2

Atmospheric Soundings

INTRODUCTION

The large-scale motions of the atmosphere are among the principal controls of our daily weather. These motions, referred to as atmospheric circulation, are also among the main controls of regional and global climate through the way they cause variations in cloudiness, wind, temperature, and precipitation. Atmospheric circulation is generally described in terms of three-dimensional distributions of momentum and thermodynamics, namely wind speed and direction, temperature, and moisture.

Accurate observations of global wind, temperature, and humidity are of paramount importance to numerical weather prediction (NWP) project activities that depend on the initial state defined by the three-dimensional structure of these quantities. Accurate observations of these quantities are also important for climate research because the energy budget of the climate system is governed substantially by their distribution. Although temperature and moisture profiles (soundings) are currently obtained from conventional meteorological observing networks operating over populated regions, the lack of global coverage, together with the steady demise of these networks, results in increasing reliance on satellite observations to fill critical gaps in observational data.

Setting the climate measurement requirements for temperature and moisture is a difficult task, given the integral way these parameters relate to many important climate processes. Table 2.1, extracted from the National Polar-orbiting Operational Environmental Satellite System (NPOESS) climate measurement requirements, the environmental data records (EDRs) (NOAA, 1997), summarizes sounding capabilities expected when NPOESS becomes operational. A number of questions can be raised regarding the adequacy of the stated EDR thresholds. For example, the threshold vertical resolution for humidity is unrealistic, and stated threshold accuracies reflect expected capabilities rather than actual climate needs. It remains an open but critical question whether or not the information extracted from current NWP systems, including systems planned for NPOESS, is at all sufficient to meet climate research requirements.

The committee's findings in Box 2.1 address the current status of space-based measurements and data and future needs in the integrated NPOESS program for research-quality atmospheric temperature and moisture data for the study of climate change.



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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN 2 Atmospheric Soundings INTRODUCTION The large-scale motions of the atmosphere are among the principal controls of our daily weather. These motions, referred to as atmospheric circulation, are also among the main controls of regional and global climate through the way they cause variations in cloudiness, wind, temperature, and precipitation. Atmospheric circulation is generally described in terms of three-dimensional distributions of momentum and thermodynamics, namely wind speed and direction, temperature, and moisture. Accurate observations of global wind, temperature, and humidity are of paramount importance to numerical weather prediction (NWP) project activities that depend on the initial state defined by the three-dimensional structure of these quantities. Accurate observations of these quantities are also important for climate research because the energy budget of the climate system is governed substantially by their distribution. Although temperature and moisture profiles (soundings) are currently obtained from conventional meteorological observing networks operating over populated regions, the lack of global coverage, together with the steady demise of these networks, results in increasing reliance on satellite observations to fill critical gaps in observational data. Setting the climate measurement requirements for temperature and moisture is a difficult task, given the integral way these parameters relate to many important climate processes. Table 2.1, extracted from the National Polar-orbiting Operational Environmental Satellite System (NPOESS) climate measurement requirements, the environmental data records (EDRs) (NOAA, 1997), summarizes sounding capabilities expected when NPOESS becomes operational. A number of questions can be raised regarding the adequacy of the stated EDR thresholds. For example, the threshold vertical resolution for humidity is unrealistic, and stated threshold accuracies reflect expected capabilities rather than actual climate needs. It remains an open but critical question whether or not the information extracted from current NWP systems, including systems planned for NPOESS, is at all sufficient to meet climate research requirements. The committee's findings in Box 2.1 address the current status of space-based measurements and data and future needs in the integrated NPOESS program for research-quality atmospheric temperature and moisture data for the study of climate change.

