C 55. /3/a • ^ ss ~^ 7 NOAA Technical Memorandum NESS 57 ^ATES O* * NIMBUS- 5 SOUNDER DATA PROCESSING SYSTEM PART I: Measurement Characteristics and Data Reduction Procedures W. L. Smith H. M. Woolf P. G. Abel C. M. Hayden M. Chalfant N. Grody Washington, D.C. June 1974 noaa NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION / National Environmental Satellite Service -K NOAA TECHNICAL MEMORANDA National Environmental Satellite Service Series The National Environmental Satellite Service (NESS) is responsible for the establishment and opera- tion of the National Operational Meteorological Satellite System and of the environmental satellite systems of NOAA. The three principal offices of NESS are Operations, Systems Engineering, and Research. NQAA Technical Memoranda NESS series facilitate rapid distribution of material that may be prelim- inary |n nature and may be published formally elsewhere at a later date. Publications 1 through 20 and 22 through 25 are in the former series, ESSA Technical Memoranda, National Environmental Satellite Center Technical Memoranda (NESCTM) . The current series, NOAA Technical Memoranda, National Environ- mental Satellite Service (NESS), includes 21, 26, and subsequent issuances. Publications listed below are available from the National Technical Information Service, U.S. De- partment of Commerce, Sills Bldg., 5285 Port Royal Road, Springfield, Va. 22151. Price: $3.00 paper copy; $1.45 microfiche. Order by accession number, when given, in parentheses. ESSA Technical Memoranda NESCTM 18 On the Statistical Relation Between Geopotential Height and Temperature-Pressure Profiles. W. L. Smith and S. Fritz, November 1969. (PB-189-276) NESCTM 19 Applications of Environmental Satellite Data to Oceanography and Hydrology. E. Paul McClain, January 1970. (PB-190-652) NESCTM 20 Mapping of Geostationary Satellite Pictures--An Operational Experiment. R. C. Doolittle, C. L. Bristor, and L. Lauritson, March 1970. (PB-191-189) NESCTM 22 Publications and Final Reports on Contracts and Grants, 1969--NESC. January 1970. (PB-190- 632) NESCTM 2 3 Estimating Mean Relative Humidity From the Surface to 500 Millibars by Use of Satellite Pic- tures. Frank J. Smigielski and Lee M. Mace, March 1970. (PB-191-741) NESCTM 24 Operational Brightness Normalization of ATS-1 Cloud Pictures. V. R. Taylor, August 1970. (PB-194-638) NESCTM 25 Aircraft Microwave Measurements of the Arctic Ice Pack. Alan E. Strong and Michael H. Flem- ing, August 1970. (PB-194-588) NOAA Technical Memoranda NESS 21 Geostationary Satellite Position and Attitude Determination Using Picture Landmarks. William J. Dambeck, August 1972. (COM-72-10916) NESS 26 Potential of Satellite Microwave Sensing for Hydrology and Oceanography Measurements. John C. Alishouse, Donald R. Baker, E. Paul McClain, and Harold W. Yates, March 1971. (C0M-71- 00544) NESS 27 A Review of Passive Microwave Remote Sensing. James J. Whalen, March 1971. (COM-72-10546) NESS 28 Calculation of Clear-Column Radiances Using Airborne Infrared Temperature Profile Radiometer Measurements Over Partly Cloudy Areas. William L. Smith, March 1971. (COM-71-00556) NESS 29 The Operational Processing of Solar Proton Monitor and Flat Plate Radiometer Data. Henry L. Phillips and Louis Rubin, May 1972. (COM-72-10719) NESS 30 Limits on the Accuracy of Infrared Radiation Measurements of Sea-Surface Temperature From a Satellite. Charles Braun, December 1971. (COM-72-10898) NESS 31 Publications and Final Reports on Contracts and Grants, 1970--NESS. December 1971. (COM-72-10303) NESS 32 On Reference Levels for Determining Height Profiles From Satellite-Measured Temperature Pro- files. Christopher M. Hayden, December 1971. (COM-72-50393) (Continued on inside back cover) NOAA Technical Memorandum NESS 57 NIMBUS- 5 SOUNDER DATA PROCESSING SYSTEM PART I: Measurement Characteristics and Data Reduction Procedures W. L. Smith H. M. Woolf P. G. Abel C. M. Hayden M. Chalfant N. Grody Washington, D.C. June 1974 Final report under NASA Contract No. S- 70249- AG t r UNITED STATES DEPARTMENT OF COMMERCE Frederick B. Dent, Secretary NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION Robert M White, Administrator National Environmental Satellite Service David S. Johnson, Director r "«fNT Ctf This memorandum was originally prepared for the GARP Project Office, National Aero- nautics and Space Administration, Goddard Space Flight Center, under Contract No. S-70249-AG. Mention of a commercial company or product does not constitute an endorsement by the NOAA National Environmental Satellite Service. Use for publicity or advertising purposes of infor- mation from this publication concerning propri- etary products or the tests of such products is not authorized. 