Retrieval of foreign-broadened water vapor continuum coefficients from emitted spectral radiance...

Retrieval of foreign-broadened watervapor continuum coefficients from

emitted spectral radiance in the H2Orotational band from 240 to 590 cm −1

Carmine Serio1, Guido Masiello1, Francesco Esposito1, Paolo DiGirolamo1, Tatiana Di Iorio2, Luca Palchetti3, Giovanni Bianchini3,Giovanni Muscari5,Giulia Pavese4, Rolando Rizzi6, Bruno Carli3,

Vincenzo Cuomo4

1Dip. Ingegeneria e Fisica dell’Ambiente, Universita della Basilicata, Potenza, Italy2Dip. Fisica, Universita di Roma ”La Sapienza”, Roma, Italy

3Istituto di Fisica Applicata ”Nello Carrara”, IFAC-CNR, Firenze, Italy4Istituto di Metodologie per l’Analisi Ambientale, IMAA-CNR, Potenza, Italy

5Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy6Dip. Fisica, Universita di Bologna, Bologna, Italy

[email protected]

Abstract: The paper presents a novel methodology to retrieve theforeign-broadened water vapor continuum absorption coefficients in thespectral range 240 to 590 cm−1 and is the first estimation of the continuumcoefficient at wave numbers smaller than 400 cm−1 under atmosphericconditions. The derivation has been accomplished by processing a suitableset of atmospheric emitted spectral radiance observations obtained duringthe March 2007 Alps campaign of the ECOWAR project (Earth COolingby WAter vapor Radiation). It is shown that, in the range 450 to 600cm−1, our findings are in good agreement with the widely used Mlawer,Tobin-Clough, Kneizys-Davies (MT CKD) continuum. Below 450 cm−1

however the MT CKD model overestimates the magnitude of the continuumcoefficient.

© 2008 Optical Society of America

OCIS codes: (010.0010) Atmospheric and oceanic optics; (010.5620) Radiative transfer;(300.6270) Spectroscopy, far infrared; (300.6300) Spectroscopy, Fourier transforms

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1. Introduction

Water vapor is the main greenhouse gas in the atmosphere and its far infrared rotation bandplays an important role particularly in the mid and upper troposphere, where it influences theEarth’s cooling rate (e.g., [1, 2]). Although much work has been done until now, e.g. [3, 4, 5], the



far-infrared portion of the atmospheric emission spectrum has not been sufficiently explored,mostly because of the lack of suitable radiometric instrumentation.

ECOWAR (Earth COoling by WAter vapor Radiation, [6, 7]) is an observational program ofatmospheric emission which aims at bridging this knowledge gap.

The present work will show new results concerning the foreign-broadened component ofthe water vapor continuum, derived from ground based observations of spectral downwellingradiance during the ECOWAR campaign in the Alps, from 3 to 17 March 2007 [6, 7]. Thespectral measurements cover the range 240 to 590 cm−1.

State of art radiative transfer models normally rely on the CKD model [8] for the parame-terization of water vapor continuum. This is a semi-empirical model which has been tuned onlaboratory and atmospheric observations. For the region 350 to 650 cm −1, laboratory measure-ments [9] at room temperature are the basis of the first quantitative development, followed by aseries of revisions as a result of high-resolution spectral observations, both from field campaignsand laboratory measurements (e.g., see [3, 4, 10, 11, 12]). Many of these field campaigns andexperiments have been, and continue to be, organized and carried out within the framework ofactivities of the US Department of Energy (DoE) ARM (Atmospheric Radiation Measurement)program (see e.g. [14]). Taking advantage of this experience and theoretical considerations, anew model has been developed building on the original CKD formulation, named MT CKD(e.g. see [13] and references therein).

Although other spectral regions have undergone significant changes since the early CKDmodel (e.g. see also the recent work in [15]), improvements in the region below 420 cm −1

have been limited by the lack of observations. In the range 350 to 420 cm −1 only Burch’sobservations are available and below 350 cm−1 there are no laboratory data yet published.Thus, in the segment 350 to 420 cm−1 our data provide the first set of observations under actualatmospheric conditions, and below 350 cm−1 they are the only experimental data set availabletoday.

Finally the foreign-broadened continuum scheme provided by MT CKD does not currentlyinclude, against theoretical evidence [16, 17], a dependence on temperature. Our data mayprovide constraints for further theoretical work on the temperature dependence of the foreign-broadened continuum.

The paper is organized as follows. Section 2 is devoted to a summary of the experimentalconditions, while the methodology to estimate continuum coefficients is discussed in section 3.Data and results are shown and discussed in section 4. Conclusions are drawn in section 5.

2. Experimental

The experimental set up of the ECOWAR campaign has been presented and discussed at alength in [6, 7], which the reader is referred to for the details. For the sake of clearness andbenefit of the reader we briefly summarize here what is essential to a proper understanding ofthe present work.

For observations from the ground, the water vapor rotational band is normally opaque be-cause of the strong absorption. However, in case of suitable dry conditions, the emission spec-trum shows narrow ”micro-windows”, or regions between absorption lines , where the at-mosphere becomes relatively more transparent. These micro-windows are fairly sensitive tocontinuum emission. For this reason the campaign took place at two close alpine stations:Cervinia (45◦ 56’ N, 7◦ 38’E) at an altitude of 2000 m and Testa Grigia (45 ◦ 56’ N, 7◦ 42’E) at an altitude of 3500 m.