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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN TABLE 2.1 NPOESS Climate Environmental Data Record Threshold Requirements for Temperature and Moisture Soundings System Capability Temperature Threshold Water Vapor Threshold (specific humidity)a Horizontal Resolution   50 km Troposphere     Clear, nadir 50 km   Clear, worst case 100 km   Cloudy, nadir 50 km   Cloudy, worst case 100 km   Stratosphere Clear 200 km   Vertical Resolution Clear     Surface-300 millibars (mbar) ±1.0 K/1 km depth 20 mbar, surface-850 mbar 300-30 mbar ±1.0 K/3 km depth 50 mbar, 850-100 mbar 30-1 mbar ±1.0 K/5 km depth   1-0.01 mbar Cloudy (>80%) ±3.5 K/5 km depth   Surface-700 mbar ±1.5 K/3 km depth   700-100 mbar ±1.5 K/3 km depth   Measurement Accuracy Clear ±0.5 K   Surface-600 mbar   ±25% 600-400 mbar   ±35% 400-100 mbar Cloudy   ±35% surface-600 mbar   ±25% 600-400 mbar   ±40% 400-100 mbar   ±40% Long-term Stability   2% Troposphere ±0.05 K/decade   Stratosphere ±0.10 K/decade   aPrimarily clear-sky. SOURCE: Adapted from NOAA (1997). A BRIEF HISTORICAL PERSPECTIVE A detailed history of atmospheric sounding up to 1991 is summarized in the review article of Smith (1991). The basic physics involved in the design of temperature and moisture sounders from Earth orbit was published in the late 1950s (King, 1958; Kaplan, 1959), followed by a number of papers describing different methods of retrieval (e.g., Houghton et al., 1984; Smith, 1991). The early measurements that tested these concepts were based on measurements obtained from filter radiometers with a spectral resolution (λ/Δλ) typically on the order of 100. As noted below, the next step in sounding technology is toward sounders with a much higher spectral resolution (λ/Δλ ~ 1000). The presence of clouds in the field of view of sounders has a detrimental effect on the quality of a retrieval. The absorption properties of cloud droplets and ice particles at infrared sounding wavelengths are so strong that even thin clouds contaminate the measurement of radiances. A number of techniques have been developed to minimize the effects of clouds on soundings. These usually require some way of identifying cloudy scenes to arrive at an equivalent clear-sky radiance quantity (such as the so-called “cloud-clearing” method of Smith, 1968). It is difficult to remove the effects of clouds entirely from the data, producing larger retrieval errors under these conditions (this is also reflected in Table 2.1). Methods accounting for the effects of clouds on the data are generally based on higher-resolution visible and infrared imaging data that are required to supplement the sounding channels.

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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN Box 2.1 Summary and Findings Present Status and Future Needs of Space-Based Atmospheric Soundings The past 20 years have witnessed considerable progress in passive infrared remote sensing of temperature profiles using radiance data obtained from filter radiometers. Currently, the combination of the High Resolution Infrared Sounder and the Microwave Sounding Unit (MSU) provides atmospheric temperature profiles with an average root mean square (rms) error of approximately 2 K and a vertical resolution of 3 to 5 km in the troposphere. Temperature retrieval algorithms applied to data from this current suite of operational sounders are mature and well understood; however, the accuracy and resolution of temperature retrieved from current sounder data fall short of numerical weather prediction (NWP) requirements. In addition, even when identical retrieval algorithms and instruments are employed, discrepancies in the data products from one spacecraft to the next reduce the utility of the data for climate monitoring. Although new technologies such as Global Positioning System satellites are expected to improve portions of the retrieval, it is hoped that the next generation of full-column sounders will overcome the shortfalls mentioned. The situation is even worse for water vapor, where characteristics of water vapor retrievals and the accuracy of retrieved water vapor measurements are less advanced. Issues that need to be considered in the remote sensing of temperature and moisture on the National Polar-orbiting Operational Environmental Satellite System (NPOESS) for climate research include the following: Current sounding systems fall short of the requirements of numerical weather prediction. This shortfall has prompted the development of next-generation sounders, beginning with the Atmospheric Infrared Sounder (AIRS) on the Earth Observing System (EOS) PM satellite followed by the Cross-track Infrared Sounder (CrIS) and Infrared Atmosphere Sounding Interferometer radiometer as part of NPOESS, that provide higher-spectral-resolution measurements. The traditional goal of sounding measurements is to deliver profiles of temperature and moisture for use in numerical weather prediction. These sounding data products also have direct and obvious climatological value. However, assimilation of radiance data has progressed at operational prediction centers, where explicit retrievals are no longer carried out in this traditional sense. Sounding data products are now derived as outputs from NWP models rather than as direct outputs from retrieval schemes. There are additional reasons to move toward increased spectral resolution in sounders: (1) improvements in signal-to-noise ratios can be realized by averaging channels with the same characteristic absorption; (2) clearer discrimination of thin clouds is possible using more highly resolved line absorption information; and (3) spectral measurements enhance the capability of providing other nonsounding information. Although additional advantages exist, sounding information content does not increase proportionally with increasing spectral resolution. Within this context it is legitimate to ask (1) what are the optimal placement and number of channels of a high-resolution instrument like AIRS or CrIS that actually contribute to retrieved soundings, (2) which channels are redundant, and (3) what is to be gained by combining a number of redundant channels. From the climate perspective, the question of whether the calibrated radiance data obtained from sounders are more basic than the sounding products derived from these radiances is unresolved. This is an especially relevant debate today, given the changing ways these radiance data are used in assimilation systems and the likelihood of changes in analysis systems in the future. For purposes of monitoring climate change, it is critical to establish the extent to which any retrieved quantity relies on the first estimate of that quantity, which is usually derived from a climatological database. Properties that are too dependent on such databases cannot provide proper measures of evolving climate change. Current analysis systems, especially as they apply to water vapor, are inadequate and unfortunately rely too much on existing but poorly known climatologies or time records. It is not obvious that this situation will improve substantially with the next generation of infrared sounders.