11 TABLE OF CONTENTS Acknowledgements v 1.0 Introduction 1 2.0 The Observational Characteristics of the Nimbus-5 Sounding Experiments 2 2.1 ITPR 2 2.1.1 Experiment Description 2 2.1.2 Calibration Procedure 5 2.2 NEMS 9 2.2.1 Experiment Description 9 2.2.2 Calibration Procedure 11 2.3 SCR 12 2.3.1 Experiment Description 12 2.3.2 Calibration Procedure 13 2.4 THIR 18 2.4.1 Experiment Description 18 2.4.2 Calibration Procedure 18 3.0 Atmospheric Transmission Functions 19 3.1 ITPR 19 3.1.1 Carbon Dioxide and Water Vapor Channels 19 3.1.2 3.7 \m and 11 ym Window Channels 19 3.2 NEMS 20 3.3 SCR 20 3.4 Empirical Adjustments to Transmission Functions 25 3.4.1 General 25 3.4.2 The ITPR Q-Branch Channel 31 4.0 Determination of Sounding Radiances 35 4.1 Surface Temperature and Clear-Column Radiance Computation Methods 35 4.1.1 Preliminary Data Processing 35 4.1.1.1 Angular Correction Model for ITPR Radiance Measurements ... 35 in 4.1.1.2 Modelling of Reflected Solar Radiation for ITPR Channel 1. . .36 4.1.2 Basic Equations i+l 4.1.3 Surface Temperature Guess Generation ,44 4.1.4 Surface Reflectivity, Surface Temperature, and Clear- Column Radiance Retrieval (From Sounder Data) Equations. . . . 44 4.1.5 Filtering Observation Pairs Having Different Cloud Properties 48 4.1.6 Detecting Clear and Overcast Air Columns . . . .' 49 4.2 Computational Procedure for Nimbus-5 ITPR Data 51 4.2.1 Definition of Grid Values of T(p s ), r s (W s ), and e s (W s ) . . . .51 4.2.2 Definition of Spatial Radiance Sets for Clear-Column Radiance Computations 52 4.2.3 Specification of ITPR Sub-Grid Values of T(p s ), r s (W s ), and e s (W s ) 52 4.2.4 Computation of Surface Temperature and Clear-Column Radiance for ITPR Sub-Grid 55 4.3 Construction of Stratospheric Difference Channels for SCR 57 4.4 Sampling of NEMS Observations 57 5.0 Retrieval Methods 58 5.1 Temperature Profile 58 5.1.1 Inversion Algorithm 58 5.1.2 First Guess 60 5.1.3 Terrain Effects. 61 5.1.4 Solutions for "Non-Clear Column Radiance" Conditions 62 5.1.5 Channel Combinations 62 5.1.6 Consistency Checks 63 5.1.7 ITPR Sub-Grid 64 5.2 Atmospheric Water Substance 65 5.2.1 From ITPR 65 5.2.2 From NEMS 66 5.3 Cloud Height Distribution 68 5.3.1 Theory 68 5.3.2 Computational Procedure 69 5.4 Total Outgoing Long-Wave Flux 70 6.0 Objective Analysis 72 6.1 Introduction 72 IV 6.2 Numerical Techniques 72 6.2.1 Neighboring Report Discrimination 72 6.2.2 Weighting Factor Determination 73 6.2.3 Report Quality Control 74 6.2.4 Gridpoint Correction 75 6.3 Computer Programs j 75 7.0 Appendix 82 | 7.1 Regression Data Base [82 7.2 System Data Flow 84 References 98 ACKNOWLEDGEMENTS The processing system described in this report was developed with the close cooperation of the NEMS and SCR experimenters. We wish to express our appreciation to Drs. D. Staelin and J. T. Houghton and their collegues at the M.I.T. and Oxford Universities, respectively, for their continual support during the development of the Nimbus- 5 data processing system. The assistance provided by the Meteorological Data Handling Center and the Technical Control Center of the Nimbus project is also greatly appreciated. Messrs. P. Gary, W. Holmes, and K. Iobst were responsible for converting the NESS-developed C.D.C. computer software, required to implement the algorithms described in this report, to run on the NASA GISS IBM 360 for D.S.T. application. Finally, but most important, we thank all the members of the Radiation Branch of NESS for their con- tributions to the development, debugging, and analysis of the results of this processing system. In particular we thank Messrs. H. Howell, L. Mannello, P. Pellegrino, R. Ryan, F. Nagle, G. Callan, W. Jacob, C. Jacobson and W. Shen for their invaluable assistance in these aspects of the system development. Our thanks to Mr. L. Mannello for editing and to Mrs. M. Schwier for typing this highly technical manuscript. Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/nimbus5sounderda00smit 1.0 Introduction Part I of this report describes the data processing system devel- oped to obtain various meteorological variables from infrared and microwave radiometric data obtained from the Nimbus- 5 spacecraft. The meteorological parameters deduced from the radiance data include: (a) surface temperature, (b) vertical temperature profile, (c) precip- itable water content, (d) total outgoing long-wave radiation flux, and (e) vertical cloud distribution. The data system enables the derivations to be made on a global basis independent of contemporary conventional data. Determinations are made with horizontal resolutions of 500 km and 150 km to satisfy the requirements for the large scale numerical forecast experiments and the fine-scale weather analysis- forecast studies being conducted as part of the Global Atmospheric Research Program (GARP). Part II of this report presents the signi- ficant results obtained from the Nimbus- 5 data processing system. The design of the sounding data processing system was completed prior to the launch of Nimbus-5 (December 11, 1972). Since the launch the processing system has undergone continual refinement to improve the accuracy of the meteorological determinations as well as to cope with unexpected pecularities of the Nimbus-5 radiance data (e.g., the erratic scan behavior of the ITPR, the spectral leaks of the SCR channels, and the incompatabilities of NEMS and ITPR data caused by their differences in spatial resolution). At the time of this writing, however, most of the goals of the Nimbus-5 data processing system have been met or exceeded. Only minor alterations and additions are needed to apply the data processing system to Nimbus-F for the quasi-real time generation of global data sets as part of the Data Systems Test (DST) The Nimbus amalgamated sounding data processing system employs the most complete, from a physics point of view, meteorological data retrieval algorithms utilized to date. For example, in the derivation of vertical temperature profiles, the effects of cloudiness, terrain elevation, surface reflectance-emittance properties, and small-scale surface temperature inhomogeneities are taken into account. Also, the retrieval methods developed do not utilize contemporary conventional data, so that the determinations are independent and their accuracy is not biased by the conventional data network. (It is felt that the satellite sounding data to be utilized in the global experiment should have as little geographical bias as possible.) The retrieval system is flexible In that it automatically operates with any combinations of infrared and microwave observations available to obtain the best possible result. 2.0 The Observational Characteristics of the Nimbus-5 Sounding Experiments The data processing system utilizes various data from four different radiometric experiments aboard Nimbus-5: the Infrared Temperature Profile Radiometer (ITPR), the Nimbus-E Microwave Spectrometer (NEMS), the Selec- tive Chopper Radiometer (SCR) and the Temperature Humidity Infrared Radiometer (THIR). As will be shown, certain data from each of these experiments provides a unique contribution to the final result. Since the engineering details of these experiments are given in the Nimbus-5 User's Guide (1972), only observational characteristics need be pre- sented here. 2.1 ITPR 2.1.1 Experiment Description The Nimbus-5 ITPR measures radiation in seven different spectral intervals. Two of the spectral intervals are in the window regions at 3.7 urn and 11 ym for the purpose of detecting clouds and obtaining surface temperatures even when a partial cloud cover exists in the instrument's field of view. There are four atmospheric tempera- ture profiling channels in the 15~"um CO2 band and a single water vapor channel at 20 ym in the rotational water vapor absorption band. The vertical weighting functions for the 4 CO2 channels are shown in figure 2-1. The instrument has a linear spatial resolution of 35 km and spatially scans in order to circumvent clouds and to obtain uniform earth coverage. Figure 2-2 illustrates the ITPR scan geometry, as well as that for NEMS and SCR which will be discussed later. As shown, the ITPR samples 140 contiguous scan elements