Two FTS instruments were the core of the instrumental set: the Interferometer for Basicobservations of the Emitted Spectral radiance of the Troposphere (I-BEST), operated fromCervinia and the Radiation Explorer in the Far InfraRed - Prototype for Applications and De-



velopment (REFIR-PAD), operated from Testa Grigia.I-BEST [18] is a Fourier Transform Spectrometer based on the commercial-off-the-shelf

ABB-Bomem MR 104 series of FTS instruments. In addition to a MCT detector, I-BEST isalso equipped with an uncooled DLaTGS (deuterated L-alanine-doped triglycene sulphate) py-roelectric detector. Interferograms are acquired at a rate of about 27 interferograms per minuteand one product cycle consists of 60 interferograms for a total integration time of ≈ 2 m and 18s. The spectral coverage is 100 to 1100 cm−1 with the DLaTGS detector and 450 to 1800 cm−1

with the MCT one. The sampling rate is 0.3931 cm−1 for an unapodized spectral resolution,Full Width at Half Maximum (FWHM) of 0.48 cm−1. An end-to-end assessment of the noisebudget of the instrument can be found in [18].

REFIR-PAD [19] is a portable FTS specifically developed in-house at IFAC for the measure-ment of the atmospheric emitted radiance over the spectral range 100 to 1100 cm −1 with aspectral sampling of 0.5 cm−1 and an unapodized spectral resolution, FWHM, of ≈ 0.6 cm−1.The interferometer uses an optical design with two input ports and two output channels. Oneinput port looks at the scene to be measured and the second one at a reference blackbody source,which allows the access and the control of the instrument self-emission. At the output ports,signals are acquired with two uncooled DLaTGS pyroelectric detectors.

Although REFIR-PAD has been designed to be operated on-board stratospheric platforms[20], minor changes to the flexible design have adapted the instrument to ground-based ob-servations. Measurements of 64 s acquisition time are taken in sequences of 4 calibrations (2measurements for the hot and 2 for the cold blackbody) and 4 atmospheric zenith observations.Each product sequence lasts about 5 minutes, including delays among single measurements.Detailed information on the REFIR noise budget can be found in [7]

In addition to these spectral observations, ancillary information, needed to characterize thethermodynamic state of the atmosphere, were measured by : 1) a VAISALA RS92k radiosondesystem; 2) a Raman Lidar capable of simultaneously getting temperature, water vapor, aerosoland cloud optical properties; 3) a Ground-Based Millimeter-wave Spectrometer (GBMS) forobservations of precipitable water vapor (PWV). The GBMS capability to measure accuratePWV values also for very low content of H2O (see, e.g. [6, 7]) has proven to be very important.

Examples of I-BEST and REFIR-PAD observations for the range 240 to 600 cm −1 are shownin Fig. 1, which also exemplify the level of instrument noise affecting the measurements. Thetwo observations refer to the same day of 9 March 2007. The instrument noise includes all noisesources which affect the calibration process (detector noise, internal blackbodies temperatureand emissivity uncertainties and so on [18, 7]).

REFIR-PAD (placed at 3500 m) clearly shows resolved micro-windows in the range 200 to350 cm−1, while I-BEST (2000 m) already shows a saturated spectrum. The total integrationtime is 2 min and 18 s for I-BEST and ≈ 5 min for REFIR-PAD.

3. Methodology

3.1. Definition of the water vapor continuum absorption

According to [8, 3] the absorption coefficient of water vapor k (units of cm 2 molecule−1) at aspecific wavenumber σ (units of cm−1) is defined by

k = klocal +Cf

(ρ f

ρo

)+Cs

(ρs

ρo

)(1)

where klocal is the local absorption coefficient, which accounts for the cumulative effects ofall lines whose center lies within 25 cm−1. The two continuum terms are the foreign-broadenedcomponent C f and the self-broadened Cs component, both expressed as cross sections (unitsof cm2 molecule−1), and ρ f and ρs are the densities of air and water vapor in molecule cm−3.



250 300 350 400 450 500 550 6000

0.05

0.1

0.15

wave number (cm−1)

Spe

ctru

m (

W/(

m2 −

cm−

1 −sr

))

250 300 350 400 450 500 550 6000

0.05

0.1

0.15


Spe

ctru

m (

W/(

m2 −

cm−

1 −sr

))

I−BESTNESR

REFIR−PADNESR

Fig. 1. Example of (unapodized) spectral observations and related instrument noise (NESRin figure): (upper panel) I-BEST and (lower panel) REFIR-PAD. The observations refer to 9March 2007. During the observations the PWV above Cervinia/ Testa Grigia was 1.15/0.54mm. Isolated spikes at the lower wave number range are the effect of point calibration errorsdue to water vapor absorption (saturated water vapor lines) within the interferometers path.

The parameter ρo is a reference broadener density defined as ρo = Po/(kbTo), where Po = 1013mbar, To = 296 K, and kb is the Boltzmann constant.

In the Earth’s lower atmosphere, continuum absorption in spectral regions near the center ofwater vapor bands is generally dominated by air-broadening, while window regions are dom-inated by self-broadening. Based on the MT CKD model, for the spectral region 240 to 590cm−1 and at altitudes and temperatures relevant to our experiment, the foreign to self absorp-tion ratio steadily increases from 4 (at 600 cm−1) to 20 (at 240 cm−1). For this reason ouranalysis is focused on C f alone.

The parameter C f can be further decomposed in

Cf = σ tanh

(hcσ2kbT

)Cf , (2)

where h is the Planck constant, c is the speed of light, and T is the temperature. In this paper,we consider and show results about Cf , which is normally referred to as Symmetrized PowerSpectral Density Function. However, for the sake of a concise notation it will be referred inthe following to as the continuum coefficient and denoted with c or c(σ) when we will need toexplicit its dependence on wave number.