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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN Radiance data, complete with calibration information, should be considered as the fundamental climate data resource in addition to retrieved sounding products. Calibrated radiances are the basic inputs to NWP analyses and the basic inputs to retrieval algorithms. NWP analyses and algorithms have changed dramatically since the launch of the first TIROS Operational Vertical Sounder (TOVS) and may also change significantly in the future. Reprocessing the radiance data will continue to be an important activity in this environment of changing approaches to analysis. Climate measurement requirements for temperature and moisture should also be expressed in terms of radiance requirements in addition to geophysical parameters. Maintenance and enhancement of existing, conventional observing networks, e.g., radiosonde networks, should be an integral part of the supporting and dedicated vicarious calibration efforts. A coordinated vicarious calibration activity must accompany the satellite measurements to monitor calibration accuracy, assess differences in output from different versions of the same instrument, and determine spurious instrument-based trends. Experience has shown that proper assessment of measurement precision follows the accumulation and analysis of a sufficiently large body of data. To provide the most useful information, the conventional networks must also be supported by a program that characterizes and calibrates the instrumentation employed to ensure quality and consistency in all geographic regions. Orbit stability should be maintained to avoid aliasing errors1 that arise from inadequate sampling of the diurnal cycle, among other errors that might affect measurement trends. Precise intersatellite calibration, based on measurement continuity with sufficient instrument overlap, is required to determine differences between versions of the same instrument on different satellites. 1Errors introduced when high-frequency occurrences are interpreted as low-frequency occurrences because of inadequate sampling. The concern over the problem of clouds motivated the inclusion of microwave sounding channels as part of the sounding instrument system. Clouds at these frequencies are almost transparent (although not transparent enough to eliminate the effects of clouds entirely). Examples of microwave sounders are the Microwave Sounding Unit (MSU) with four channels across the 57 GHz oxygen band, the Defense Meteorological Satellite Program (DMSP) Microwave Temperature Sounder (SSM/T/1) and the DMSP Microwave Water Vapor Profiler (SSM/T/ 2) with channels at 118 GHz and across the 183 GHz absorption line of water vapor, and the more recent Advanced Microwave Sounding Units A and B (AMSU-A and AMSU-B). Although this section addresses soundings from the perspective of polar orbiters, the same observations apply to instruments in geosynchronous Earth orbit (GEO). For example, the GEO instruments (including Polar-orbiting Operational Environmental Satellites, POES) have in general lacked the precise characterization capability and stability necessary for later reconstruction of long-term climate data sets. Additionally, the sheer volume of GEO data has created difficulties for scientists who wish to access the data for postprocessing. Finally, because specific sectors of the globe are monitored for largely national missions, national interests come into play when decisions

