Measurement of the water vapour vertical profile and of the Earth’s outgoing far infrared flux

Our understanding of global warming depends on the accuracy with which the atmospheric components that modulate the Earth’s radiation budget are known. Many uncertainties still exist on the radiative e ﬀ ect of water in the di ﬀ erent spectral regions, among which the far infrared where few observations have been made. An assess- 5 ment is shown of the atmospheric outgoing ﬂux obtained from a balloon-borne platform with wideband spectrally resolved nadir measurements at the top-of-atmosphere over the full spectral range, including the far infrared, from 100 to 1400 cm − 1 , made by a Fourier transform spectrometer with uncooled detectors. From these measurements, we retrieve 15 pieces of information about water vapour and temperature proﬁles, and 10 surface temperature, with a precision of 5% for the mean water vapour proﬁle and a major improvement of the upper troposphere-lower stratosphere knowledge. The retrieved atmospheric state makes it possible to calculate the emitted radiance as a function of the zenith angle and to determine the outgoing radiation ﬂux, proving that spectrally resolved observations can be used to derive accurate information on the integrated 15 ﬂux. While the retrieved temperature is in good agreement with ECMWF analysis, the retrieved water vapour proﬁle di ﬀ ers signiﬁcantly, and, depending on time and location, the derived ﬂux di ﬀ ers in the far infrared (0–600 cm − 1 ) from that derived from ECMWF by 2–3.5 W/m 2 ± 0.4 W/m 2 . The observed discrepancy is larger than current estimates of radiative forcing due to CO 2 increases since pre-industrial time. The error with which 20 the ﬂux is determined is caused mainly by calibration uncertainties while detector noise has a negligible e ﬀ ect, proving that uncooled detectors are adequate for top of the atmosphere radiometry.

EGU erning the climate system (Pierrehumbert, 2002). The atmospheric water, in the form of both vapour and clouds, is the most important greenhouse components trapping the outgoing longwave radiation (OLR) (Harries, 1996). Even if its main contribution to climate changes is through feedback processes occurring as a consequence of a man-induced temperature variation driven by the increased CO 2 concentration, it has 5 recently been found that also long term increases in stratospheric water vapour may be considered to be in part a forcing term (Held and Soden, 2000). Changes in the distribution of water vapour and the associated radiative forcing and feedback are well recognised as fundamental processes to be characterised in predicting future climate (Lindzen, 1990;Chahine, 1992;Harries, 1997;Stuber et al., 2005). 2007 IPCC report 10 identifies the estimate of the strength of different feedbacks as a key uncertainty in global circulation model predictions (Randall et al., 2007). Despite its prominent spectroscopic signatures in the OLR, the quantitative measurement of the water vapour volume mixing ratio (VMR) is made difficult by its variability and its large vertical (and to a lesser extent horizontal) concentration gradients. 15 Furthermore, also the spectroscopy of water vapour poses some problems. The high concentration of this species in the lower troposphere makes relevant several spectroscopic processes (self and foreign broadening, pressure shift, and continuum absorption) (Tobin et al., 1999) that are difficult to observe in laboratory conditions and require a field validation. In this context, Sinha and Harries (1995) pointed out the lack 20 of validation of far infrared (FIR) model line parameters of water vapour under atmospheric conditions and stressed that FIR parameterisation in climate models should be validated by observational programs.
The radiative balance of the troposphere is influenced strongly by radiative cooling associated with the emission of FIR radiation by water vapour. The water vapour ro- 25 tational band is extremely intense, especially at band centre around 200-300 cm −1 , and so emits to space from the upper troposphere. Atmospheric fluxes calculations (Clough et al., 1992)  EGU pact on the clear-sky greenhouse effect. Water can manifest itself also in the form of cirrus clouds and cirrus cloud feedback is the major source of discrepancy between models of climate predictions. The prevalence and persistence of cirrus cloud systems, especially in the tropical upper troposphere, implies that cirrus clouds play an important role in climate (Liou, 1986).
Radiative studies of cirrus clouds show that the clouds may cool radiatively or heat the upper atmosphere in the thermal infrared wavelengths depending upon height, thickness and microphysics of the particles (Cox, 1971;Stephens et al., 1990). Cirrus clouds have been recognised as important components of feedback processes to climate forcings (Randall et al., 1989;Del Genio et al., 1996;Chou and Neelin, 1999). 10 The OLR flux is strongly modulated by cirrus, nevertheless, the available operative sensors give no direct information on cloud microphysics and cirrus clouds represent a major observational gap.
In this contest, in June 2005 we performed a new spectral measurement, described in Sect. 2, covering the FIR portion of the Earth's emission spectrum, from a strato-15 spheric balloon flown in tropical region in the North-East of Brazil. As described in Sect. 3, this spectral measurement allows the retrieval of temperature and water vapour vertical profiles up to the upper troposphere level. A comparison of our results with the atmospheric status obtained from the ECMWF (European Centre for Medium-range Weather Forecast) analysis is shown in Sect. 4. In Sect. 5 the difference from ECMWF 20 found on the water vapour concentration profile is used to address the effect on the calculation of the outgoing longwave radiation flux at the flight altitude level.