3.2. Methodology to estimate continuum coefficients from down-welling spectral radiances

In closure experiments, the state of the atmosphere has to be independently measured in itsmore important thermodynamic components, temperature and water vapor profiles. Ideally thevarious instruments, radiometers, Lidar, GBMS and radiosonde, should probe exactly the same



air mass, in order to minimize co-location artifacts. However problems of accuracy, bias andtime lag make it difficult to get ancillary information which is radiometrically consistent withthe observed spectral radiances.

3.2.1. Adjusting the temperature profile

Both I-BEST and REFIR are partly insulated from the environment, so that they operate inconditions which are different from the atmosphere at same altitude. For this reason the ra-diosonde and/or Lidar temperature profile, in their lowest altitude range, must be scaled to thislocal environment, a process which is accomplished using the spectral radiance observed in themost absorbing portion of the CO2 band. The details of this form of adjustment or scaling ofthe temperature profile to the spectral observations has been discussed and presented in [21]. Ithas been systematically applied to REFIR and I-BEST spectra used in this work.

After performing this temperature correction , we could well experience other problems, suchas the so-called problem of dry bias in the humidity profile (e.g., [22], and time lag betweenvarious instruments. Since these biases and uncertainties propagate to the estimates of the con-tinuum coefficients, a procedure, which retrieves continuum coefficients, while simultaneouslyadjusting H2O and temperature profiles, has been developed to improve the agreement withobserved radiances. This procedure is discussed in the next section.

3.2.2. The Inversion algorithm

Let r be the vector of spectral radiance, of size N. Let L denote the number of atmosphericlayers used in the forward model for the discretization of the radiative transfer equation, and letF(s;v) be the forward model which is a function of a suitable set of spectroscopic parameters,s and of the atmospheric state vector, v. We have

r = F(s;v) (3)

Temperature (T) and water vapor (q) profiles are part of the state vector. In their discrete formthey have size equal to the number of atmospheric layers. In the same way the continuumcoefficients vector (c) is part of the set of spectroscopic parameters, and for each wave numberthe size of c is L. Thus if we consider N channels or wave numbers, σ i, i = 1, . . . ,N, the vectorc will be a column vector with L×N elements,

c = (c1(σ1), . . . ,cL(σ1), . . . ,c1(σi), . . . ,cL(σi), . . . ,c1(σN), . . . ,cL(σN))t (4)

where t means transpose.Let c0,T0,q0 be an initial guess of the continuum coefficients, temperature and water vapor

mixing ratio profiles, respectively. Equation (3) may be developed in Taylor series to give

r = r0 +Kc(c− c0)+KT (T−T0)+Kq(q−q0)+higher order terms (5)

In the above equation r0 = F(s0;v0), and KT and Kq are the usual derivative matrices, orJacobians, for temperature and water vapor respectively and their size is N×L. The matrix K c isagain a derivative matrix: the continuum coefficient Jacobian. Since the continuum coefficientsalso depend on the wavenumber, the size of the matrix K c is N ×N1, where N1 = L×N. Itsrow of index i contains the L derivatives (computed at the corresponding initial or first guessvalues),

(∂F

∂c1(σi), · · · , ∂F

∂cL(σi)

)(6)



Consistently with the definition of c given in (4), the above values have to be arranged on theline of index i from the position (i−1)∗L+1 to i∗L, the remaining elements of the row haveto be set to zero.

Since we are dealing with closure experiment and great care is taken in suitably probingand sounding the atmosphere with independent instruments, the true atmospheric state vector,which governs the emitted spectral radiance, is assumed to be in the linear region of the Taylorexpansion above. Similarly we can assume that the vector c is in the linear region defined bythe Taylor expansion of the radiative transfer equation. With this in mind we can neglect thehigher order terms in Eq. (5) and consider the linear form

y = Kcxc +KT xT +Kqxq (7)

withy = r− r0; xc = c− c0; xT = T−T0; xq = q−q0 (8)

Linearization of the radiative transfer equation with respect to the continuum coefficient hasbeen checked in simulation and it has been found to hold quite well even for variations of thecontinuum coefficient of ± 50% at all levels and wave numbers.

In case higher order terms were important, which might happen if the final solution wasnot in the linear region around the first guess state, we could resort to one of the many iterativeapproaches available in the literature, e.g. the well known Gauss-Newton method [23]. Howeverfor the analysis here shown one iteration step was enough to bring the spectral residual withinthe error bars.

If we look at Eq. (7) from the side of the parameter space, we have N ×L+L+L unknownsagainst N spectral data points. However, the number of unknowns can be reduced consideringthat the first guess profiles for (T,q) already provide a good state vector to synthesize andinterpret the spectral observations. On this line, we can parameterize (T,q) in terms of the firstguess values, a choice which can also improve the conditioning of the inverse problem.

Towards this objective, we consider

T = T0 + fT T0; q = q0 + fqq0 (9)

which, upon insertion in Eq. (7), gives

y = Kcxc +a fT +b fq (10)

with a and b column vectors of size N, defined by

a = KT T0; b = Kqq0 (11)

The second of these two assumptions just says that for water vapor we expect that the maindifference between first guess and truth lies in the columnar amount rather than in the shape ofthe profile. In this context, it is well known that radiosonde observations can suffer from a drybias, which is normally accounted for by scaling the observed profiles to, e.g., microwave ra-diometer measurements [22]. Our approach, besides using microwave radiometer observations,allows to refine the dry bias correction directly from the spectral observations at hand. By doingso, the resulting water vapor continuum coefficients will not be biased by uncertainties in thecolumnar amount of water vapor.

