## Abstract

The paper presents a novel methodology to retrieve the foreign-broadened water vapor continuum absorption coefficients in the spectral range 240 to 590 cm^{-1} and is the first estimation of the continuum coefficient at wave numbers smaller than 400 cm^{-1} under atmospheric conditions. The derivation has been accomplished by processing a suitable set of atmospheric emitted spectral radiance observations obtained during the March 2007 Alps campaign of the ECOWAR project (Earth COoling by WAter vapor Radiation). It is shown that, in the range 450 to 600 cm^{-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 continuum coefficient.

©2008 Optical Society of America

1. Introduction

Water vapor is the main greenhouse gas in the atmosphere and its far infrared rotation band plays an important role particularly in the mid and upper troposphere, where it influences the Earth’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 of atmospheric emission which aims at bridging this knowledge gap.

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

State of art radiative transfer models normally rely on the CKD model [8] for the parameterization of water vapor continuum. This is a semi-empirical model which has been tuned on laboratory and atmospheric observations. For the region 350 to 650 cm^{-1}, laboratory measurements [9] at room temperature are the basis of the first quantitative development, followed by a series of revisions as a result of high-resolution spectral observations, both from field campaigns and laboratory measurements (e.g., see [3, 4, 10, 11, 12]). Many of these field campaigns and experiments have been, and continue to be, organized and carried out within the framework of activities of the US Department of Energy (DoE) ARM (Atmospheric Radiation Measurement) program (see e.g. [14]). Taking advantage of this experience and theoretical considerations, a new 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 CKD model (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’s observations 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 actual atmospheric conditions, and below 350 cm^{-1} they are the only experimental data set available today.

Finally the foreign-broadened continuum scheme provided by MT CKD does not currently include, against theoretical evidence [16, 17], a dependence on temperature. Our data may provide 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 experimental conditions, 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 a length in [6, 7], which the reader is referred to for the details. For the sake of clearness and benefit of the reader we briefly summarize here what is essential to a proper understanding of the present work.

For observations from the ground, the water vapor rotational band is normally opaque because of the strong absorption. However, in case of suitable dry conditions, the emission spectrum shows narrow “micro-windows”, or regions between absorption lines, where the atmosphere becomes relatively more transparent. These micro-windows are fairly sensitive to continuum 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 Basic observations of the Emitted Spectral radiance of the Troposphere (I-BEST), operated from Cervinia 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 is also equipped with an uncooled DLaTGS (deuterated L-alanine-doped triglycene sulphate) pyroelectric detector. Interferograms are acquired at a rate of about 27 interferograms per minute and one product cycle consists of 60 interferograms for a total integration time of ≈2 m and 18 s. 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 noise budget of the instrument can be found in [18].

REFIR-PAD [19] is a portable FTS specifically developed in-house at IFAC for the measurement of the atmospheric emitted radiance over the spectral range 100 to 1100 cm^{-1} with a spectral 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. One input 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 observations. Measurements of 64 s acquisition time are taken in sequences of 4 calibrations (2 measurements 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 the thermodynamic state of the atmosphere, were measured by : 1) a VAISALA RS92k radiosonde system; 2) a Raman Lidar capable of simultaneously getting temperature, water vapor, aerosol and cloud optical properties; 3) a Ground-Based Millimeter-wave Spectrometer (GBMS) for observations of precipitable water vapor (PWV). The GBMS capability to measure accurate PWV values also for very low content of H_{2}O (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 shown in Fig. 1, which also exemplify the level of instrument noise affecting the measurements. The two observations refer to the same day of 9 March 2007. The instrument noise includes all noise sources which affect the calibration process (detector noise, internal blackbodies temperature and emissivity uncertainties and so on [18, 7]).

