A study of the NOAA 16 AMSU-A brightness temperatures observed over Libyan Desert

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D14, 4226, /2001JD001158, 2002 A study of the NOAA 16 AMSU-A brightness temperatures observed over Libyan Desert Tsan Mo Office of Research and Applications, NOAA/NESDIS, Camp Springs, Maryland, USA Received 31 July 2001; revised 30 December 2001; accepted 15 January 2002; published 31 July [1] The brightness temperatures over the southeastern Libyan Desert (21 23 N; E) from the NOAA-16 Advanced Microwave Sounding Unit-A (AMSU-A) were investigated for the months of January and March Angular distributions of the data from each month show remarkably stable patterns. The stable pattern of angular distributions can be potentially useful for postlaunch calibration and validation of the AMSU-A instrument, if a long-term trend of the angular distributions can be established. Angular distributions from the three window channels (channels 1, 2, and 15 with frequencies centered at 23.8, 31.4, and 89 GHz, respectively) and one near-surface sounding channel (channel 3 at 50.3 GHz) were simulated with a parametric model using the radiative transfer equation and a soil dielectric-emissivity model that generates the required soil emissivity as a function of zenith angle. The simulated results agree well with the data over the Libyan Desert area. The best-fit results indicate that radiation sensed by each channel comes from different thermal sampling depth and that these window channels could be used for temperature sounding in soils. The effect of spacecraft roll error on the angular distribution was also investigated. It was found that 1 roll error would produce a left-right asymmetry of 2.6 K in the angular distribution. INDEX TERMS: 3337 Meteorology and Atmospheric Dynamics: Numerical modeling and data assimilation; 3359 Meteorology and Atmospheric Dynamics: Radiative processes; 3360 Meteorology and Atmospheric Dynamics: Remote sensing; 3367 Meteorology and Atmospheric Dynamics: Theoretical modeling; KEYWORDS: remote sensing, AMSU-A measurements, brightness temperatures, atmospheric temperature sounding, satellite data, microwave radiometers 1. Introduction [2] The Advanced Microwave Sounding Unit-A (AMSU- A) on NOAA-16, which was launched in September 2000, is the second of a new generation of total-power microwave radiometers for the NOAA-K, L, M, N, and N series of Polar-orbiting Operational Environmental Satellites (POES). Each AMSU-A instrument is composed of two separate units: AMSU-A2 with two channels at 23.8 and 31.4 GHz; and AMSU-A1 with 12 channels in the range of 50.3 to 57.3 GHz plus one channel at 89.0 GHz. In total, AMSU-A furnishes 15 channels. Description of the AMSU-A instrument and its radiometric performance was reported elsewhere [Mo, 1996]. A brief functional description of the AMSU-A instruments is given in Appendix A. [3] Prior to launch, each of the AMSU-A flight models were tested and calibrated in a thermal-vacuum (TV) chamber by the instrument contractor. NOAA instrument calibration scientist evaluates and analyzes these prelaunch calibration data to derive the calibration parameters input data set (CPIDS), which is used in the NOAA operational calibration processing to produce the AMSU-A 1B data sets [Mo, 1996]. Particularly, the nonlinearity, which is of the order of 1 K or less, cannot be evaluated by the two-point This paper is not subject to U.S. copyright. Published in 2002 by the American Geophysical Union. calibration in orbit, but must be determined from the prelaunch calibration data. [4] After each launch, a systematic postlaunch calibration and validation of the AMSU-A instrument performance is conducted with on-orbit data. The long-term trends of the housekeeping sensors and radiometric counts from the cold and warm targets are also monitored for checking the instrument performance [Mo, 1999c]. It is also desirable to have an Earth target for evaluation of the instrument performance. Various desert areas have been used for calibrating spaceborne active microwave remote sensors. The present study was undertaken to characterize a radiometrically stable target by examining the NOAA-16 AMSU-A data collected over the southeastern Libyan Desert (21 23 N; E) for the two months of January and March The AMSU-A data over such a radiometrically stable desert area show a remarkably stable angular distribution, which should be of considerable interest to data users interested in understanding their remote-sensing measurements. A parametric model using the radiative transfer equation was developed for theoretical interpretation of the data from the window and nearsurface channels. The model assumes a uniform desert soil surface with an effective soil temperature which may vary with the thermal sampling depth for individual channels. Comparison of the model results with the data shows good agreement. The theoretical model is developed in section 2, ACL 16-1