The first assumption made in (9), allows to scale also the temperature profile to reach aradiometric consistency, although this scaling has been checked to be less important than thatfor the water vapor.



The linear form (10) allows, in principle, to account for possible dependence on temperatureof the foreign-broadened continuum, a possibility which is in agreement with theoretical calcu-lations, e.g. [16, 17]. However, one should consider that we use strictly micro-window channelsto derive the continuum coefficients and that ground based observations are sensitive only tothe continuum emission from atmospheric layers close to the instrument. To discuss this pointwe can define the effective (emitting) temperature Te(σ j) for the channel σ j according to

Te(σ j) =∑L

i=1 | ∂F∂ci(σ j)

| Ti

∑Li=1 | ∂F

∂ci(σ j)| (12)

where Ti is the atmospheric temperature for the layer i. This definition is equivalent to that givenby [15].

For the case of the REFIR-PAD observations, the micro-window channels used in the analy-sis are shown in Fig. 2. The same figure also illustrates the effective temperature for the casestudy of 9 March 2007. For this day we observed the lowest total columnar amount of watervapor, that is 0.54 mm. An example of the continuum coefficient Jacobian, referring to the samewindow channels, is shown in Fig. 3. It is possible to see that the Jacobian peaks at a nearlyconstant altitude level, as the wave number varies in the range 240 to 590 cm −1. As a conse-quence, to account in the inverse problem for the potential emission by the entire atmosphericcolumn is only an unnecessary complication. This is not to say that we neglect the temperaturedependence, but rather that the continuum coefficients are determined by a common effec-tive temperature. The concept of effective temperature also allows us to identify homogenouswindow channels since they are characterized by the lowest effective temperature. Thereforea channel whose effective temperature largely deviate from the lowest values is likely to beaffected by line absorption and therefore not suitable to derive continuum coefficients.

In the light of the above discussion, we consider a simplified form of Eq. (7), in which, foreach channel, the L coefficients along the atmospheric column are collapsed into one singleeffective continuum coefficient.

With this last assumption, the vector, c becomes a vector of size N, whose elements are thecontinuum coefficients at the N waveumbers, σ1, . . . ,σN . Note that even with this simplification,the layer derivative ∂F/∂c j(σi) does depend on the layer (even when computed at the samewavenumber!). Thus, we still need to compute the full dimensional N ×N 1 Jacobian and thenconsider the summation of the Jacobian elements over the column, that is over the indices,1, . . . ,L.

This operation contracts the matrix Kc to the lower size or dimension N ×N, and it can beformally performed by considering a suitable contraction kernel. Let us consider the L×Nmatrices, Hi, with i = 1, . . . ,N, whose elements are zero apart from those on the column ofindex, i, which have to be set equal to 1. Let us consider the matrix H, obtained by verticalconcatenation of the individuals, H i, that is

H =

⎛⎜⎜⎜⎜⎜⎜⎝

H1

H2

. . .Hi

. . .HN

⎞⎟⎟⎟⎟⎟⎟⎠

(13)

Let K be the N ×N matrix given byK = Kc ·H (14)



250 300 350 400 450 500 550 600−0.05

0

0.05

0.1

0.15


Rad

ianc

e (W

/(m

2 −cm

−1 −

sr))

250 300 350 400 450 500 550 600250

252

254

256

waven umber (cm−1)

Te(σ

)

Fig. 2. REFIR-PAD synthetic spectrum (upper panel), simulated according to the at-mospheric conditions observed on the day 9 March 2007, showing the window channels(red dots); (lower panel) the effective temperature of the window channels.

Fig. 3. Example of a continuum coefficient Jacobian for the spectral range of interest to ouranalysis.



then we can reduce the problem (10), to a new problem with N + 2 unknowns, N for thewavenumber-dependent continuum coefficients, one for the temperature scaling factor, and onefor the water vapor scaling factor:

y = Kxc +a fT +b fq (15)

where xc contains the differentiated values of the N continuum coefficients.Even in this form, the above equation contains more unknowns than data points. Let us

consider M diverse spectra, for which we assume to have M corresponding (T 0,q0) couples,then let us consider the N ×M column vector, y obtained by vertical concatenation of theindividual data vectors, y

y =(yt

1,yt2, . . .,y

tj, . . .,y

tM

)t(16)

For this vector we can write the relation

y = Kxc +AfT +Bfq (17)

where the matrices A and B are of size N ×M and are obtained by horizontal concatenation ofthe M individual column vectors, a and b, respectively,

A =(

a1, . . . ,a j, . . . ,aM)

; B =(

b1, . . . ,b j, . . . ,bM)

(18)

Furthermore, the two column vectors of size M, fT and fq contain the corresponding scalingfactors for each single pair, (T0 j,q0 j). Finally, note that the term Kxc is left unchanged by co-adding M spectra, since we consider a time span for which the temperature profile may vary,but not to an extent to significantly affect Cf .

In the end, the problem (17) has N×M data points for N +M +M = N +2M unknowns, andit can be further compacted by considering the linear form

y = Gx (19)

with G obtained by the horizontal concatenation of the three matrices, K c,A,B,

G = (Kc,A,B) (20)

and

x =

⎛⎝ xc

fT

fq

⎞⎠ (21)

To have an idea of the size of the problem above, consider that for the full range 240 to 590cm−1 we have N=251. By co-adding up to a maximum of M=20 clear sky spectra (recordedover a time period of at most 2 hours) we have 5002 data points in the range 240 to 590 cm −1.In addition, we also use 60 non-window channels from 745 to 800 cm −1, at wave numberssensitive to water vapor line absorption and temperature. For these channels the Jacobian, K c isjust set to zero, therefore they do not contribute to the inversion of the continuum coefficients,but they provide additional information to constrain the water vapor and temperature scalingfactors.

