Comparison of 6.7 micron Radiances Computed from Aircraft Soundings and Observed from GOES-VAS

Eric P. Salathé, Jr. and Ronald B. Smith

Department of Geology and Geophysics Yale University New Haven, Connecticut


This document is extracted from a manuscript Accepted in J. Geophys. Research
INDEX

1. Introduction

2. Data

3. Radiative Transfer

4. Results

5. Conclusions

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Abstract

Radiances observed by the GOES-VAS 6.7 um channel are compared to computations from simultaneous soundings of temperature and moisture. The soundings were measured using high precision instruments aboard the NCAR Sabreliner during ERICA, over Edmonton, Alberta, and over Champaign, IL. Three radiation codes are used to simulate the satellite observations, a narrow band model and two line-by-line codes, FASCODE2 and the Goddard Laboratory for Atmospheres line-by-line model (GLA-LBL). This comparison shows that all three models overestimate the observed brightness temperatures but reproduce the full range in observed brightness temperatures. Possible sources for this bias are investigated, such as transmission through a cloudy lower boundary, scattering by thin high-level cirrus, and water vapor continuum absorption. It is concluded that no one mechanism can alone account for the observed discrepancies.

1. Introduction index down

Increasing awareness of the role of upper-tropospheric water vapor in climate has emphasized the importance of its measurement and of understanding the radiation field of the upper troposphere (Starr and Melfi, 1991; Lindzen, 1990; Rind et al., 1991). The operational radiosonde network does not produce reliable moisture information above 500mb (Elliott and Gaffen, 1991; Gaffen et al., 1991), and, unless hygrometer modifications are made in the near future, global monitoring of upper-tropospheric moisture must rely on satellite remote sensing techniques. Infrared sounding is the most developed technique for upper-tropospheric water vapor measurements, but it will be increasingly complimented by other remote sensing techniques (e.g. passive microwave sounding (Schuessel and Emery, 1990; Tjemkes et al., 1991), SAGE solar occultation observations (McCormick et al., 1993), and lidar (Melfi et al., 1989; Browell et al., 1979; Cahen et al., 1982)). Methods for deriving soundings of atmospheric moisture from passive infrared radiance observations have been improving for many years (Smith et al., 1979; Chedin et al., 1985; Hayden1988), and radiance data for sounding purposes are collected by the VAS system on GOES satellites (Smith, 1983) and the TOVS system on NOAA polar orbiters (Susskind 1993). These measurements will be improved considerably in the next generation of GOES satellites (Starr and Melfi, 1991). Upper-tropospheric moisture estimates derived from these infrared radiances depend upon observations of radiation emitted in the strong 6.5 um vibrational-rotational band of water vapor. Most satellite sounding systems include a channel that measures radiance at about 6.7 um, which detects radiation emitted by water vapor above 400mb.

Given the paucity of reliable in situ moisture measurements above 500mb, it is difficult to assess the modeling of upper-tropospheric radiative processes from which satellite moisture profiles are derived. In this paper, we present precise temperature and moisture profiles collected from the NCAR Sabreliner during two recent field projects. We compute radiances from these soundings using three independent radiation codes for comparison to simultaneous observations from the GOES-VAS 6.7 um channel. These comparisons test the validity of radiation codes and satellite observations and, by extension, the ability to accurately infer water vapor concentrations from satellite observations.

Most previous attempts to compute satellite radiances using balloon soundings of temperature and moisture yielded poor results for channels in the strongly absorbing 6.5 um water vapor band (i.e. 6.7 um and 7.2 um channels) (Poc et al., 1980; Chesters et al., 1985; Hayden, 1988). Hayden (1988), for example, computed GOES-VAS channel 10 (6.7 um) brightness temperatures that overestimate the observations by an average of 5.27 K, with a correlation to the observations of only 0.59. Menzel et al. (1981), on the contrary, found good correspondence between observed and computed brightness temperatures for the same channel. It is not clear, however, what assumptions went into the Menzel et al. (1981) calculation and whether an adjustment was made to the transmission function for this channel as is traditional in VAS analysis (Hayden, 1988). Satellite radiance observations in the water vapor channels are sensitive to moisture at levels above where the balloon instrument is reliable, so the uncertainty in the moisture profiles of these earlier studies limits a useful comparison of the computed and observed radiances. To compute radiances in channels where carbon dioxide is the principal absorber, only the temperature profile must be measured, which is quite accurately accomplished by radiosondes. Chesters et al. (1985) compared computed and observed brightness temperatures from the VAS channels that depend only on atmospheric temperature and found agreement to within +/-1 K. The aircraft-based moisture measurements used in the present study should eliminate some of the uncertainties that were unavoidable in the earlier balloon-based studies of radiances in the VAS water vapor channel.