Spectroscopic measurements of the outgoing longwave radiation
In June 2005 the first wideband spectrally resolved measurements including the FIR portion of the atmospheric thermal emission were performed from stratospheric bal- spectral range, with 0.625 cm −1 resolution. The instrument is partially cooled: aft op-5 tics at 180 K, and detectors at 4.2 K. REFIR-PAD measurements were performed with a FTS with Mach-Zehnder configuration covering the 100-1400 cm −1 spectral range with 0.5 cm −1 resolution. REFIR-PAD is a prototype developed as a field demonstrator of a satellite instrument designed in the framework of the European REFIR space mission 10 (European-Commission, 2000;Rizzi et al., 2002). It is a compact and innovative FTS with double-input/double-output port configuration designed for measuring with high accuracy the wideband atmospheric emission without requiring any cooled components (Palchetti et al., 2005;Bianchini et al., 2006). This instrument is optimised as a small and light payload and uses uncooled optics and detectors. The capability of 15 an uncooled instrument to provide information on the status of the atmosphere and its radiative properties is assessed in the present paper.
REFIR-PAD acquired 540 nadir spectra of the atmospheric emission during a stratospheric flight at the mean floating altitude of 34 km for about 8 h . The experiment was launched onboard a gondola that hosted the LPMAA IASI-balloon  Table 1. An accurate characterisation of the level 1 analysis producing calibrated spectra can be found in . The noise equivalent spectral radiance (NESR) turned out to be in the range of 0.8-2.5 mW/(m 2 sr cm −1 ) with the lower values between 200 and 600 cm −1 . The mean calibration error was about 0.1 K with a peak-to-peak value of about ±0.3 K. The total radiometric error has been 5 calculated as a function of frequency for each calibrated spectrum taking into account both the detector noise component and the systematic calibration errors.

Retrieval of water vapour and temperature vertical profiles
Nadir wideband spectral measurements have been used to retrieve the vertical profiles of atmospheric temperature and water vapour concentration, and the surface 10 (skin) brightness temperature (BT). Vertical profile of temperature is retrieved exploiting the carbon dioxide band at 668 cm −1 . A trend corrected value of carbon dioxide of 378 ppmv is considered. The water vapour profile is retrieved exploiting both the vibro-rotational band and the FIR pure rotational band below 600 cm −1 . The software devoted to the analysis of REFIR-PAD measurements has been developed at IFAC. 15 The main features of the retrieval code can be described by making reference to two main blocks: the forward model and the inverse model.

Forward model
The forward model simulates REFIR-PAD wideband measurements using line-by-line radiative transfer (RT) calculation. The code computes the radiance that reaches the 20 instrument, and simulates the instrumental effects (instrumental lineshape and field of view). Assuming a uniform layered atmosphere, the RT has been implemented using the Curtis-Godson (Houghton, 2002) values associating a temperature and pressure equivalent value to each species in the layer in order to evaluate the averaged value of the cross-section. The atmospheric lineshapes are modelled with a modified Introduction  (Rothman et al., 2005) with recent updates for the air broadened half widths provided by Gordon et al. (2007). The atmospheric continuum is modelled according to the work by Clough et al. (2005) considering the contribution 5 of water vapour lines external to the region of ±25 cm −1 from the line centre. For CO 2 a dedicated database and lineshape has been adopted in order to take into account the line-mixing effect (Niro et al., 2005a,b).