One the side of the parameter space, we have 300 (continuum coefficients)+2*20 ( f T and fq

parameters)=340 unknowns. These unknowns can be estimated by usual Least-Squares meth-ods. The problem is now sufficiently well-conditioned to be inverted without further constraints.In other words we can retrieve the unknowns by considering unconstrained Least-Squares (e.g.[23])

ˆx =(GtS−1G

)−1Gt S−1y (22)



with S the covariance matrix of the spectral observations, the covariance matrix of the estimateis given by

Sx =(GtS−1G

)−1(23)

One important aspect, which derives from the properties of unconstrained Least-Squares, is thatthe solution (22) is unbiased for the vector, x.

The above methodology, which to our knowledge is original for the problem at hand, allowsto simultaneously retrieve the continuum coefficients along with the scaling factors for the watervapor and temperature profiles. The methodology also provides a proper treatment for the noiseterm and allows to estimate the a-posteriori covariance matrix of the observations.

Since the continuum is expected to vary slowly with wave-number, in practice the retrievedcoefficients are first combined in bins spanning ≈ 10 wavenumbers (about 10 data points),and then the mean and uncertainty for each bin are computed. The mean is considered to berepresentative of the channel corresponding to the centroid of the bin.

Even for a diagonal S, that is in case of uncorrelated radiance errors, the retrieved coefficientsare in general correlated, a fact which depends on the structure of the spectral radiance . Thus,the standard deviation of each binned coefficient has to be obtained by considering variancesand co-variances, as well.

Let ck, k = j1, . . . , jn, the n coefficients within a bin and j1, . . . , jn the n channel numberswithin the same bin, the variance-weighted mean is defined as usual,

c =jn

∑k= j1

wkck; with wk =S−1

x (k,k)

∑ jnl= j1

S−1x (l, l)

, k = j1, . . . , jn (24)

where Sx(k,k) is the variance element (k,k) of the a-posteriori covariance matrix given by Eq.(23). The variance of the above weighted average is given by

s2c =

jn

∑k1,k2= j1

wk1 wk2 Sx(k1,k2) (25)

Failure to include a proper treatment of covariances would necessarily lead to underestimatethe uncertainty in the final continuum coefficient estimate. Even in the case in which any singlechannel were processed at a time, nearby continuum coefficients would be correlated becausethe radiances are.

3.2.3. Forward model

The forward model we have used in the analysis is LBLRTM (e.g. [13]) version 11.3, releasedon November 2007, along with the spectroscopic database HITRAN 2004+ [24]. Synthetic ra-diances have been computed with an atmospheric layering of L = 90 layers. Jacobian derivativematrices for temperature, water vapor and continuum coefficients have been computed with afinite difference scheme. LBLRTM version 11.3 makes use of the MT CKD version 2.1 for thecontinuum model. This model has been assumed as first guess in all the retrieval calculationsshown in the next section.

The atmospheric state vector used for the first guess must include minor and trace speciesother than water vapor. These were obtained from the Air Force Geophysics Laboratory(AFGL) compilation [27]. The mid-latitude winter model of the atmosphere was used to com-plete the atmospheric state vector.

Both REFIR-PAD and I-BEST spectral observations were Gaussian apodized, with aGaussian filter with a half width at half maximum of 0.5 cm−1. The apodization process helps



to improve the signal-to-noise ratio and remove possible inhomogeneities caused by Instrumen-tal Spectral Response Function (ISRF) uncertainties [25]. In view of the featureless behavior ofthe continuum absorption, the apodization does not imply any important loss of information.

The observational covariance matrix S was assumed to be diagonal and made up of instru-ment noise (at the un-apodized level) as well as forward model noise. Finally, it was consistentlytransformed [26] to reflect the apodization process.

As already mentioned, the instrument noise has been discussed for I-BEST in [18], whiledetails for REFIR-PAD can be found in [7]. The forward model uncertainty is due to the dis-cretization process of the radiative transfer equation and to uncertainty in spectroscopic lineparameters. The water vapor line parameters, especially line widths, are of major concern. Ac-cording to [24] a half width uncertainty of 3% for strong lines and 10% for weak lines and aline strenght uncertainty of 2% has been assumed. Perturbing with these uncertainties the spec-troscopic data base, we estimated a radiance uncertainty less than 0.2×10−3 W/(m2-cm−1-sr).This can be compared to the instrument noise which at best is of order 0.5×10 −3 W/(m2-cm−1-sr).

The effect of spectroscopic uncertainty has also been checked by comparing the HITRANrelease for 2000 and the current one, 2004+. The source of spectroscopic noise can be mostlysummarized in the terms klocal in Eq. 1. While the continuum is retrieved in our scheme, k local

is simply computed from the given data base. We have checked that the two diverse version ofHITRAN introduce on average an uncertainty of 3% in the continuum coefficients.

Finally, possible uncertainties arising from temperature and water vapor profiles are not in-cluded in the covariance matrix since these parameters are simultaneously retrieved with thecontinuum coefficients.

4. Results

During the first case study (9 March 2007) we observed the driest condition during the cam-paign (PWV=0.54 mm). For this day the REFIR-PAD was operated from the Testa Grigia Sta-tion (3500 m) together with the GBMS radiometer. Ten spectra were selected, which wereacquired from 07:36:27 to 09:20:51 UTC. The GBMS radiometer was crucial for the analysiswe are reporting. In fact, radiosonde measurements for water vapor were affected by a con-siderable dry bias. Only after rescaling the water profile to the PWV values observed with theGBMS the retrieval analysis converged. This result evidences once again the need of having areliable measurement at very low water vapor load.