2. Data index up down

The data used in this paper are soundings of the atmospheric temperature and moisture measured from the NCAR Sabreliner and 6.7um radiances observed by the VAS instrument on the GOES-7 satellite.

a) Aircraft Data

During two recent field projects we conducted detailed soundings of the upper troposphere and lower stratosphere from the NCAR Sabreliner. Temperature was measured with a Rosemont platinum resistance sensor with accuracy of 1 K, resolution of 0.006 K, and response time of 0.1s (see NCAR-RAF Bulletins 3 and 9). Moisture was measured with a newly developed frostpoint hygrometer. The rapid response and large range of this hygrometer is accomplished by using a cryogenically cooled mirror (Spyers-Duran, 1990). This cryogenic hygrometer responds at about 1s, resolves 0.05 K variations in frost point, and has a frost point range of -10deg.C to -90deg.C. Cloud particle concentration was measured by a forward scattering spectrometer probe (FSSP) that detects the concentration and size distribution of cloud particles.

Twelve vertical atmospheric profiles were extracted from the data. The soundings generally extend to an altitude of 12 km into the lower stratosphere. Above this altitude, there is very little water vapor (Mastenbrook, 1980; Ellsaesser, 1983), and hence little contribution to the outgoing radiance near 6.7 um. For the purposes of radiative transfer calculations, the profiles of temperature and moisture were extrapolated to an altitude of 100 km. The lower boundary for the radiative transfer may be either the surface or a cloud. When a cloud is present in the profile, its altitude and temperature were judged using the IR window channel brightness temperature and the observed temperature profile, this process will be described fully below.

b) Evaluation of Water Vapor Measurement

The accuracy of the hygrometer is critical to this study and an attempt was made verify the NCAR-RAF specifications given above. Under ice-saturated conditions, the frostpoint should equal the ambient temperature, so the frostpoint observed in deep cold clouds provides an in situ calibration of the hygrometer against the temperature probe.

We conducted a series of soundings with the Sabreliner in conjunction with the release of Vaisala radiosondes. The results from one set of soundings are shown in figure 2. During these soundings, the aircraft passed within 4 km of the balloon launch site and the balloon was released midway in the aircraft descent. The regions marked as cloudy were determined both by the FSSP and by sight. Assuming the atmosphere was saturated with respect to ice within the cloud regions, the Vaisala sonde appears more accurate at low levels, the two agree at mid troposphere, and the cryogenic hygrometer is more accurate in the upper troposphere. The cryogenic hygrometer generally does not respond well at frost points above about -20[[ring]]C; also the lowest segment of the aircraft sounding was taken during an unusually rapid descent due to deteriorating weather conditions, and hence the cryogenic hygrometer may not have been able to respond quickly enough to the rapid moistening as the aircraft passed through the cloud. In cases where the cryogenic hygrometer measurement is clearly bad at low altitudes, the frost point is substituted with the value from a conventional chilled mirror hygrometer also aboard the aircraft. In very dry cold air (below -40[[ring]]C) in the upper troposphere, the frost point depression (ambient temperature minus frostpoint) measured by the humicap sensor becomes nearly constant as the instrument appears to respond more to the ambient temperature than to the features in the moisture profile.

c) Satellite Data

The VAS channel 10 is referred to as the 6.7 um or water vapor (WV) channel since its filter function is centered at a wavelength of 6.725 um (or wavenumber 1487.0 cm[-1]) in the 6.5 um vibrational-rotational absorption band of water. (See for example, Montgomery and Uccellini, 1985 and Chesters et al., 1982 for a detailed description of the GOES-VAS system.) Figure 3 shows the WV channel filter function along with a high resolution spectrum of radiance computed using the Goddard Laboratory for Atmospheres line-by-line code and a typical aircraft profile.

The sloping aircraft soundings will cross many satellite image pixels as the aircraft travels horizontally. Figure 4 shows a typical example of the brightness temperature observed over the track of an aircraft sounding from the hourly images spanning the flight time. There are slight variations in the atmosphere over this distance and time, on the order of +/-2 K. For comparison with the computed radiance, the mean brightness temperature over the upper tropospheric section of the aircraft track from the image closest in time to the sounding is chosen.

