3. Radiative Transfer
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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.
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.
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.
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.
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]].
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.
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.
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
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.
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