Before performing the inversion for water vapor continuum, the temperature profiles wereadjusted according to the procedure outlined in section 3.2.1 and the water vapor profiles wererescaled to agree with the PWV values observed by the GBMS instrument. Clear sky waschecked by means of inspection of the spectra and through a visible sky-camera operating bythe station of Cervinia complemented by direct observation at the time the measurements weretaken.

With REFIR-PAD we could explore the widest spectral range, extending from 240 to 560cm−1 and, in addition, the coldest emitting temperature during the campaign. Spectral rangesand emitting temperatures for the three day analyzed in the paper are shown in Fig. 4.

On 10 and 14 of March we have used observations from Cervinia station taken with the I-BEST FTS. On March 10 the instrument was operated with the DLaTGS detector and the cutoff wave number was around 360 cm−1. The observed PWV was 1.5 mm and the effective tem-perature was found to be ≈ 267 K. The observations were acquired from 21:17:27 to 22:10:24UTC, and 20 spectra were in the end selected and considered for the analysis. On March 14I-BEST was operated with the MCT detector and the cut-off wave number was around 460cm−1. The observed PWV was about 5 mm and the observed effective temperature was around



250 300 350 400 450 500 550 600245

250

255

260

265

270

275


Te(s

igm

a) (

K)

March 9March 10March 14

Fig. 4. Window channels, spectral ranges and effective temperatures for the three daysanalyzed in the paper. Spectral ranges differ each from other because they refer to differentinstruments and detector modes (see text).

269 K. The observations were acquired from 18:59:43 to 20:42:54 UTC, and 20 spectra werein the end considered for the analysis.

The observations for both days 10 and 14 were taken during nighttime and the Raman Lidarwas operated for the full period of measurements. In addition, radiosonde launches (3 ascentsfor day 10 and 2 for day 14, in coincidence with the FTS and Lidar observations) were per-formed for the calibration of the Lidar water vapor and temperature profiles. These profileswere provided with a resolution of 20 min and interpolated to the observation time of FTSmeasurements. Clear-sky was rigorously determined by inspecting LIDAR backscattering ratiotime maps at 355, 532 and 1064 nm [6]. The first guess for the state vector was provided byLidar observations for water vapor and temperature. The water vapor profiles were not scaledto the GBMS observations, since the GBMS instrument was operated from the Testa Grigiastation.

The analysis for the water vapor continuum is shown in Fig. 5 and Tab. 1. Figure 5 alsoprovides a comparison with adjusted Burch’s data. Our results and calculations apply to thecontinuum as defined, e.g., in [8, 3], whereas original Burch’s data [9] are not consistent withthis definition. For this reason, the Burch data we show in Fig. 5 have been adjusted to beconsistent with the local lineshape definition and spectral line parameters used in this work.Also, according to [3], an uncertainty of 15% has been assumed for these data.

In the range 420 to 600 cm−1, which is the spectral interval most explored until now bothin laboratory conditions and field observations, our findings are highly consistent with theMT CKD model whatever the detector, instrument and water vapor load may be. This resultalso gives credibility, confidence and reliability to our data and inversion methodology.

Our results exhibit larger discrepancy with model and laboratory data in the range 350 to420 cm−1, which has benefited until now only of limited laboratory observations. We finddiscrepancies which may reach values as large as 40% (see, e.g., Tab. 1). For this range we havethe overlap of two case studies (days 9 and 10 of March) with different emitting temperature(253 K against 267 K). However, the data points overlap within the error bars and no furtherconclusion can be derived as far as the dependence on temperature.

Our observations provide the very first set of water vapor continuum from atmospheric ob-servations in the range 240 to 350 cm−1. Although less pronounced than in the range 350 to420 cm−1, we still observe a trend for less absorption in comparison with the MT CKD model



250 300 350 400 450 500 550 600

10−26

10−25

10−24

10−23


Con

tinuu

m C

oeffi

cien

t (cm

−1 −

mol

ecul

e−cm

−2 )−

1

MT_CKD 1.0MT_CKD 2.1Burch (1974)Fit REFIRFit I−BEST (dtgs)Fit I−BEST (mct)

Fig. 5. Water vapor continuum coefficients (C f ) for the range 240 to 590 cm−1 as derivedfrom our analysis and comparison with two versions of MT CKD model [13] and Burch’sdata (adapted from [5].)

and Burch’s data.Our results reveal less continuum absorption than predicted by Burch’s laboratory observa-

tions, in agreement with previous studies [3, 4, 5]. The trend toward lesser absorption is alsoclearly evident in going from MT CKD version 1 to MT CKD version 2.1. These results leadus to conclude that foreign-broadened water vapor continuum has a slight positive dependenceon temperature, as predicted by theory [16, 17]. In fact Burch’s data refer to a temperature of296 K, while ours fall in the range 250 to 270 K. The slight positive dependence on temperaturealso explains the trend in modeling less water vapor absorption in order to agree with field ex-periments. Indeed, these experiments [3, 4, 5] have been performed at Arctic or mountain sites,hence, at temperature much lower than Burch’s 296 K.