2 ACL 16-2 MO: NOAA-16 AMSU-A BRIGHTNESS TEMPERATURES OBSERVED OVER LIBYAN DESERT Figure 1. Calculated soil surface emissivities e s as a function of zenith angle for channels 1 3 and 15. The AMSU-A emissivity e s is defined in equation (3) with p = v (i.e., vertical polarization). The calculated emissivities with an assumed soil moisture content 0.05 cm 3 /cm 3 include the cross-polarization component H vh that was calculated from measured antenna patterns. the results are presented in section 3, and a discussion is given in section 4. A brief functional description of AMSU-A is given in Appendix A. 2. Theoretical Model [5] Brightness temperatures measured by AMSU-A are influenced by the surface emission, the upward atmospheric radiation, the surface-reflected downward emission of the atmosphere, and the cosmic background radiation reflected at the surface. By integrating the radiative transfer equation, the brightness temperature T B for the window and nearsurface channels can be written in terms of the soil surface temperature T S, surface emissivity e S, atmospheric temperature T A, transmittance t, and the cosmic background temperature T C = 2.73K [Schwarzschild, 1990]. In window channels where only the surface and low-level atmosphere are sensed, one can use a mean effective temperature for the atmosphere instead of a profile. This simplifies the solution of the radiative transfer equation to the form T B ¼ te S T S þ ð1 t ÞT A þ tð1 e S where the transmittance t is defined by t sec qz t ¼ e ð2þ Þð1 tþt A þ t 2 ð1 e S ÞT C ð1þ where t is the atmospheric optical thickness and q Z is the local zenith angle. It should be noted that the quantities T B, e S, and t also depend on frequency, polarization, and zenith angle which are understood in our equations for simplicity. In equation (1), the first term is the surface emission attenuated by the atmosphere, the second one represents the upwelling atmospheric radiation, the third one is the downwelling atmospheric radiation reflected at the surface and attenuated by the atmosphere, and the last term denotes the attenuated downwelling cosmic radiation reflected at the surface and attenuated by the atmosphere again. [6] The polarization of individual AMSU-A channels varies with scan angle due to the rotating-reflector and fixed-feedhorn antenna design. At each scan angle q S,the AMSU-A sensed surface emissivity e s contains mixed vertical (v) and horizontal (h) polarizations. Due to imperfect cross-polarization isolation in the antenna, there is also a small fraction of cross-polarized component in the measured antenna patterns. Near the nadir, the upwelling vertical and horizontal emissivities are essentially the same over large scan regions. For regions near the edges of the scan, the degree of cross-polarization mixing becomes important for the window channels. This cross-polarization fraction, H pq (where p and q are the polarization indices with p 6¼ q), which can be computed from the measured antenna patterns [Mo, 2000], is incorporated into the AMSU-A emissivity model to obtain the soil emissivity e s with mixed polarizations as follows, e S ¼ 1 h pq e p ðq Z Þcos 2 q S þ e q ðq Z þ h pq e q ðq Z Þcos 2 q S þ e p ðq Z Þsin 2 q S Þsin 2 q S where e p and e q with the polarization indices, p and q (either can be h or v, but p 6¼ q) represent either horizontally (h) or vertically (v) polarized surface emissivities. These can be accurately calculated from the Fresnel formula as a function ð3þ

3 MO: NOAA-16 AMSU-A BRIGHTNESS TEMPERATURES OBSERVED OVER LIBYAN DESERT ACL 16-3 Figure 2. NOAA-16 AMSU-A brightness temperatures observed over the southeastern Libyan Desert in January Data from the ascending pass (1400 LT) are denoted by the pluses, and those from the descending pass (0200 LT) are shown as crosses. The solid curves are simulations as discussed in the text. of soil dielectric property, for which models have been developed by Wang and Schmugge [1980] and Calvet et al. [1995]. The empirical model by Wang and Schmugge, which will be referred to as the WS model, was developed using measurements at 1.4 and 5 GHz for computing the soil dielectric constant that is required in the Fresnel emissivity formula for calculating the e p and e q. It has been shown that calculated soil dielectric constants with the WS model are in good agreement with measured results over a large range of volumetric soil moisture of cm 3 /cm 3. Calvetetal. [1995] modified the WS model and extended it to higher frequencies up to 90 GHz. In this study, this modified WS model was used to calculate the soil dielectric constant required in the Fresnel emissivity formula. Prigent et al.