within three different grids, one to the right, one at the center, and one to the left of the sub-satellite track as the satellite moves along its orbit. One novel feature of the ITPR is the simultaneous measurement of the radiances in the 3.7-ym and 11- ym window regions which enables the detection of clouds within the instrument's field of view and the estimation of surface temperatures under partly cloudy sky conditions. Since molecular absorption is small in the 3.7 _ ym and 11-ym window regions, these ITPR window channels sense only the radia- tion from the earth's surface and any clouds within the instrument's field of view. When sensing a uniform and opaque scene (e.g., the earth's surface) they observe the same brightness temperatures. When sensing a non-uniform scene (e.g., broken clouds), different brightness temperatures are observed in the two window channels. This is because of the vastly different radiance dependence upon scene temperature for the two different wavelengths, a phenomenon described by Planck's law. At 11 ym, the radiance is approximately proportional to 0.1 0.3 0.5 0.7 1.0 3 - _Q 5 _E 7 3 10 v> «/> V 30 50 70 100 300 500 700 1000 Fig. 2 - 1 0.3 0.4 cJt /dlnp 0.6 0.7 c u ® c o (/> m < o aHh~™rl K| m o c/> CO Q. CN CN CD the fifth power of temperature whereas at 3.7-ym, the radiance is approximately proportional to the fifteenth power of temperature. Consequently, when looking at a scene composed of targets of different temperature, the 3.7-ym radiance will have a much larger relative contribution from the higher temperature target than will the 11-ym radiance. As a consequence, the 3.7-ym channel senses a higher brightness temperature than the 11-ym channel when the instrument's field of view is composed of a non-uniform temperature scene. Figure 2-3 gives black and white pictures created from the ITPR brightness temperature window channel data obtained in two different scan grids. The first scan grid (figure 2- 3a) was observed over the South Pacific Ocean. The images of both the 11-ym and 3.7-ym window channel data clearly reveal the clouds (colder and lighter regions) within the scan grid. The cloud features, especially the high cloud band, are even more clearly depicted in the pictorial image of the brightness temperature differences for the two window channels. The light regions correspond to the large window channel differences observed in cloudy fields of view and the dark regions to observations of the opaque ocean surface. The second grid (figure 2- 3b) was observed just two minutes later over the northeast coast of Australia. In this case, both window channels sense the cold (light) land surface in contrast to the slightly warmer ocean surface. It is evident from the window channel difference image that this feature is a surface coastline and not a cloud edge, since the window channel differences are small and their image is uncorrelated with either of the window channel images. These examples illustrate how simultaneous measurements in the 3.7~ym and ll _ ym window channels can be used to detect the existence of clouds within the instrument's field of view unambiguously from a temperature contrast caused by a change in surface characteristics . 2.1.2 Calibration Procedure At the end of each scan grid, the ITPR automatically views a reference blackbody target, which is nominally at 24°C, and space to provide the digital output to radiance calibration. The calibration is linear so that B (v n * Trm) r -i R < v i> = T T f T 3 t t \ V (v i } " V s C^i) > V BB (vj_) - V s (V£) L x s i j » where R (v-[) is the radiance, for channel vj_, corresponding to the out- put, V(v-j_), the subscripts BB and S refer to blackbody and space values, respectively, and B (v* T BB ) is the Planck radiance corresponding to the blackbody temperature Tgg. (1) CM fs O CN _Q E a> 0) Q CO CO CN "** c Li.' CS CN .