Our inversion methodology allows for a compensation of possible biases in the water va-por load (parameter fq) and bulk temperature of the atmosphere (parameter f T ). The inversionanalysis is particularly sensitive to fq which is shown in Tab. 2 and Tab. 3 for each individualspectrum used in the analysis. For the case study of 9 March 2007 (REFIR-PAD observations),Tab. 2 also shows the scaling factor of the radiosonde profiles performed with the GBMS ob-servations. It is seen from Tab. 2 that the retrieved f q is not negligible, which demonstrates theneed of retrieving this parameter even when a preliminary GBMS scaling has been applied.

For the two remaining days (see Tab. 3), we observed retrieved values for f q much largerthan those for the previous case. These larger deviations are expected, since in contrast to TestaGrigia station, Lidar water vapor profiles were not scaled to the PMW obtained by the GBMS.However, we think that the PWV variations calculated through the parameter f q are not only theresult of bias, but they may also reflect the high variability of water vapor in the high mountainsetting where our observations were taken (e.g., see [6, 7]).

For temperature, the parameter fT was found to vary randomly around zero, suggesting that



the adjustment we perform for the temperature profile in the lowest atmosphere (see section3.2.1) is already enough to account for most of the residual uncertainties in temperature.

wave number Symmetrized Spectral Density FunctionCf (×10−26)(cm−1) (cm−1 molecule cm−2)−1

REFIR I-BEST I-BEST Average MT CKD 2.1 f ±Δ f(dtgs) (mct) (%)

240 860 ± 120 861.6 1029 −16±11250 629.9 800.2 −21±12260 460 ± 90 459.5 606.6 −24±15270 430 ± 70 429.7 475.5 −10±15280 343.6 371.0 −7±18290 270 ± 60 274.9 278.6 −1±21300 230 ± 60 230.3 229.0 1±26310 130 ± 30 126.2 183.1 −31±16320 140 ± 30 137.1 145.4 −6±20330 80 ± 40 80.07 120.7 −34±33340 73 ± 24 73.45 95.90 −23±26350 49 ± 28 48.78 80.63 −40±34360 50 ± 8 42 ± 9 46.29 64.54 −28±9370 42 ± 8 38 ± 8 40.24 52.98 −24±11380 26 ± 7 26 ± 8 25.80 43.65 −41±12390 25 ± 4 27 ± 4 26.09 34.42 −24±8400 20 ± 4 18 ± 5 18.71 28.65 −35±11410 18 ± 2 19 ± 2 18.61 23.39 −20±6420 16.22 19.70 −18±7430 13 ± 2 15 ± 2 14.16 16.21 −13±8440 13 ± 2 12 ± 2. 12.76 13.77 −7±10450 10 ± 2 11 ± 2 10.52 11.50 −9±12460 8.4 ± 1.5 9.4 ± 1.6 9.8 ± 0.3 9.785 9.577 2±3470 7.0 ± 1.9 8.1 ± 1.9 7.7 ± 0.3 7.668 8.188 −6±3480 5.8 ± 1.0 6.7 ± 0.9 5.8 ± 0.2 5.788 7.093 −18±2490 5.2 ± 0.8 6.2 ± 0.8 5.4 ± 0.1 5.450 6.005 −9±1500 3.5 ± 0.9 4.9 ± 0.6 4.2 ± 0.1 4.244 5.121 −17±1510 3.7 ± 0.8 5.2 ± 0.8 4.4 ± 0.1 4.408 4.336 2±2520 3.4 ± 1.0 4.6 ± 0.8 4.0 ± 0.1 4.047 3.710 9±2530 2.3 ± 0.8 3.5 ± 0.4 2.69 ± 0.06 2.716 3.201 −15±1540 1.9 ± 0.7 3.0 ± 0.4 2.14 ± 0.06 2.161 2.741 −21±2550 2.0 ± 0.7 3.0 ± 0.5 2.52 ± 0.08 2.523 2.339 8±3560 1.5 ± 0.5 2.3 ± 0.2 1.77 ± 0.04 1.780 1.981 −10±1570 1.80 ± 0.06 1.798 1.713 5±3580 1.61 ± 0.07 1.609 1.473 9±4590 1.36 ± 0.05 1.356 1.285 6±4

Table 1. Summary of the water vapor continuum coefficients, expressed as symmetrizedspectral density function, C f , obtained in our analysis. The column average is the meanvalue of the three set of observations; the column has been filled through interpolation forwave numbers at which we have no observations. A comparison with the MT CKD (version2.1) values is provided in the table. The last column gives the percentage variation f =100×(Average-MT CKD)/(MT CKD) and the related uncertainty.

Finally, we have performed a spectral residual analysis to check that the retrieved continuumcoefficients were consistent with the observed spectral radiances.

Figure 6 shows the mean observed radiance spectrum for the March 9 case. The same figurealso shows the residual (observed - calculated) using the MT CKD model. The plot highlightsthe spectral difference at the window channels used in this analysis. The MT CKD model warmbias is evident in the region 240 to 500 cm−1 and reaches its largest values in between 350and 400 cm−1. We again stress that this spectral interval has not been ever investigated in



Date From To fq as from inversion fq as from GBMS(UTC) (UTC) (%) (%)

09-Mar-2007 07:36:27 07:41:36 5.3 9.007:47:27 07:52:36 5.0 1107:58:33 08:03:42 2.1 1408:09:33 08:14:42 -0.6 1508:20:33 08:25:43 -4.1 1508:31:34 08:36:44 -4.2 1608:42:35 08:47:44 -2.2 1608:53:35 08:58:44 -4.0 1709:04:37 09:09:45 -6.5 1909:15:41 09:20:51 -4.1 21