In this paper we will also consider the GOES-7 channel 8 or IR window observations of radiances at 11.170 um (895.3 cm[-1]). Since the atmosphere is nearly transparent at this wavelength, this channel gives the temperature of the opaque lower boundary for the radiative transfer calculation. This technique introduces errors that will be discussed in the next section.

3. Radiative Transfer index up down

The 6.7 um radiances are computed as described in, for example, Liou, 1980. In this paper, radiances will be expressed in terms of brightness temperature. The computed brightness temperature is the inverse Planck function evaluated at the center wavenumber of channel 10 ([[nu]]=1487.0cm[-1]). Given an accurate profile of the atmospheric temperature and humidity, the difficulties in computing the brightness temperature are in estimating the surface term and modeling the transmissivity. These two terms are the subjects of the next two sub-sections.

The zenith angle is found geometrically from the positions of the satellite and sounding location. GOES-7 is the only remaining geostationary satellite in orbit over the U.S., it is shuttled between positions over the East and West coasts depending upon the season. Thus, during the ERICA project the satellite's viewing angle changed each day and its daily position must be taken into account. The range of zenith angles in this investigation is from 44[[ring]] to 57[[ring]].

a) Clear Atmosphere Transmission

In this study we use three independent atmospheric transmission models. The first is a narrow band model (NBM) that uses the Goody random line parameterization and the Curtis-Godson parameterization for the dependence of the line parameters on temperature and pressure (Goody and Young, 1989; Rodgers and Walshaw, 1966). The NBM is an approximate method for radiative transfer that although not as accurate as other methods, gives high spectral resolution and very fast computational speed. The second model is FASCODE2 (Fast Atmospheric Signature Code), a line-by-line code available from AFGL (Clough et al., 1981, 1992). The third model was developed at the NASA Goddard Laboratory for Atmospheres (GLA) (Ridgeway et al., 1991) snf also uses line-by-line calculations. The two line-by-line codes both use the HITRAN86 spectral data as well. An important difference between the two models is in the treatment of continuum absorption and line shape (Clough, 1992). The inclusion of this effect in FASCODE2 should yield lower brightness temperatures compared to the GLA model.

b) Lower Boundary

The atmospheric profiles selected from the aircraft data were chosen so that the atmospheric column may be assumed clear above a solid lower boundary that may be either the ground, sea surface, or a low cloud. The temperature of the lower boundary is taken from the GOES IR window channel brightness temperature, TIR, and its altitude, zIR, is judged by comparing this temperature to the aircraft sounding. There are several ways this can introduce errors into the calculated radiances. 1) If water vapor continuum absorption reduces the radiance in the atmospheric window, then TIR will be too low and zIR too high (assuming decreasing temperature with height). 2) The boundary may not emit as a black body. 3) If the cloud top is thin, the effective boundary may not be well defined, and TIR will be warmer than the actual cloud top (where the cloud particle concentration goes to zero).

When the lower boundary is land or cloud (as opposed to sea surface), its emission may differ from that of a black body, and may be described by I(nu,z0)=epsilon*B(nu,T0) where epsilon is the emissivity of the surface (potentially dependent on wavenumber) and T0 and z0 are the actual boundary conditions. The emissivity of a cloud depends on the scattering processes in the cloud and can be related to the Mie parameters by an analytic two-stream solution of the scattering radiative transfer equations (see Salathe and Smith 1994).

Assuming the lower boundary radiates as a black body at the IR window brightness temperature introduces an error when the emmissivity is not one, and especially when the boundary is an elevated cloud top. This problem is treated by considering radiative transfer in a cloudy atmosphere as described in the next section.

c) Cloudy Atmosphere Transmission

The scattering of radiation in the infrared window by high clouds is well known. It is likely that the atmospheric columns for which we computed radiances are contaminated by thin cirrus. In order to study the influence of cloud scattering and absorption processes upon the computed 6.7 um brightness temperatures, these effects were included in the radiative transfer calculations for idealized cases; the results are discussed below. The transfer of radiation in an absorbing and scattering atmosphere was computed using a multiple scattering model as described in Salathe and Smith (1994).