— CN o '-O <<* ~ O ,_ u o ~D uu LU o o CO 6 v> V "> CO " 3 O *~~ u CN U CO CN — CN CN r- u CN E o i* , IV _C O U I CO O CO JC U cr E CO JC U 00 _ r < oo CN _C E O O U CO o CO u CO CO WO o IS E E io CO CN Table 2-1 gives a listing of -the ITPR data, for each channel, obtained during a sample calibration sequence. The three columns for each channel are the raw digital counts, the calibrated radiances (mw/m^ - sr - cm"-'-) and the equivalent blackbody temperatures (°K). As shown during the housing calibration, the instrument's out- put is exceptionally stable. However, a peculiarity, which has been noticed throughout the duration of the experiment exists in the space observations. In several channels (e.g. 1, 2, 3, and 7) there is a significant radiance signal when the scan mirror is in the space view position. This signal is diagnosed from the fact that the signal ob- served as the scan mirror moves out of this position towards earth Is lower (a higher digital count value for sample 34) than is observed in the space position. It appears that channels 1, 2, 3, and 7 are the most significantly affected. These channels are at the top of the optical unit. It thus appears reasonable to assume that some material is hanging down from the spacecraft which partially obstructs the fields of view of the upper telescopes when viewing space. Since channels 1 and 2 occupy the same telescope (i.e., have exactly the same field of view), it is possible to deter- mine from their "space" signals the temperature of the radiating material and percentage of the field of view being obstructed. Assuming the obstructing material is a blackbody, the radiance measured in the space position is given by R(v) = a B (v,T) (2) where a is the fractional field of view obstruction and B (v,T) is the Planck radiance. Since channels 1 and 2 occupy the same telescope it follows that R(l) RT2T B(1,T) B(2,T) (3) since a is the same for the two channels. It follows from (1) that 1(1, T) 1(2, T) B(1,T BB ) B(2,T BB ) V BB (2) - V S (2) VbbCD - v s (i)_ V(l) - v s (i) _V(2) - v s (2)_ (4) where Vg is the true space signal. 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It can be seen from figure 2-4 that the temperature of the obstruction is 29°C. It follows from (2) that the percentage obstruction a = R(2) B(2,29°C) 112.6 121.4 741-765 155-765 = 3.6% (6) Since portions of the spacecraft are also at 29°C, the calculated values support the assumption that part of the spacecraft (or an attached cable or piece of insulation) is probably contaminating the ITPR's space view. As a result, the instrument output signal obtained In sample 34 as the instrument's scan mirror sweeps down toward earth was assumed to be the "true" space signal and used to calibrate the ITPR data. 2.2 NEMS 2.2.1 Experiment Description The NEMS experiment was developed primarily to sense the atmospheric temperature profile even through clouds. This is accom- plished by detecting the thermal radiation at three frequencies around the 60 GHz oxygen resonance. Simultaneous measurement of the radiation (brightness temperature) is accomplished using three separate microwave radiometer receivers, each having its own antenna and calibration net- work. To obtain a set of nearly independent radiation measure- ments, the frequencies of 53.65, 54.90 and 58.80 GHz were chosen, resulting in a set of weighting functions which peak at approximately 650, 250 and 80 mb, respectively (figure 2-1). By linearly combining the radiation measurements of these frequencies, the vertical temperature profile is constructed. As shown in figure 2- 2 , the instrument has a horizontal spatial resolution of 100 n. mi. Although clouds are generally present within the field of view, the oxygen channels are generally insensitive to the clouds. Clouds do not alter the 54. 90- and 58. 80- GHz brightness temperatures and only infrequently affect the lower-peaking channel at 53.65 GHz, where a maximum attenuation of 3°K has been observed. This result correlates with theoretical considerations, which show less than a 3°K attenuation by a nimbostratus type cloud having 0.10 S/cm2 of liquid water. Clouds having larger liquid water content generally do not fill the entire 100 n. mi. field of view so that their effects are smaller. o ^t 00 CO o CO ^ CO CM CO u o 0) k. o 3 CO o L. The D channels are all sensitive to sunlight. During daytime calibrations, sunlight is usually scattered into the detector optics, rendering such calibrations useless. On these channels, there- fore, only calibrations performed in the earth's umbra are accepted. is A further problem has been the (infrequent) inci- dence of "moonshine" into the space viewing part. This occurs every month and invalidates the calibration involved over a period of about 2 days. This problem has been overcome by rejecting all space view signals which fall outside pre-set limits. 