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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN regarding sharing of data arise. Nevertheless, data from GEO sources, with their unique simultaneous “full-disk” observations of the planet, should be considered a part of the overall strategy for monitoring climate variation. Such data can be used to cross-calibrate POES data and fill in the gaps in the typical POES swath. OBSERVING STRATEGIES Temperature and moisture profiling relies on spectral measurements of radiation emitted by absorbing gases in the atmosphere. If the distribution and absorption of a gas are known, as they are for the uniformly mixed gases of CO2 and O2, then the detected emission is proportional to the temperature of that volume of gas. For other gases such as H2O that are not uniformly mixed, the emission depends on both temperature and the concentration of the gas itself. Therefore, profiling water vapor requires having simultaneous data on temperature, a requirement that complicates the process. The strength of the absorption by the gas more or less determines the levels at which the emission occurs and provides a way of profiling information as a function of height. Emission in strongly absorbed regions occurs higher in the atmosphere than does emission at weakly absorbed wavelengths. This property is characterized by the contribution, or weighting, function. The shape of the weighting function, important because it essentially defines the vertical resolution of the sounding measurements, depends on a number of factors. There are two primary factors: (1) vertical distribution of the absorbing gas—or, stated differently, the scale height of the atmosphere, which establishes the upper limit to the resolution, which is approximately 1 km, and (2) spectral resolution of the measurement, which also affects the vertical resolution. An instrument that effectively averages over many wavelengths smears out the individual weighting functions of each wavelength, producing a more broadened function and reducing the resolution. Increasing spectral resolution will increase vertical resolution, but only to the point of the upper limit. An unavoidable consequence of the broad nature of the weighting functions is that a function at one (spectral) channel significantly overlaps the functions associated with adjacent (spectral) channels. This overlapping property is the source of the two most significant problems in sounding retrievals: (1) the measurements are not entirely independent, leading to inverse solutions that are not unique, and (2) the inversions are unstable, with small errors (measurement and other) producing large changes to the solutions. Sounding Product Issues For the reasons mentioned above, limiting solutions to some a priori or initial guess is a necessary step in obtaining meaningful profiles of temperature and moisture. This constraint arises from some profile information obtained from a climatological database of one sort or another. Errors introduced by these limitations are not a major concern if it is known that initial estimates do not propagate into the final retrieval. For characterizing climate and especially for monitoring change, it is thus critical to establish the extent to which any retrieved quantity relies on an initial estimate, which is usually derived from an unreliable climatological database. If the analysis of any properties is too dependent on such information, it will not provide proper measures of evolving climate change. Unfortunately, water vapor information obtained from current sounders relies heavily on a priori data (Engelen and Stephens, 1998). It is not obvious that the water vapor information derived from the new sounders being developed for use on NPOESS and other future platforms will alter this situation. Another important factor in the retrieval of moisture soundings concerns the accuracy of the forward model used to simulate the measured spectral radiances. The major source of error in water vapor retrievals does not stem from radiance calibration errors but rather from errors of the forward model. These errors remain large, and efforts are now under way to establish some understanding of their nature. Radiance Data Product Issues Operational sounders have provided continuous, quasi-global data since the late 1970s with the launch of the first version of the TIROS Operational Vertical Sounder (TOVS). Radiance data from multiple versions of the TOVS flown on a series of National Oceanic and Atmospheric Administration (NOAA) polar-orbiting spacecraft