REFIR-PAD (placed at 3500 m) clearly shows resolved micro-windows in the range 200 to 350 cm^{-1}, while I-BEST (2000 m) already shows a saturated spectrum. The total integration time 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 a specific wavenumber σ (units of cm^{-1}) is defined by

where *k*
* _{local}* is the local absorption coefficient, which accounts for the cumulative effects of all lines whose center lies within 25 cm

^{-1}. The two

*continuum*terms are the foreign-broadened component

*C*and the self-broadened

_{f}*C*component, both expressed as cross sections (units of cm

_{s}^{2}molecule

^{-1}), and

*ρ*and

_{f}*ρ*are the densities of air and water vapor in molecule cm

_{s}^{-3}. The parameter

*ρ*is a reference broadener density defined as

_{o}*ρ*=

_{o}*P*/(

_{o}*k*), where

_{b}T_{o}*P*=1013mbar,

_{o}*T*=296 K, and

_{o}*k*is the Boltzmann constant.

_{b}In the Earth’s lower atmosphere, continuum absorption in spectral regions near the center of water vapor bands is generally dominated by air-broadening, while window regions are dominated by self-broadening. Based on the MT _CKD model, for the spectral region 240 to 590 cm^{-1} and at altitudes and temperatures relevant to our experiment, the foreign to self absorption ratio steadily increases from 4 (at 600 cm^{-1}) to 20 (at 240 cm^{-1}). For this reason our analysis is focused on *C _{f}* alone.

The parameter *C _{f}* can be further decomposed in

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 *C̃ _{f}*, which is normally referred to as

*Symmetrized Power Spectral Density Function*. However, for the sake of a concise notation it will be referred in the following to as

*the continuum coefficient*and denoted with

*c*or

*c*(σ) when we will need to explicit 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 its more important thermodynamic components, temperature and water vapor profiles. Ideally the various 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 and time lag make it difficult to get ancillary information which is radiometrically consistent with the 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 in conditions which are different from the atmosphere at same altitude. For this reason the radiosonde and/or Lidar temperature profile, in their lowest altitude range, must be scaled to this local environment, a process which is accomplished using the spectral radiance observed in the most absorbing portion of the CO_{2} band. The details of this form of adjustment or scaling of the temperature profile to the spectral observations has been discussed and presented in [21]. It has been systematically applied to REFIR and I-BEST spectra used in this work.

After performing this temperature correction, we could well experience other problems, such as the so-called problem of dry bias in the humidity profile (e.g., [22], and time lag between various instruments. Since these biases and uncertainties propagate to the estimates of the continuum coefficients, a procedure, which retrieves continuum coefficients, while simultaneously adjusting H_{2}O and temperature profiles, has been developed to improve the agreement with observed 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 atmospheric layers used in the forward model for the discretization of the radiative transfer equation, and let *F*(**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

Temperature (**T**) and water vapor (**q**) profiles are part of the state vector. In their discrete form they have size equal to the number of atmospheric layers. In the same way the continuum coefficients vector (**c**) is part of the set of spectroscopic parameters, and for each wave number the size of **c** is *L*. Thus if we consider *N* channels or wave numbers, σ* _{i}*,

*i*=1,…,

*N*, the vector

**c**will be a column vector with

*L*×

*N*elements,

where *t* means transpose.

Let **c**0,**T**0,**q**0 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

In the above equation **r**
_{0}=*F*(**s**
_{0};**v**
_{0}), and **K**
* _{T}* and

**K**

*are the usual derivative matrices, or Jacobians, for temperature and water vapor respectively and their size is*

_{q}*N*×

*L*. The matrix

**K**

*is again a derivative matrix: the continuum coefficient Jacobian. Since the continuum coefficients also depend on the wavenumber, the size of the matrix*

_{c}**K**

*is*

_{c}*N*×

*N*

_{1}, where

*N*

_{1}=

*L*×

*N*. Its row of index

*i*contains the

*L*derivatives (computed at the corresponding initial or first guess values),

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

Since we are dealing with closure experiment and great care is taken in suitably probing and 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 Taylor expansion above. Similarly we can assume that the vector **c** is in the linear region defined by the Taylor expansion of the radiative transfer equation. With this in mind we can neglect the higher order terms in Eq. (5) and consider the linear form

with

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

In case higher order terms were important, which might happen if the final solution was not in the linear region around the first guess state, we could resort to one of the many iterative approaches available in the literature, e.g. the well known Gauss-Newton method [23]. However for the analysis here shown one iteration step was enough to bring the spectral residual within the error bars.