4 ACL 16-4 MO: NOAA-16 AMSU-A BRIGHTNESS TEMPERATURES OBSERVED OVER LIBYAN DESERT Table 1. Best-Fit Parameters Used to Simulate the Observed Brightness Temperatures From the Window Channels as Shown in Figures 2 and 3 Ascending Pass Descending Pass AMSU-A Channel T S,K T A,K t(0 ) T S,K T A,K t(0 ) January March [2000] used an emissivity formula similar to equation (3) but without the cross-polarization component (i.e., H pq =0).As noted above, the cross-polarization term becomes important near the edges of the scan for the window channels. [7] Effect of soil roughness on soil emissivities is ignored in this study, as the statistical properties of the rough surface, including the surface height standard deviation and its horizontal correlation length [Mo and Schmugge, 1987] are unknown. Inclusion of the surface roughness in the model will raise the emissivities given in Figure 1 slightly but not change the substance of the results presented in this study. As the wavelength (i.e., l = 0.34 cm) at channel 15 is smaller than those of other channels, surface roughness may induce a relatively large effect on channel 15. [8] The local zenith angle q Z is related to the scan angle q S according to the relation, q Z ¼ sin 1 R þ H R sin q S where R = km is the Earth s radius and H, which denotes the height of satellite, equals 870 km for NOAA-16, an afternoon satellite with local equatorial crossing time (LECT) at 0200 local time (LT) during descending (southbound) pass and 1400 LT during ascending (northbound) pass. The maximum q Z values occur at the AMSU-A outmost scan positions 1 and 30 where calculation from equation (4) produces q Z = ±58.1. In this study, we only simulate the AMSU-A data at channels 1, 2, 3 and 15, which all have p = v and q = h. Thus, equation (3) with p = v and q = h (but p 6¼ q) will be used to compute the surface emissivities, e S, for these channels. The calculated H pq values for these four channels are 0.030, 0.025, 0.031, and 0.012, respectively. Figure 1 shows the calculated soil surface emissivity as a function of zenith angle q Z from equation (3) for channels 1 3 and 15 with an assumed volumetric soil moisture content of 0.05 cm 3 /cm 3, a relatively low value that is appropriate for a dry desert soil condition. For soil moisture below a certain value, which is referred to as wilting point (WP) in the WS model, water molecules are tightly bounded to soil particles and can not move freely. Under such conditions, water in soils behaves like ice, its effect on soil dielectric constant is small, and plants begin to wilt as it is difficult to extract water from soils. According to the WS model, the WP ranges from ð4þ to 0.05 cm 3 /cm 3 for sandy soils. Thus the soil surface emissivities calculated with a soil moisture content of 0.05 cm 3 /cm 3 (Figure 1) will be used in equation (1) to simulate the NOAA-16 AMSU-A data in channels 1, 2, 3, and 15. The frequency-dependence of e S is relatively weak at the AMSU-A channel frequency range (Figure 1). Similar results were also reported by Calvet et al. [1995] and Prigent et al. [2000]. The complex soil dielectric constants calculated with cm 3 /cm 3 soil moisture content are i0.37, i0.39, i0.40, and i0.33 for channels 1 3 and 15, respectively. [9] To calculate the brightness temperature T B as defined in equation (1), one needs to know the soil surface temperature T S, the atmospheric temperature T A, and the transmittance t(0 ) at nadir, in addition to surface emissivities as shown in Figure 1. The parameter T A can be estimated from other sources [Kalnay et al., 1996] and the transmittance t can be calculated [Rosenkranz, 1995]; however, their precise values are unknown for the particular time and location as in our cases. Thus a nonlinear least squares fitting method is used to match the theoretical model calculations (equation (1)) with the observed angular distributions of the AMSU-A brightness temperatures. In the fitting process, the three quantities T S, T A, and t(0 ) = exp ( t), with the surface emissivities fixed (Figure 1), are varied to produce sets of angular distributions of calculated brightness temperatures that match the observations. The best-fit parametric values then represent the soil surface temperature T S, the atmospheric temperature T A, and the transmittance t at nadir. 