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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN have been combined to produce radiance climatological databases, or climatologies. Two examples of these radiance climatologies are found in the work of Spencer and Christy (1992) and Bates et al. (1996). These studies pointed to a number of common issues that arise when combining data from different satellites to produce a climatology: To establish the precision of the long time series of radiance data required for identifying trends in data records, it will be necessary to identify and remove biases that arise from (a) incomplete or changing sampling practices throughout the data record, (b) changes in instrument orientation (drifts), and (c) measurement differences between different versions of the same instrument. Sufficient overlap in the measurement obtained with different versions of a given instrument can be used to determine the magnitude of measurement differences and thereby to remove biases in the data. An approach often used to assess the likely magnitude of resulting errors that arise from effects of diurnal aliasing is to sample data from geostationary satellites (e.g., Salby and Callaghan, 1997). In addition to the problem of temporal sampling, the NOAA spacecraft that carry the TOVS are placed in a nominal Sun-synchronous orbit. Unfortunately, these orbits drift at a disturbing rate. Orbital drifts and decays create spurious trends in the data (e.g., Wentz and Schabel, 1998). In addition to drifts, there have been periods of time since 1981 when data from only one satellite were available, which is a further source of bias associated with inadequate sampling of the diurnal cycle. Both Bates et al. (1996) and Christy et al. (1995) introduced procedures to account for biases that arise from intersatellite sensor differences. To determine the accuracy of radiance data over a protracted period of time, a comparison of multiple measurements is essential. Reliance on prelaunch calibration is questionable, given the usual changes in instrument responsivities in orbit. The method of vicarious calibration, such as that used routinely to calibrate geostationary water vapor channels (e.g., Van de Berg et al., 1995), is required in addition to on-orbit calibration. Difficulties in vicarious calibration of water vapor channels arise through the lack of accuracy of radiosonde data on upper tropospheric water vapor. This data inaccuracy limits the ability to match measured and simulated radiances. Christy et al. (1995) provided an example of a vicarious calibration approach that they used to assess the precision of the MSU radiances. They compared MSU temperature variations simulated from radiosonde data with actual measured temperatures. Radiance data ultimately require some form of interpretation relative to more conventional climate parameters. Much of the controversy associated with analyses of radiance trends has to do with the interpretation of the data. EVOLUTION STRATEGY At the time of the Global Weather Experiment in 1979, it was hoped that the use of satellite-derived temperature and moisture profiles would extend the range of useful synoptic-scale forecasts beyond a few days to a week or more. Although NWP systems have improved over the last decade, it has become increasingly difficult to demonstrate that temperature profiles retrieved from satellite sounding data have a consistent positive impact on Northern Hemisphere forecasts (e.g., Eyre et al., 1992; Smith, 1991). This difficulty has led to the belated recognition that the information content of temperature data obtained from current sounders is low, relative to temperature “knowledge” already contained in NWP systems. It is argued that low information content and thus minimal impact on forecasts result from the poor vertical resolution of the data. The next-generation satellite sounders, beginning with the Atmospheric Infrared Sounder (AIRS) on NASA's Earth Observing System Afternoon Satellite (EOS PM), are expected to provide information at higher vertical resolution and thus presumably have a more positive influence on forecasts. Evolution to Higher Spectral Resolution There are a number of reasons to move toward increased spectral resolution in sounders: (1) improvements in the signal-to-noise ratio can be realized by averaging channels with the same characteristic absorption; (2) clearer