Table 2. Scaling factors for the water vapor profiles as retrieved from the inversion process,for the case study of 9 March 2007 (Testa Grigia station). The scaling factors derived fromthe GBMS observations are shown, as well. The starting and end time refer to acquisitiontime period of the corresponding REFIR spectrum

Date From To fq Date From To fq

(UTC) (UTC) (%) (UTC) (UTC) (%)10-Mar-2007 21:17:27 21:19:45 -3.6 14-Mar-2007 18:59:43 19:02:00 -2.7

21:22:04 21:24:22 -2.5 19:02:00 19:04:18 -0.521:24:22 21:26:40 -3.4 19:47:52 19:50:09 -0.921:26:40 21:28:58 -1.6 19:45:34 19:47:52 -0.721:28:58 21:31:16 -6.3 19:52:27 19:54:45 -0.221:31:16 21:33:34 -7.3 19:43:17 19:45:34 -0.221:33:34 21:35:52 -4.1 19:40:59 19:43:17 0.421:35:52 21:38:10 -4.6 19:50:09 19:52:27 -0.221:38:10 21:40:28 -8.0 19:54:45 19:57:02 0.221:40:28 21:42:46 -3.8 19:59:20 20:01:37 0.821:42:46 21:45:05 -5.2 18:57:25 18:59:43 -5.421:45:05 21:47:23 -7.3 19:57:02 19:59:20 0.721:47:23 21:49:41 -6.8 20:01:37 20:03:55 1.521:49:41 21:51:59 -10.2 19:38:42 19:40:59 1.421:51:59 21:54:17 -8.6 19:36:24 19:38:42 1.921:54:17 21:56:35 -11.0 20:03:55 20:06:12 2.321:56:35 21:58:53 -7.8 20:06:12 20:08:30 2.821:58:53 22:01:11 -9.0 20:08:30 20:10:48 3.522:01:11 22:03:29 -5.5 20:42:54 20:45:11 2.822:08:06 22:10:24 -1.8 20:40:36 20:42:54 3.5

Table 3. As Tab. 2 but for the two case studies on 10 and 14 March 2007 (Cervinia station).Starting and end time refer to the acquisition time period of each I-BEST spectrum. Forthese two cases the water vapor first guess profiles were derived from Lidar observationsand no preliminary scaling was applied before entering the inversion process.

atmospheric conditions until the present study. Figure 6 also shows the spectral residual usingthe adjusted coefficients according to our analysis. It is clear that the warm bias is largelyremoved and the computations gain higher consistency with the observations. Also note that inthe segment 450 to 600 cm−1, our analysis coincides with the MT CKD model.

Outside the window regions there is no benefit, as expected, from the change of the contin-uum coefficients. The isolated spikes at the lower wave numbers range are the effect of pointcalibration errors due to the presence of strong water vapor absorption within the interferometerpath.



250 300 350 400 450 500 550 6000

0.05

0.1


radi

ance

(W

/(m

2 −cm

−1 −

sr))

250 300 350 400 450 500 550 600−0.01

−0.005

0

0.005

0.01


diffe

renc

e (W

/(m

2 −cm

−1 −

sr))

obs−calc (mt_ckd 2.1)obs−calc (this work)

REFIR obs.mt_ckd 2.1 calc.this worksel. channels

Fig. 6. Mean observed and calculated radiance spectrum for the day 9 March 2007 (upperpanel) and observed minus calculated (lower panel). The window channels are evidencedwith dot symbols. Calculations are shown using MT CKD (version 2.1) and continuumcoefficients determined from the three case studies presented in this work.

5. Conclusions

We have analyzed spectral radiances in the range 240 to 590 cm−1 and derived water vaporcontinuum coefficients, which have been compared to model and laboratory data. The spectralradiances have been recorded during the March 2007 ECOWAR field campaign in the Alps andencompass a variation in the precipitable water vapor from 0.5 to 5 mm during the observationperiod.

A suitable inverse methodology was developed to retrieve the continuum coefficients, whichallows us to remove possible uncertainties arising from the input state of the atmosphere (initialguess for temperature and water vapor profile).

Our findings are in good agreement with the MT CKD model in the range 450 to 600 cm −1,which in the past has highly benefited from field observations at the SHEBA Ice station [3].These results gives confidence on our methodology and spectral data and positively support thefindings we have shown for the remaining far infrared range, 240 to 450 cm −1. In this range,for which our analysis provides the very first validation of the MT CKD model in atmosphericconditions, we found the MT CKD model overestimates the observations.

The coefficients from this work were derived from spectra sensitive to a range of temper-atures from 253 K to 270 K. Comparison with the 296 K Burch’s data has provided someevidence that Cf could have a positive temperature dependence, as suggested by theoreticalwork [16, 17]. However, on this point our analysis cannot be conclusive. It is fair to stress,indeed, the MT CKD water vapor continuum model does depend on available spectroscopicparameters such as water vapor line positions, strengths and widths. Thus, the discrepancy wehave revealed could be the effect of relative large errors in the water vapor line absorption spec-troscopy. However, although line spectroscopy errors do exist, it is unlikely that they are the



dominant effect at the typical spectral resolution of our interest (that is ≈ 0.5 cm−1), mostly onthe basis of the fair fit we could achieve in non-window regions.

In conclusion, our results once again stress the importance of continuum parameterizationsbased on data taken in actual atmospheric conditions and, in agreement with the early work[28], the need of field experiments in the far infrared.

Acknowledgments

Work supported by MIUR PRIN 2005, project # 2005025202/Area 02. We thank the Istitutodi Fisica dello Spazio Interplanetario, the Centro Nazionale di Meteorologia e ClimatologiaAeronautica, and the town of Valtournenche.



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