Inversion
The retrieval procedure (Carli et al., 2007) uses the constrained Non-linear Least- 10 Square Fit (NLSF) approach: the cost function to be minimised takes into account the a priori information (optimal estimation approach) and the Marquardt lambda parameter (Rodgers, 2000). The retrieval algorithm enables us to fit the wideband spectrum to find more quantities simultaneously (multi-target retrieval) in order to best account for the errors due to the interfering unknowns. 15 REFIR-PAD measurements have been analysed by simultaneously fitting the water vapour profile, the temperature profile and the Earth skin BT using the spectrum from 100 to 1000 cm −1 . As a priori information, the IG2 database (Remedios, 1999) for an equatorial atmosphere in July 2005 has been used. The pressure profile at the altitude grid provided by ECMWF database has been obtained by imposing the hydrostatic 20 equilibrium with a pressure reference level at 1000 hPa. The a priori errors that have been used are 100% for water vapour profile and a linearly decreasing error from 9.8 K at an altitude of 1 km to 2.3 K at an altitude of 33 km for the temperature profile. The convergence is established using the chi-square test. The final reduced chi-square close to one indicates the agreement between the forward model and measurements 25 and the correctness of the estimated measurement noise. The correlations among the products are contained in the correlation matrix exported by the program.
In Fig. 1 and Fig. 2  EGU the analysis is given. The plots show the retrieved profiles (red lines) with the constrained error together with the initial guess profile (blue lines) and the profile obtained from the ECMWF operational analysis (green lines). The results show a good agreement with ECMWF for the temperature profile and for water vapour below 10 km altitude. Above 10 km, REFIR-PAD measurement found a drier atmosphere which alters the result of the calculation of the OLR flux, as it will shown in Sect. 5. The retrieval altitude grid has been optimised in order to maximise the total number of independent retrieved unknowns and to better exploit the sounding capability of the REFIR-PAD instrument. The analysis of the averaging kernel profiles for temperature and water vapour VMR, shown in Fig. 3 and Fig. 4 respectively, was used to select 10 the vertical retrieval grid. The results shows that REFIR-PAD measurements provide information up to 33 km for temperature, and up to about 17 km for water vapour, with a vertical resolution of about 2 km for both quantities.
The degrees of freedom of the retrieval, i.e. the number of independent new pieces of information provided by the trace values of the averaging kernel matrix, are for atmo-15 spheric temperature, water vapour, and surface skin BT, 7, 7, and 1, respectively. The information content coming from the FIR region improves the water vapour retrieval in the upper troposphere relative to retrievals only performed in the rotovibrational band (Mertens, 2002).

Error budget 20
The error analysis takes into account both the random measurement noise (NESR) due to the detector and the spectrally-correlated calibration uncertainty. In the case of the REFIR-PAD measurement, the NESR is due to the uncooled pyroelectric detectors and, as we have seen in Sect. 2, it is in the range of 0.8-2.5 mW/(m 2 sr cm −1 ). Also the measurement noise of the calibration spectra contributes to this error, which has 25 no correlation among the different spectral channels. The second effect is instead calculated with 1σ-error corresponding to the peak error of 0.3 K in the knowledge of the calibration sources temperature and it is less than 1.2 mW/(m 2 sr cm −1 ). This error EGU is correlated among the different spectral channels. An in-deep analysis of these errors and of their spectral features can be found in . A full variance-covariance matrix of these errors is used to assess the error propagation in the retrieved atmospheric state. In such a way, an error of about 2 K constant at different altitudes is found for the temperature profile, and an error varying from 22% 5 at ground to 35% at 17 km altitude for water vapour. These errors are shown by error bars in Figs. 1 and 2. The skin BT is retrieved with an errore of about 0.4 K.

Data analysis: atmospheric state
Some thin scattered clouds were present at low altitude at the beginning of the flight, but apart a small effect observed soon after launch, the atmosphere resulted to be transparent enough to assume clear sky in our analysis. The vertical profiles of water vapour VMR and temperature, and the skin BT have been retrieved for each measurement sequence during the flight from 08:05 to 15:47 UTC. A mean spectrum is obtained for each sequence by a weighted average of 10 spectra acquired in about 6 min.
In order to check the validity of the vertical profiles of temperature and water vapour 15 retrieved from REFIR-PAD measurements, we relied on correlative data obtained from ECMWF operational analysis. Vertical profiles of temperature and relative humidity (converted to water vapour VMR) for the region of Teresina, Brazil and for the duration of the balloon flight were obtained from the ECMWF data archive, with a spatial resolution of 1 • ×1 • in latitude and longitude and with a temporal resolution of 6 h. These 20 profiles were linearly interpolated to the average geolocation and time of each REFIR-PAD sequence. The resulting temperature and water vapour distributions were used for validation purposes. The REFIR-PAD profiles retrieved during the flight were compared with the ECMWF correlative data. The comparisons are shown in Fig. 5 for the temperature profiles and in Fig. 6 for the water vapour profiles. The differences for temperature are generally low and in particularly they seldom exceed 2%. For the water vapour VMR, instead Fig. 6