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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN discrimination of thin clouds is possible using more highly resolved line absorption information; and (3) spectral measurements enhance the capability of providing other nonsounding information, for example, about clouds and particle sizes. Given these advantages, however, sounding information content does not increase proportionally with increasing spectral resolution. Within the context of AIRS measurements of temperature, analyses of the significance of the information (e.g., Twomey, 1996; Rodgers, 1996) revealed that the AIRS spectra contained about 14 pieces of independent information on vertical temperature profiles, which translates roughly to the 1 km vertical resolution limit noted previously. Therefore, it is legitimate to ask which channels of a high-resolution instrument such as AIRS or the Cross-track Infrared Sounder (CrIS) optimally contribute to retrieved soundings, which channels are redundant, and what is to be gained by combining a number of redundant channels (Rodgers, 1996). Evolution to Assimilation of Radiance Data As an understanding of the true information content of sounding data emerged in the 1990s, alternate approaches were developed to account for it and for the error characteristics of the data. These methods are based on the assimilation of the radiance data into the NWP system, which could weight the information more appropriately based on the proper error characteristics of the data (Eyre and Lorenc, 1989). Assimilation of radiance data has produced a clear, positive impact on NWP. For example, McNally and Vesperini (1996) showed how assimilating TOVS radiance data in the European Center for Medium-Range Weather Forecasts significantly improves the analysis of many aspects of the hydrological cycle, leading to better forecasts. CHALLENGES AHEAD In the near future, new, more highly resolved spectral measurements promise to improve researchers' ability to profile temperature in the atmosphere and to improve the present inadequate techniques for profiling water vapor. How the sounding data contribute to observing and understanding Earth's climate will depend in part on whether current instrumentation can meet the EDR requirements (see Table 2.1) for the vertical resolution proposed for water vapor. Traditionally, sounding data have delivered profiles of temperature and moisture for use in numerical weather prediction. These sounding data products have direct and obvious climatological value. However, radiance assimilation at operational prediction centers no longer carries out explicit retrievals in the traditional sense. These sounding products are now derived as outputs from NWP models. Whether the optimal use of new-generation, higher-spectral-resolution sounding data will continue the present trend of using radiance data directly is still an open issue. Nevertheless, the value of carefully calibrated radiance data not only for assimilation purposes, but also as a resource for climate data, clearly emerges from all current studies. REFERENCES Bates, J.J., X. Wu, and D.L. Jackson. 1996. Interannual variability of upper-tropospheric water vapor band brightness temperature. J. Climate 9: 427-438. Christy, J.R., R.W. Spencer, and R.T. McNider. 1995. Reducing noise in the MSU daily lower-tropospheric global temperature data set. J. Climate 8: 888-896. Engelen, R., and G.L. Stephens. 1998. Characterization of water vapour from TOVS/HIRS and SSMT-2 measurements . Q.J.R. Meteorol. Soc. 125: 331-351. Eyre, J.R., and A. Lorenc. 1989. Direct use of satellite sounding radiances in numerical weather prediction . Meteorol. Mag. 118: 3-16. Eyre, J.R., E. Andersson, and A.P. McNally. 1992. Direct use of satellite sounding radiances in numerical weather prediction . NATO ASI Series 9: 365-380. Houghton, J.T, F.W. Taylor, and C.D. Rodgers. 1984. Remote Sounding of Atmospheres. New York: Cambridge University Press. Kaplan, L.D. 1959. Inferences of atmospheric structures from satellite radiance measurements . J. Opt. Soc. Am. 49: 1004. King, J.I.F. 1958. The radiative heat transfer of planet Earth. Scientific Uses of Earth Satellites, 2nd revised Ed. Ann Arbor: University of Michigan Press. McNally, A.P., and M. Vesperini. 1996. Variational analysis of humidity information from TOVS. Q.J.R. Meteorol. Soc. 122: 1521-1544.

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ISSUES IN THE INTEGRATION OF RESEARCH AND OPERATIONAL SATELLITE SYSTEMS FOR CLIMATE RESEARCH: I. SCIENCE AND DESIGN National Oceanic and Atmospheric Administration (NOAA). 1997. Climate Measurement Requirements for the National Polar-orbiting Operational Environmental Satellite System (NPOESS): Workshop Report, Herbert Jacobowitz (ed.), Office of Research Applications, NESDIS-NOAA, February. 77 pp. Rodgers, C.D. 1976. Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation. Rev. Geophys. Space Phys. 14: 609-624. Rodgers, C.D. 1996. Information content and optimization of high spectral resolution measurements. SPIE 2830: 136-147. Salby, M., and P. Callaghan. 1997. Sampling error in climate properties derived from satellite measurements: consequences of undersampled diurnal variability. J. Climate 10: 18-36. Smith, W.L. 1968. An improved method for calculating tropospheric temperature and moisture from satellite radiometer measurements. Mon. Weather Rev. 96: 387-396. Smith, W.L. 1991. Atmospheric sounding from satellites. Q.J.R. Meteorol. Soc. 117. Spencer, R., and J. Christy. 1992. Precision and radiosonde validation of satellite grid point temperature anomalies, Part I: MSU channel 2. J. Climate 5: 847-857. Twomey, S. 1996. Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements. New York: Dover. Van de Berg, L.C.L., J. Schmetz, and J. Whitlock. 1995. On the calibration of the Meteosat water vapor channel. J. Geophys. Res. 100: 21069-21076. Wentz, F., and M. Schabel. 1998. Effects of orbital decay on satellite derived lower tropospheric temperature trends. Nature 394(6694): 661-664.