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

Towards this objective, we consider

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

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

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

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

The linear form (10) allows, in principle, to account for possible dependence on temperature of the foreign-broadened continuum, a possibility which is in agreement with theoretical calculations, e.g. [16, 17]. However, one should consider that we use strictly micro-window channels to derive the continuum coefficients and that ground based observations are sensitive only to the continuum emission from atmospheric layers close to the instrument. To discuss this point we can define the effective (emitting) temperature *T _{e}*(

*σ*

*) for the channel*

_{j}*σ*

*according to*

_{j}where *T _{i}* is the atmospheric temperature for the layer

*i*. This definition is equivalent to that given by [15].

For the case of the REFIR-PAD observations, the micro-window channels used in the analysis are shown in Fig. 2. The same figure also illustrates the effective temperature for the case study of 9 March 2007. For this day we observed the lowest total columnar amount of water vapor, that is 0.54 mm. An example of the continuum coefficient Jacobian, referring to the same window channels, is shown in Fig. 3. It is possible to see that the Jacobian peaks at a nearly constant altitude level, as the wave number varies in the range 240 to 590 cm^{-1}. As a consequence, to account in the inverse problem for the potential emission by the entire atmospheric column is only an unnecessary complication. This is not to say that we neglect the temperature dependence, but rather that the continuum coefficients are determined by a common effective temperature. The concept of effective temperature also allows us to identify *homogenous* window channels since they are characterized by the lowest effective temperature. Therefore a channel whose effective temperature largely deviate from the lowest values is likely to be affected 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, for each channel, the *L* coefficients along the atmospheric column are collapsed into one single effective continuum coefficient.

With this last assumption, the vector, c becomes a vector of size *N*, whose elements are the continuum coefficients at the *N* waveumbers,*σ*
_{1},…,*σ _{N}*. Note that even with this simplification, the layer derivative

*∂F*/

*∂c*(

_{j}*σ*) does depend on the layer (even when computed at the same wavenumber!). Thus, we still need to compute the full dimensional

_{i}*N*×

*N*

_{1}Jacobian and then consider the summation of the Jacobian elements over the column, that is over the indices, 1,…,

*L*.

This operation contracts the matrix **K**
* _{c}* to the lower size or dimension

*N*×

*N*, and it can be formally performed by considering a suitable contraction kernel. Let us consider the

*L*×

*N*matrices,

**H**

*, with*

_{i}*i*=1,…,

*N*, whose elements are zero apart from those on the column of index,

*i*, which have to be set equal to 1. Let us consider the matrix

**H**, obtained by vertical concatenation of the individuals,

**H**

*, that is*

_{i}Let **K** be the *N*×*N* matrix given by

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

where **x̃**
* _{c}* 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},**q**
_{0}) couples, then let us consider the *N*×*M* column vector, **ỹ** obtained by vertical concatenation of the individual data vectors, **y**

For this vector we can write the relation

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

Furthermore, the two column vectors of size *M*, **f̃**
* _{T}* and

**f̃**

*contain the corresponding scaling factors for each single pair, (*

_{q}**T**

_{0j},

**q**

_{0j}). Finally, note that the term

**K̃x**

*is left unchanged by coadding*

_{c}*M*spectra, since we consider a time span for which the temperature profile may vary, but not to an extent to significantly affect

*C̃*.