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shows that the retrieved profiles are characterised by a drier upper troposphere, about 60% less that the ECMWF VMR in in the region from 12 km to tropopause. The greater differences observed at lower altitudes at the beginning of the flight are possibly due to a pixel contamination produced by the presence of clouds. In Fig. 7, we report the mean values of the residuals of the fitting process, obtained 5 by averaging over the duration of the flight the difference between the observed spectral radiance and its simulated values after last iteration (red line). The average of the residuals is compared with the mean value over the flight of the measurement error, computed as the root mean square of the diagonal elements of the variance-covariance matrix of the observations. The residuals are generally well within the mean measure-10 ment error, with isolated exceptions that peak around 460 cm −1 and 590 cm −1 , proving that no significant unaccounted systematic error is present in the data analysis . In Fig. 8, the time series of the temperature values at the retrieval altitudes are displayed for the lower troposphere. The ground skin BT increment due to the solar 15 irradiation was detected starting from the sunrise occuring at sequence #19. A small increment of temperature is also observed in the first layer of the atmosphere.
Since the atmospheric state is sufficiently uniform in time and location along the flight, the retrieval standard error, described in Sect. 3.3, can be compared with the standard deviation of all the measurements. The comparison shows a good agreement 20 between the two sets of values for both temperature and water vapour. This allows to consider the mean standard error of the mean measurement, which resulted to be less than 0.5 K for temperature mean profile, and about 3-5% for water vapour mean profile.

Data analysis: outgoing longwave radiation flux
The evaluation of the OLR by using directional non-spectral measurements, such 25 as satellite single view observations, is affected by an error due to the angular distribution model used for the calculation of the emission anisotropy factor EGU in the radiance-to-flux conversion, see e.g. the ERBE and CERES experiments (Suttles et al., 1992;Wielicki et al., 1996). It was shown that statistical methods developed for deriving the anisotropy factor for different viewing conditions are affected by an error of about 4.6 W/m 2 for the best situation of nadir observations (Clerbaux et al., 2003).

5
Our spectrally resolved measurement provides the capability of retrieving the atmospheric parameters, that primarily determine the OLR emission, i.e. the vertical profiles of T and water vapour, and the surface emission. Based on this information and using a RT model, such as that described in Sect. 3.1, it is possible to simulate the emission L(σ,θ) as a function of the wavenumber σ and the zenith angle θ. In the case of 10 an horizontally uniform atmosphere, the angular integral defining the OLR flux F OLR is accurately calculated with the following equation (1) and has a variance equal to: where S is the variance covariance matrix of the retrieved atmospheric parameters, J 1 and J 2 are the jacobian matrices where x i are the retrieved parameters.

15
A comparison with the fluxes calculated for the ECMWF atmospheric states has been performed in the two extreme cases at sunrise and at the end of flight. Also the fluxes obtained with the ECMWF atmosphere show an increase with time, but both the ECMWF fluxes and their increase are less that what obtained with REFIR-PAD data. The FIR spectral region from 0 to 600 cm −1 is here considered in detail because in this 20 spectral region new observations are obtained by REFIR-PAD and low altitude clouds have a negligible effect on the TOA radiance. The result is shown in Fig. 9, where in the top panel the differences between the spectral fluxes calculated for the retrieved and the ECMWF water vapour and temperature profiles are shown for the sunrise (blue line), and for the end of the flight (red line). In the bottom panel, the results are reported 25 as the cumulative integral of the spectral differences and they are compared with the cumulative integral of the expected error (dashed lines). The Fig. 9

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This result clearly identifies the differences with the estimations made with the ECMWF atmospheric analysis and the importance of the characterisation of the FIR region for the exact calculation of the OLR fluxes. The error with which the flux is determined is caused mainly by calibration uncertainties while detector noise has a negligible effect. This is a further demonstration that uncooled detectors are adequate 5 for a detailed radiometric observations.

Conclusions
The results of the first flight of REFIR-PAD have been shown. The instrument performed the spectral measurement of the OLR from 100 to 1400 cm −1 in the tropical region in June 2005. This spectrally resolved measurement has allowed the retrieval of 10 the atmospheric state with sufficient precision to improve the accuracy with which the integrated outgoing radiation flux can be calculated, proving that spectral information can be used to infer the angular distribution of the radiance.
While the temperature profile is in good agreement with the ECMWF analysis, the retrieved water vapour VMR profile differs of about 60% at the upper troposphere -15 lower-stratosphere altitude. This difference allows to calculate the difference in terms of the OLR flux at the flight altitude of 34 km due to the FIR region which resulted to be as large as 3.5 W/m 2 with an error of about 0.4 W/m 2 . A difference of 3.5 W/m 2 is an important term in the determination of the total OLR since it is comparable to or even greater than the estimation of the radiative forcing of the CO 2 increases since 20 pre-industrial times. Furthermore, we have shown that the flux error is mainly due to the radiometric calibration uncertainty while the random detector noise has a negligible effect, proving the feasibility of climatological studies with instruments that use uncooled detectors.
This measurement that is limited in time and space can not be representative of a bias in ECMWF analysis, but underlines a shortcoming in the knowledge of the Earth's radiation budget. We argue that a comprehensive characterisation of the outgoing ra-Introduction