3. Results [10] Figure 2 shows the scatterplots of the Libyan Desert brightness temperatures observed over 31 days in January The pluses denote the ascending data, and the crosses represent the descending data. These brightness temperatures, which represent individual measurements at various fields of view (FOV), are obtained from the AMSU-A antenna temperatures by adding an antenna pattern correction at each FOV to account for the antenna sidelobe contributions as described by Mo [1999a, 2000]. The solid curves on channels 1, 2, 3, and 15 represent the simulated results using equation (1) and the best-fit parameters in Table 1. The general features of the data are as follows: (1) The simulations, as represented by the solid curves on channels 1 3, and 15, are in good agreement with the observations at these channels after fitting the data with the T S, T A, and atmospheric transmittance as given in Table 1. (2) There is little left-right asymmetry in the angular distributions in the window channels. (3) Brightness temperatures from sounding channels gradually decrease from channels 3 to 9, and then increase from channels 9 to 14. These temperatures provide a typical profile of atmospheric temperature with channel 9 at the tropopause and channel 14 at the stratopause. (4) Channels 1 8 and 15 sense temperatures at levels below the tropopause and their angular distributions show limb darkening. (5) Channels sense temperatures at levels above the tropopause and their angular distributions show limb brightening. (6) Channel 14 measures the atmospheric temperatures around the stratopause (1 mbar). (7) Channels 1 3 and 15 show

5 MO: NOAA-16 AMSU-A BRIGHTNESS TEMPERATURES OBSERVED OVER LIBYAN DESERT ACL 16-5 Figure 3. Same as Figure 2, except the data were taken in March that the daytime (1400 LT) temperatures in sunlight from the ascending pass are about 8 K higher than the nighttime (0200 LT) temperatures from the descending pass. The temperature difference between daytime and nighttime at channel 4 is about 4 K. (8) For channels 5 14, there are no noticeable differences between the ascending (daytime) and descending (nighttime) data. (9) Surface emissivity has large effect on both the window channels (i.e.,1, 2, and 15) and the near-surface sounding channel 3. This can be seen from the patterns of angular distributions in Figures 2 and 3, which show two peaks located at FOVs 6 and 24, respectively, in channels 1 3 and 15, but not in other channels. These peak locations correspond to that of the surface emissivities (Figure 1). Also, the atmospheric transmittance approaches zero at the frequencies of channels 4 14 [Prigent et al., 2000]; therefore surface emission can not reach the radiometers onboard the satellite. [11] In spite of the long time period of 31 days, the individual AMSU-A data points (Figure 2) over the desert area show a remarkably stable pattern of angular distribu-

6 ACL 16-6 MO: NOAA-16 AMSU-A BRIGHTNESS TEMPERATURES OBSERVED OVER LIBYAN DESERT tions which offer considerable interest to data users for understanding the source of contributions to these remotesensing measurements. Since the angular distributions of the window and the near-surface channels closely resemble that of the surface emissivities as shown in Figure 1, one would expect that these angular distributions can be simulated using equations (1) to (3). [12] The solid curves in Figure 2 represent the simulated results which were calculated from equation (1) with the best-fit parametric values listed in Table 1. The ascending and descending data were fitted separately and both simulated results are shown in Figure 2. One can see that the simulated results at the four channels (i.e., channels 1-3 and 15) agree very well with the observed brightness temperatures, particularly, the angular patterns are well reproduced. [13] Table 1 shows that the best-fit T S values at channel 15 are higher than those at other channels during ascending passes (daytime), but reversed during descending passes (nighttime). This shows that radiation sensed by each channel comes from different thermal sampling depth (i.e. skin depth; Ulaby et al. [1986]) which is proportional to its channel wavelength. The wavelengths of channels 1 3 and 15 are 1.26, 0.96, 0.60, and 0.34 cm, respectively. As channel 15 has the smallest wavelength (or skin depth), it senses the radiation from the topmost surface layer, which is warmer than a deeper soil layer during daytime, but colder in nighttime. This demonstrates that these window channels could be used for temperature sounding in soils analogous to the use of other channels for temperature sounding in the atmosphere. [14] The global reanalysis data [Kalnay et al., 1996] from the National Center for Environmental Prediction (NCEP) gives the daily averaged (over area) nearsurface air temperatures (1000 mbar) in the region near the Libyan Desert area. From these daily averaged reanalysis data, one can compute the monthly mean