_{f}In the end, the problem (17) has *N*×*M* data points for *N*+*M*+*M*=*N*+2*M* unknowns, and it can be further compacted by considering the linear form

with **G** obtained by the horizontal concatenation of the three matrices, **K**
* _{c}*,

**A**,

**B**,

and

To have an idea of the size of the problem above, consider that for the full range 240 to 590 cm^{-1} we have N=251. By co-adding up to a maximum of M=20 clear sky spectra (recorded over 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 numbers sensitive to water vapor line absorption and temperature. For these channels the Jacobian, **K**
* _{c}* is just 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 scaling factors.

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

*f*parameters)=340 unknowns. These unknowns can be estimated by usual Least-Squares methods. 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])

_{q}with **S** the covariance matrix of the spectral observations, the covariance matrix of the estimate is given by

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

The above methodology, which to our knowledge is original for the problem at hand, allows to *simultaneously* retrieve the continuum coefficients along with the scaling factors for the water vapor and temperature profiles. The methodology also provides a proper treatment for the noise term 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 retrieved coefficients 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 be representative 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 coefficients are 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 variances and co-variances, as well.

Let *ck*, *k*=*j*1,…, *j _{n}*, the

*n*coefficients within a bin and

*j*1,…,

*j*the

_{n}*n*channel numbers within the same bin, the variance-weighted mean is defined as usual,

where *S _{x}*(

*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

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

#### 3.2.3. Forward model

The forward model we have used in the analysis is LBLRTM (e.g. [13]) version 11.3, released on November 2007, along with the spectroscopic database HITRAN 2004+[24]. Synthetic radiances have been computed with an atmospheric layering of *L*=90 layers. Jacobian derivative matrices for temperature, water vapor and continuum coefficients have been computed with a finite difference scheme. LBLRTM version 11.3 makes use of the MT CKD version 2.1 for the continuum model. This model has been assumed as first guess in all the retrieval calculations shown in the next section.

The atmospheric state vector used for the first guess must include minor and trace species other 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 complete the atmospheric state vector.

Both REFIR-PAD and I-BEST spectral observations were Gaussian apodized, with a Gaussian 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 Instrumental Spectral Response Function (ISRF) uncertainties [25]. In view of the featureless behavior of the 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 instrument noise (at the un-apodized level) as well as forward model noise. Finally, it was consistently transformed [26] to reflect the apodization process.

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

The effect of spectroscopic uncertainty has also been checked by comparing the HITRAN release for 2000 and the current one, 2004+. The source of spectroscopic noise can be mostly summarized in the terms *k*
* _{local}* in Eq. 1. While the continuum is retrieved in our scheme,

*k*

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

_{local}Finally, possible uncertainties arising from temperature and water vapor profiles are not included in the covariance matrix since these parameters are simultaneously retrieved with the continuum coefficients.

## 4. Results

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

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

With REFIR-PAD we could explore the widest spectral range, extending from 240 to 560 cm^{-1} and, in addition, the coldest emitting temperature during the campaign. Spectral ranges and 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 cut off wave number was around 360 cm^{-1}. The observed PWV was 1.5 mm and the effective temperature was found to be ≈ 267 K. The observations were acquired from 21:17:27 to 22:10:24 UTC, and 20 spectra were in the end selected and considered for the analysis. On March 14 I-BEST was operated with the MCT detector and the cut-off wave number was around 460 cm^{-1}. The observed PWV was about 5 mm and the observed effective temperature was around 269 K. The observations were acquired from 18:59:43 to 20:42:54 UTC, and 20 spectra were in the end considered for the analysis.