The first problem introduced by cloud scattering occurs when the observed IR channel brightness temperature does not correspond to ambient temperatures at the cloud top as observed from the aircraft, which indicates the cloud either is not opaque to infrared radiation or is not emitting as a black body. This is the case with sounding E017 in Figure 5; a thin cloud was observed in this sounding with particle concentrations ~2 cm[-3]. The observed IR brightness temperature of 239 K corresponds to the ambient temperature at about 6 km, which is 2 km below the cloud top (Table 1). The results of our calculations indicate that the black-body assumption in fact underestimates the WV channel brightness temperature.

The second problem introduced by clouds is the possibility of undetected thin cirrus contaminating what is assumed to be a clear atmospheric path. For example, sounding e044 (Figure 7) was conducted downwind of a dense warm-front cirrus cloud. While no cloud particles were detected in this sounding, it does contain several very moist and well mixed layers that may contain ice particles either at concentrations and sizes below the instrument threshold or in other regions of the satellite image pixel. Thus it seems that undetected cirrus clouds do not influence the WV channel brightness temperature by more than 2K.

4. Results index up down

The brightness temperatures observed over the aircraft soundings were simulated as described above. The technique was to assume a clear air column over a black lower boundary. The lower boundary temperature was taken from the corresponding IR window channel pixel, and its height judged by comparing this temperature to the aircraft temperature sounding. Table 1 summarizes the results of this comparison study. This table presents the satellite and aircraft lower boundary conditions, type of lower boundary, and the brightness temperatures observed by GOES and computed by each of the models.

Table 1. Summary of results


 
Sounding    GOES-IR          Aircraft       Surf     6.7 um Brightness Temp (K)            
 name        TIR     zIR     Tsurf   zsurf   Type     GOES      FASCOD   GLA      NBM      

 E017        -34.   6.2       -40.   7.0     cloud   232.9      233.6   234.0    234.5     
 E043        -15.   2.4       -24.   4.0     cloud   233.6      237.8   239.4    241.8     
 E044        -6.    1.8       0.     0.0     ground  242.6      245.5   247.6    250.1     
 E054        -32.   5.0       -32.   5.0     cloud   227.4      232.2   234.0    234.3     
 E060        -4.    1.0       -10.   2.0     cloud   235.4      239.6   242.0    245.9     
 E067        -32.5  4.0        --     --     cloud   224.4      226.5   228.6    229.8     
 E072        -24.   0.0       -22.    0.0   ground   228.1      228.2   231.3    233.3     
 E083        3.     0.0        4.     0.0   ground   245.6      246.0   247.4    250.4     
 E084        1.     0.0        -5.    0.7   ground   235.5      239.9   242.1    246.3     
 C063        -19.   4.2       -10.    3.0    cloud   229.0      237.1   239.1    240.7     
 C083        -9.    2.0       -10.    1.0    cloud   233.0      240.2   241.6    244.7     
 C103        -10.   2.5       -5.    0.0     cloud   233.0      237.4   239.8    242.9     

In Figure 9 the computed brightness temperatures are plotted against the GOES observations. The thick lines show the linear trend of the results of each model, and the thin line indicates where computed and observed values are equal. The linear correlation for each set of computed values, shown in Table 2, is quite high and the slopes are nearly one. For each model, however, the computed brightness temperatures are on average greater than the observed brightness temperatures. FASCODE2 radiances reproduce the GOES observations best with the narrow band model giving the largest disparity. For all three models, the average difference or bias between computed and observed brightness temperatures is positive. This bias implies that the aircraft humidity measurements indicate a drier atmosphere than would be inferred from the satellite observation, or that the atmosphere is more opaque than indicated by the models. The bias in the FASCODE2 computations of 3.64 K is only slightly better than the 5.27 K bias found by Hayden (1988); the scatter, however, is significantly reduced.

The standard deviation of the bias in Table 2 is the deviation of the differences between individual computed and observed values from the mean bias. For each model, the bias is larger than its standard deviation. Furthermore, the deviations are nearly the same for each set of model results, and are comparable to the +/-2 K misalignment error estimated from Fig. 4 (Section 2c). It is likely, therefore, that the scatter is due to random errors such as a misalignment of aircraft sounding and satellite observation, and are not model dependent.

The only significant process with a known systematic influence that has been neglected in these calculation is oxygen continuum absorption, and its inclusion would reduce the bias in each model by about 0.5 K (see discussion in section 3a). Applying this correction for oxygen continuum and methane absorption to the results yields a bias of 3.1 K for FASCODE, 5.0 K for the GLA model, and 7.4 K for the NBM.