values of K and K, respectively, for the months of January and March These monthly mean near-surface air temperatures provide a first guide for setting the T A values in fitting ascending (daytime) and descending (nighttime) data. The best-fit t(0 ) values in Table 1 closely resemble the atmospheric transmittances calculated with a winter subarctic atmospheric profiles by Prigent et al. [2000]. This is perhaps attributed to low atmospheric water vapor in both cases. Also, the small variation in the t(0 ) values (Table 1) between the ascending and descending passes is most likely due to changes in the atmospheric water vapor. [15] Figure 3 shows the same Libyan Desert brightness temperatures but for the month of March Angular distributions in Figures 2 and 3 show similar patterns, except that the brightness temperatures from the window channels in Figure 3 are approximately 7 K higher than the corresponding ones in Figure 2. This seasonal effect is expected because the desert surface and near-surface atmospheric temperatures in March are warmer than those in January. However, the magnitudes of the observed brightness temperatures from the high-altitude sounding channels 4 14 are about the same for both January and March data. Best-fit parameters for March data are listed in the lower part of Table Conclusion [16] Brightness temperatures over the southeastern Libyan Desert (21 23 N; E). were extracted from the NOAA-16 AMSU-A 1B data for the months of January and March Angular distributions of the data from each month show remarkably stable patterns. For the four window channels (i.e., channels 1 3 and 15), ascending (daytime 1400 LT in the sun) and descending (nighttime 0200 LT in dark) measurements differ by about 8 K, for channel 4, the difference is about 4 K, but for other channels, there is little difference between the ascending and descending measurements. The stable pattern of angular distributions can be potentially useful for postlaunch calibration and validation of the AMSU-A instruments, if a long-term trend of the angular distributions can be established. [17] Angular distributions of the window channels do not suggest that the AMSU-A data have any angular-dependent bias which might originates from a roll error as reported by some data users. Any roll error will produce noticeable leftright asymmetry in the angular distribution of the data because the soil emissivity (Figure 1) varies rapidly as a function of zenith angle at the outmost FOVs. One can estimate the magnitude of the left-right asymmetry by calculating the dt B /dq Z at the outmost FOV if any roll error exists. At either FOV 1 or 30, the corresponding change in brightness temperature dt B /dq Z can be obtained from equation (1). Using the best-fit parameters in Table 1, one can obtain the results of dt B /dq Z = 1.32, 1.26, 0.54, and 1.21 K/deg at channels 1 3 and 15, respectively, for the January data. The left-right asymmetries induced by such roll errors in the corresponding channels would equal 2 dt B / dq Z = 2.6, 2.5, 1.1, and 2.4 K/deg, which would be noticeable if they exist. The data in the window channels as shown in Figures 2 and 3 do not show such roll error induced asymmetries. [18] A simple model for simulating the brightness temperatures at the three window channels and one near-surface channel was developed. The model was based on integration of the radiation transfer equation that uses a mean temperature for the low-level atmosphere. Soil emissivity was calculated from the Fresnel formula using an empirical model for soil dielectric constant as a function of soil moisture [Wang and Schmugge, 1980; Calvet et al., 1995]. The simulated angular distributions of brightness temperatures for window channels 1 3, and 15 are in good agreement with the NOAA-16 AMSU-A measurements. The best-fit results reveal that radiation sensed by each channel comes from different thermal sampling depth. For high-altitude sounding channels (i.e., channels 4 14), the observed brightness temperatures at each FOV correspond to atmospheric temperatures of different altitudes, and therefore, profiles of atmospheric temperatures are required in equation (1) to reproduce the angular distributions. This is beyond the scope of this paper, but it may be more easily handled by more complete radiative transfer models [Rosenkranz, 1995; Goldberg et al., 2001]. Appendix A: Functional Description of AMSU-A [19] Each AMSU-A instrument is composed of two separate units: AMSU-A2 with two channels at 23.8 and 31.4 GHz; and AMSU-A1 with 12 channels in the range of

