

As an example for the results that can be achieved Fig. 8.12 shows across section of the first flight leg, tangential to the SE part of the storm.In the aerosol distribution, not shown here, the narrow rain band that wastraversed around 11:50 UT is clearly visible. Here cloud tops exceeded

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 235

Fig. 8.11. GOES-8 image of hurricane “Bonnie” on August 26, 1998, with the flighttrack of the DC-8 carrying LASE superimposed.

Fig. 8.12. Water vapor distribution on the flight leg from 11:28 to 12:13 UT. Thehorizontal black line at 8 km indicates the flight level. Horizontal resolution is 14 km(about 1 min), vertical resolution is 330 m for the lower part and 550 m for the middleand upper troposphere.

236 Jens Bösenberg

7 km altitude. The marine boundary layer in the inflow region of thehurricane is also well determined, it extends to about 1 km height. Thespecific humidity exceeds 15 g/kg in the boundary layer, and a region ofmoist air extends up to about 5 km, remarkably higher than the aerosollayer. In the upper troposphere the region to the NE of the rain band isclearly drier than the region to the SW of it, a fact that is also reflected inthe enhanced cloud cover beyond 8 km in that sector. For further resultsand a detailed discussion the reader is referred to [32].

The example clearly shows that lidar measurements with airbornesystems can make a unique contribution to studies of important weatherphenomena that cannot be obtained by other methods. Airborne DIALhas been applied to studies of several other atmospheric phenomena thatrange from boundary layer processes to stratospheric intrusions. Withthe level of maturity that has been reached for the methodology andtechnology it is expected that these systems will be employed in a largevariety of dedicated studies of atmospheric processes.

8.5 Temperature Profiling

The potential of the DIAL technique for temperature profiling was firstintroduced by Mason [33] and developed further by Schwemmer andWilkerson [34], Korb and Weng [35, 36], and Mégie [10]. To the author’sknowledge only one attempt to perform range-resolved temperaturemeasurements with this technique has been reported so far [2].

The method is based on Eq. (8.1), which describes the dependenceof the absorption coefficient on the number density of the absorber,the temperature-dependent strength of the absorption line, and thetemperature- and pressure-dependent line shape. In most DIAL appli-cations this is used to determine the density of the absorbing gas fromthe measured absorption coefficient and the known line strength and lineshape, but if the absorber density is known it can also be used to determinethe temperature-dependent line strength and from that the temperatureitself. For this method oxygen is used as an absorber because it is knownto have a constant mixing ratio in the atmosphere up to high altitudes,and because it has suitable absorption lines in an easily accessible partof the spectrum.

Although the method appears simple in principle, a more detailedlook shows that several problems need to be addressed. Let us first rewrite

8 Differential-Absorption Lidar for Water Vapor and Temperature Profiling 237

Eq. (8.1) for direct application to temperature profiling:

α(ν, p, T ) = qO2(1 − qH2O)p

kBTS(T , ε)!(ν − ν0, pi, T ), (8.19)

where qO2 and qH2O denote the mixing ratios of oxygen and water vapor,respectively. The first obvious complication is that the water vapor profilehas to be known, too, which calls for a combination with a water vaporDIAL. Second, Eq. (8.19) represents a nonlinear relation between α andT which cannot be solved for T analytically. However, there is a robustand fast converging iterative solution [36] which will not be given indetail here. It must also be noted that the atmospheric pressure profileneeds to be known, which is generally calculated from the measuredpressure at ground level and the temperature profile. Because the latteris initially unknown, again an iterative procedure is involved which alsoconverges fast.

In the choice of a suitable absorption line, a trade-off must be madebetween high temperature sensitivity of the absorption cross section,which is largest for high initial-state energy, and a suitable magnitudeof the absorption coefficient, which decreases with increasing initial-state energy. It turns out that suitable lines have a temperature sensitivityof the absorption cross section on the order of only 1–3% K−1. Thisimplicates that the absorption coefficient must be determined with lessthan 1% error to retrieve the temperature with the required accuracy ofbetter than 1 K. This makes clear why temperature profiling using DIALis extremely demanding systematically as well as technically. It alsomakes clear why this technique has so far not been used in practicalapplications.

It is beyond the scope of this chapter to discuss all possible system-atic errors; for this, the reader is referred to [2]. There it is demonstratedtheoretically as well as experimentally that the problem of the insuffi-ciently known contribution of Doppler-broadened Rayleigh scattering tothe total signal is the main source of uncertainty of the resulting temper-ature profile, provided that all other systematic and experimental errorshave been reduced to the greatest possible extent. While in regions ofdominating aerosol backscatter, specifically the well-mixed boundarylayer, the observed errors were below 1 K, the observed temperatureerror exceeded 3 K at the top of the boundary layer where strong gradi-ents in aerosol backscatter were observed. It is probably because of thesedifficulties, in combination with the availability of other measurement

238 Jens Bösenberg

methods, see e.g., Chapter 10 of this volume, that no further attempts touse the DIAL technique for temperature profiling have been reported.

8.6 Conclusions

The application of differential absorption lidar to narrow lines of therotational-vibrational spectrum of water vapor or oxygen for humidityand temperature profiling is technically demanding with respect to thelaser source and the data acquisition. Many details need to be consideredcarefully in system design and data evaluation. If that is done properly thetechnique is very powerful, in particular for water-vapor profiling. Themain strengths of DIAL in ground-based applications are its excellentdaytime performance for high-resolution studies in the boundary layerand high-accuracy routine observations in the lower half of the tropo-sphere, as well as its independence from external calibrations. Suitabilityfor airborne and probably also for spaceborne applications is definitelyanother very important feature of the method.

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