Comparing the entries in Table 1 indicates that cases with agreement in the IR and aircraft derived lower boundary (E017, E054, E072, E083, E084) give on average better agreement between computed and observed brightness temperatures. The average difference between the FASCODE and GOES brightness temperatures for these five cases is only 2.08 K compared to 3.64 K for all cases. The bias shows no clear relationship to boundary height. Thus, it is unlikely that errors in the boundary emission are at fault, since these errors become small when the boundary is low and its radiative contribution diminishes relative to the atmospheric emission.

Of the radiation models considered here, only FASCODE included water vapor continuum absorption at 6.7 um. Since the results from FASCODE are considerably better than for the other two models, and continuum absorption is the most important difference between FASCODE and the GLA model, it seems likely that continuum absorption is significant in the upper troposphere and in the vibrational band of water vapor. Comparison with the bias of the GLA results (Table 2) and with FASCODE computations with the continuum absorption suppressed, indicates that the continuum in FASCODE reduces the outgoing brightness temperature by about 1-2 K. This difference is seen also for the U.S. Standard Atmosphere calculation in Appendix A. This disparity is certainly smaller than the observed bias. Given the lack of observational verification of water vapor continuum absorption models, however, it is possible that future improvements in the modeling of continuum absorption may yield changes of this magnitude. Thus, in combination with other effects (such as cloud particle absorption), improvements in modeling continuum absorption may reduce the disagreement with satellite observations.

One way to express the magnitude of the radiance bias is to determine, assuming our radiance calculations are perfect, the amount of additional water vapor needed to reduce the calculated radiances to the observed values. A full doubling of the specific humidity is required. This moisture concentration adjustment lies well outside the error in our hygrometer and in some cases gives super-saturated air. Thus, this means of expressing the bias does not help to explain it but rather indicates its significance and the potential problems in determining moisture from radiance observations.

Table 2. Summary of statistics for each model (the corrected bias includes the effect of oxygen and methane absorption)


                   FASCODE      GLA       NBM    

Correlation         0.91        0.90      0.88    
Slope               0.91        0.88      0.98    
Bias (K)            3.6         5.5       7.9
corrected Bias (K)  3.1         5.0       7.4                           

5. Conclusions index up

There is a positive bias between observed and computed WV channel radiances for each of the radiation models used in this study. A number of assumptions and sources of error enter the computation that may contribute to this bias:

  1. Non-Black Lower Boundary. The assumption that the lower boundary radiates like a black body at the IR window channel brightness temperature was discussed in sections 3 and 4. This technique was found to cancel the unmodeled radiative effects at a cloud top. If the emissivity of the boundary is in fact much smaller at 6.7 um than at 11.2 um, then this assumption may contribute to the bias, but there is no reason to believe the emissivities take such values.
  2. Neglect of trace gas absorption. The exclusion of gaseous constituents other than water vapor was made after finding their influence to be less than 0.5 K. O2 absorption constituted the bulk of the 0.5 K reduction. Recent measurements of the collision-induced absorption by O2 (Orlando et al., 1991) have shown that earlier parameterizations (Timofeyev and Tonkov, 1978) overestimate this effect, so it is unlikely that the O2 contribution is any greater.
  3. Misalignment of observations. Errors arising from misalignment of the satellite observations and the aircraft soundings would neither be systematic nor to amount to as much as 5 K.
  4. Transmission model. The results from the three models are quite close, and FASCODE and GLA have been extensively tested against other radiation models (Ellingson, 1991). Hence these results are as accurate as possible given present knowledge of radiative transfer in clear air (but see #8 below)
  5. Satellite calibration. The present GOES satellite radiometer is calibrated against a hot source and space (Chesters et al., 1982). The space reference is considerably outside the range of observations so there may be some uncertainty in the calibration. While the 6.7 um channel is essentially impossible to operationally ground truth, the other channels are verified (Chesters et al., 1985; Hayden, 1988), and since the same radiometer is used for all channels it is unlikely to be severely in error.
  6. Cryogenic hygrometer. This instrument has been discussed above, and it is highly unlikely to be reporting moisture levels in error by the amount indicated by the bias.
  7. Zenith angle. The computed radiance depends on the zenith angle to the satellite, which varied daily during ERICA. The satellite position was fixed during Edmonton, so the lack of any difference in the comparisons from the two projects indicates that an error in the zenith angle is not significant. At mid-latitude values of the zenith angle, the sensitivity of the computed brightness temperature is about 0.1 K for a degree of angle.
  8. Continuum absorption. The theory and measurement of water vapor continuum absorption is area of ongoing research (Grant, 1990; Aref'yev, 1991) and there is much variation in how it is modeled in radiation codes. As discussed above, the difference in the GLA and FASCODE results indicates advances in modeling continuum absorption is unlikely to account for the full bias in computed radiances, but may be significant in combination with other effects. The results in this paper do not allow an assessment of the modeling of continuum absorption, but they do make clear that this process is essential to properly modeling upper-tropospheric radiation.
  9. Scattering by thin high clouds. The effects of clouds on the radiation have been neglected in computing the brightness temperatures in Table 1 since the only detected clouds in the soundings presented were assumed to be opaque and to form the lower boundary. As discussed above, the possibility of thin high clouds escaping detection is quite real. However, the simple scattering calculations presented in section 3c indicated that for thin cirrus to have a significant effect on the WV channel radiance, they would be quite evident in the IR channel images. But this may reduce the bias in combination with other effects.
Table 3 summarizes several of these sources of uncertainty and the likely magnitude of their influence on the computed brightness temperature. A negative value indicates that the error or assumptions in the calculations tend to underestimate the brightness temperature, and positive values indicate an overestimate. It must be concluded that no one mechanism accounts for the discrepancy between the observed and computed radiances. Several of the mechanisms discussed above may combine to produce the bias; alternatively, one mechanism may be much greater than we currently understand it to be.