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

The analysis for the water vapor continuum is shown in Fig. 5 and Tab. 1. Figure 5 also provides a comparison with *adjusted* Burch’s data. Our results and calculations apply to the continuum as defined, e.g., in [8, 3], whereas original Burch’s data [9] are not consistent with this definition. For this reason, the Burch data we show in Fig. 5 have been adjusted to be consistent 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 both in laboratory conditions and field observations, our findings are highly consistent with the MT CKD model whatever the detector, instrument and water vapor load may be. This result also 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 to 420 cm-1, which has benefited until now only of limited laboratory observations. We find discrepancies which may reach values as large as 40% (see, e.g., Tab. 1). For this range we have the 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 further conclusion can be derived as far as the dependence on temperature.

Our observations provide the very first set of water vapor continuum from atmospheric observations in the range 240 to 350 cm^{-1}. Although less pronounced than in the range 350 to 420 cm^{-1}, we still observe a trend for less absorption in comparison with the MT _CKD model and Burch’s data.

Our results reveal less continuum absorption than predicted by Burch’s laboratory observations, in agreement with previous studies [3, 4, 5]. The trend toward lesser absorption is also clearly evident in going from MT _CKD version 1 to MT CKD version 2.1. These results lead us to conclude that foreign-broadened water vapor continuum has a slight positive dependence on temperature, as predicted by theory [16, 17]. In fact Burch’s data refer to a temperature of 296 K, while ours fall in the range 250 to 270 K. The slight positive dependence on temperature also explains the trend in modeling less water vapor absorption in order to agree with field experiments. 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 vapor load (parameter *f _{q}*) and bulk temperature of the atmosphere (parameter

*f*). The inversion analysis is particularly sensitive to

_{T}*f*which is shown in Tab. 2 and Tab. 3 for each individual spectrum 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 observations. It is seen from Tab. 2 that the retrieved

_{q}*f*is not negligible, which demonstrates the need of retrieving this parameter even when a preliminary GBMS scaling has been applied.

_{q}For the two remaining days (see Tab. 3), we observed retrieved values for *f _{q}* much larger than those for the previous case. These larger deviations are expected, since in contrast to Testa Grigia 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*are not only the result of bias, but they may also reflect the high variability of water vapor in the high mountain setting where our observations were taken (e.g., see [6, 7]).

_{q}For temperature, the parameter *f _{T}* was found to vary randomly around zero, suggesting that the adjustment we perform for the temperature profile in the lowest atmosphere (see section 3.2.1) is already enough to account for most of the residual uncertainties in temperature.

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

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

atmospheric conditions until the present study. Figure 6 also shows the spectral residual using the adjusted coefficients according to our analysis. It is clear that the warm bias is largely removed and the computations gain higher consistency with the observations. Also note that in the 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 continuum coefficients. The isolated spikes at the lower wave numbers range are the effect of point calibration errors due to the presence of strong water vapor absorption within the interferometer path.

## 5. Conclusions

We have analyzed spectral radiances in the range 240 to 590 cm^{-1} and derived water vapor continuum coefficients, which have been compared to model and laboratory data. The spectral radiances have been recorded during the March 2007 ECOWAR field campaign in the Alps and encompass a variation in the precipitable water vapor from 0.5 to 5 mm during the observation period.

A suitable inverse methodology was developed to retrieve the continuum coefficients, which allows us to remove possible uncertainties arising from the input state of the atmosphere (initial guess 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 the findings 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 atmospheric conditions, we found the MT CKD model overestimates the observations.

The coefficients from this work were derived from spectra sensitive to a range of temperatures from 253 K to 270 K. Comparison with the 296 K Burch’s data has provided some evidence that *C̃ _{f}* could have a positive temperature dependence, as suggested by theoretical work [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 spectroscopic parameters such as water vapor line positions, strengths and widths. Thus, the discrepancy we have revealed could be the effect of relative large errors in the water vapor line absorption spectroscopy. 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 on the basis of the fair fit we could achieve in non-window regions.

In conclusion, our results once again stress the importance of continuum parameterizations based 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 Istituto di Fisica dello Spazio Interplanetario, the Centro Nazionale di Meteorologia e Climatologia Aeronautica, and the town of Valtournenche.

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