7 MO: NOAA-16 AMSU-A BRIGHTNESS TEMPERATURES OBSERVED OVER LIBYAN DESERT ACL 16-7 Table A1. NOAA-16 AMSU-A Channel Characteristics and Specifications Channel Number Central Channel Frequency, a MHz Number of Bands Measured 3-dB RF Bandwidth, MHz Specification NEDT, K Measured Beam Efficiency, b % Polarization (NADIR) 1 23, V , V , V , V , ± H , H , V , H fo = 57, H fo ± H 11 fo ± ± / / H 12 fo ± ± / / H 13 fo ± ± / / H 14 fo ± ± / / H 15 88, V 3.29 a Measured at 18 C. b Measured. c Specification is required to have 3.3 ± 10% for all channels. FOV, c deg 50.3 to 57.3 GHz plus one channel at 89.0 GHz. In total, AMSU-A furnishes 15 channels. AMSU-A1 uses two antenna systems (A1-1 and A1-2), providing a set of 12 oxygen band channels (3 14) for retrieving the atmospheric temperature profile from the Earth s surface to about 50 km, or from 1000 to 1 mbar. The remaining three channels (1, 2 from A2 and 15 from A1-1) provide aid to the retrieval of temperature soundings by correction of surface emissivity, atmospheric liquid water, and total precipitable water. These window channels also provide information on precipitation, sea ice, and snow coverage. [20] Table A1 lists some of the main NOAA-16 AMSU- A channel characteristics, including the channel central frequency, number of bands, band width, and radiometric temperature sensitivity (or noise equivalent uncertainty in temperature, NEDT) for each channel. Details of these quantities can be found elsewhere [Mo, 1999a, 1999b]. The main beam efficiencies and beam widths for individual channels were calculated using measured AMSU-A antenna patterns [Mo, 2000]. Each of the AMSU-A antenna systems has a nominal FOV of at the half-power points and scans cross-track with a maximum angle of ± (beam centers) from the nadir and each separated by The antenna reflectors execute one complete revolution every 8 s during which 30 Earth scene resolution cells (also referred to as beam positions) are sampled in a stepped-scan fashion. Onboard calibration is obtained by viewing the cold space (background brightness temperature 2.73 K) and an internal blackbody target every 8 s for each scan line. Beam positions 1 and 30 are the outmost scan positions of the Earth views, while beam positions 15 and 16 are at 1.65 and 1.65 from the nadir, respectively. References Calvet, J., J. Wigneron, A. Chanzy, S. Raju, and L. Laguerre, Microwave dielectric properties of a silt-loam at high frequencies, IEEE Trans. Geosci. Remote Sens., 33, , Goldberg, M. D., D. S. Crosby, and L. Chou, The limb adjustment of AMSU-A observations: Methodology and validation, J. Appl. Meteorol., 40, 70 83, Kalnay, E., et al., The NMC/NCAR CDAS/Reanalysis Project, Bull. Am. Meteorol. Soc., 77, , Mo, T., Prelaunch calibration of the Advanced Microwave Sounding Unit- A for NOAA-K, IEEE Trans. Microwave Theory Tech., 44, , Mo, T., AMSU-A antenna pattern corrections, IEEE Trans. Geosci. Remote Sens., 37, , 1999a. Mo, T., Calibration of the Advanced Microwave Sounding Unit-A radiometers for NOAA-L and NOAA-M, Tech. Rep. NESDIS 92, Natl. Oceanic and Atmos. Admin., Washington, D. C., 1999b. Mo, T., Post launch evaluation of the Advanced Microwave Sounding Unit- A on the NOAA-15 satellite, in Earth Observing Systems IV, edited by W. Barnes, Proc. SPIE Int. Soc. Opt. Eng., 3750, , 1999c. Mo, T., NOAA-L and NOAA-M AMSU-A antenna pattern corrections, Tech. Rep. NESDIS 98, Natl. Oceanic and Atmos. Admin., Washington, D. C., Mo, T., and T. J. Schmugge, A parameterization of the effect of surface roughness on microwave emission, IEEE Trans. Geosci. Remote Sens., 25, , Prigent, C., J. P. Wigneron, W. B. Rossow, and J. R. Pardo-Carrion, Frequency and angular variations of land surface microwave emissivities: Can we estimate SSM/T and AMSU emissivities from SSM/I emissivities?, IEEE Trans. Geosci. Remote Sens., 38, , Rosenkranz, P. W., A rapid atmospheric transmittance algorithm for microwave sounding channels, IEEE Trans. Geosci. Remote Sens., 33, , Schwarzschild, B., COBE satellite finds no hint of excess in the cosmic microwave spectrum, Phys. Today, 43, 17 20, Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing, vol. 3, chap. 18, p. 1418, Artech House, Norwood, Mass., Wang, R. J., and T. J. Schmugge, An empirical model for the complex dielectric permittivity of soils as a function of water content, IEEE Trans. Geosci. Remote Sens., 18, , [21] Acknowledgments. The author would like to thank Michael Weinreb for his review and constructive comments on the original manuscript. Comments and suggestions by three anonymous reviewers resulted in improvement of the final manuscript. T. Mo, Office of Research and Applications, NOAA/NESDIS, 5200 Auth Road, Camp Springs, MD 20746, USA. (tsan.mo@noaa.gov)