Table 3. Summary of Error Sources


     Process or Error                Magnitude                  type of error        

        Emissivity               < -0.23 to -1.3 K            systematic          
       Trace Gases                     +0.5 K                    systematic          
        Alignment                      +/-2 K                      random            
   Cryogenic Hygrometer      +/-10% spec hum->+/-0.4 K      systematic or random     
       Zenith Angle            +/-5[[ring]]->+/-0.6 K       systematic or random     
        continuum                     <+/-2 K                 systematic          
        scattering                     <+2 K                  systematic          

In conclusion, state-of-the-art radiation codes predict considerably higher outgoing radiances at 6.7 um than are observed from space by the GOES satellite. After taking into account the systematic effect of additional trace gas absorption, FASCODE yields brightness temperatures on average 3.1 K too high, the GLA model 5.0 K too high, and the NBM 7.3 K too high. These results reflect the varied capabilities of the three radiative transfer models. FASCODE and the GLA model employ line-by-line calculations, and are often taken as standards for radiative transfer calculations. The disparity between these two codes is most likely attributable to water vapor continuum absorption, which is not accounted for in the GLA model.

Assuming that the moisture and temperature profiles are correctly measured and that the satellite observations are correct, the atmosphere is more opaque than the radiation models indicate. If water vapor is the only absorber, its upper-tropospheric concentration would have to be doubled to produce the opacity in the radiation models needed to match the satellite observations. Since FASCODE yields excellent agreement with observations of downwelling radiance (Smith, 1990), the problem seems to be unique to modeling the radiative properties of the upper troposphere in the strongly absorbing water vapor vibrational band.

Inaccurate modeling of the radiation field at this altitude and wavelength has implications for both modeling and monitoring climate change. While the observations used in this study do not allow a resolution of the problem, the results suggest possible mechanisms that may enhance the opacity of the upper troposphere. These are absorption of radiation by trace gases and non-gaseous material (ice and other aerosol) and water vapor continuum absorption. Uncertainties in these processes and in upper-tropospheric radiation in general must be resolved before we can confidently move forward in modeling and monitoring upper-tropospheric moist and radiative processes and their effects on the climate.


Acknowledgments

Paul Gluhosky at Yale played an invaluable role in supporting our research during the field projects and in developing software to view and analyze the aircraft and satellite data. Jielun Sun's earlier work at Yale in radiative transfer made many aspects of this work easier. Dave Kratz at NASA/GSFC supplied the Goody random line parameters and useful suggestions in developing the NBM. Bill Ridgeway of Applied Research Corp. (ARC) made the GLA line-by-line code available. The NCAR/RAF pilots and research staff ably supported our field projects. Jim Warnock and his colleagues at NOAA/ERL conducted the Vaisala soundings. The GOES-VAS data were provided by the Space Science and Engineering Center and the University of Wisconsin. This work was supported under NSF Atmospheric Science Division grant ATM-912390 and DOE/NIGEC grant DE-FC03-90ER61010, and the first author was supported by a NASA Global Change Research Fellowship.

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