2.4 THIR 2.4.1 Experiment Description The THIR is a high resolution scanning radiometer with two channels, one in the 10.5- to 12.5-um (11.5 urn) window region, the other in the 6.5- to 7.0-ym (6.7 ym) water vapor band. In the Nimbus- 5 sounding data processing system, only the 11.5-ym window measurements are utilized. The radiometer consists of an optical system (com- prising a scan mirror, a telescope, and a dichroic beam-splitter) and an electronics module. Incoming radiant energy is detected by means of germanium-immersed thermistor bolometers. The instrument's field of view and scan geometry are such that essentially full coverage of the earth is obtained. However, in order to simplify the THIR data handling, the sounding data processing system does not make use of the full resolution THIR observations. The THIR swath is divided into six segments, containing equal numbers of earth views. In each segment, the lowest voltage (corresponding to the highest scene brightness temperature) is extracted from the observations in two swaths. Statistical filtering is applied to pre- vent the inclusion of noise spikes. This processing is done at NASA; the sampled data is then relayed to the sounding data processing center along with the VIP data for the same orbits. 2.4.2 Calibration Procedure The THIR detectors view, in sequence, the in-flight blackbody calibration target (part of the housing), outer space, earth, space, and again the calibration target. The space and housing views are used in the in-flight calibration of the data, along with the housing temperature, which is monitored by thermistors and telemetered to the ground stations. The THIR output signals are converted to scene radiances using the in-flight calibration data in an identical fashion as the ITPR calibration discussed earlier. 19 3.0 Atmospheric Transmission Functions 3.1 ITPR 3.1.1 C0 2 and H 2 Channels Due to the excessive computer time required for "exact" computations by spectral integration of atmospheric trans- mission in the infrared; simplified band models were developed which permitted rapid computations for the ITPR spectral intervals. The details of these models are given by Davis (1972). Briefly, analy- tical representations of the atmospheric transmittance for the ITPR channels in select spectral intervals of the rotational band of water vapor and the 15 urn band of carbon dioxide were designed in terms of universal functions of absorber amount, pressure and temperature. Spectral averages of theoretical homogeneous - path transmittances , available by line-computations by R. Drayson (University of Michigan) and H. Bolle (University of Munich) were used as input data. Appro- priate coefficients for converting actual non-homogeneous optical paths into equivalent homogeneous paths were derived concurrently with the parameters of each analytical representation. The derived analytical formula and coefficients for computing the atmospheric transmission for the ITPR PUO and C0 2 channels are also given by Davis (1972) and thus need not be repeated here. 3.1.2 Window Channels (3.7 ym and 11 ym) The transmission functions for the 3.7-ym and 11-ym window channel regions are assumed to have the following generally accepted exponential forms (McClatchey, 1970): for the 11 ym window channel; T Total = T H 2 0, Lines * T H 2 Cont., and for the 3.7-ym window channel; T Total = T H 2 0, Lines ■ T C0 2 Cont. • T N 2 Cont. • T H 2 Cont. In the above expressions, T H 2 Lines = exp | - ft - \ PW Ho j ' dP " " ? (14) T H 2 0Cont. =exp j- JL_ ^ PW? \™^ dP ( 15 ) 20 T C0 2 Cont. = exp - C, N 2 Cont, = exp - C n £fc)>H (16) (17) where g is the acceleration due to gravity, P is pressure (P = 1000 mb), W is water vapor mixing ratio. T is tenroerature (T = 273°K), and the mixing ratios of CCU and N 2 (C c and C ) are assumed to be constant. The constants used in these expressions are derived from McClatchey's data and given in the table below: Channel 8 K C c C n 3.7 um 11 um 0.035 0.05 6 10 0.33xl0 _1+ 0.28xl0 -4 Experimental vertification of the window channel transmission functions had been obtained at Jackass Flats, Nevada in November of 1972. The transmission measurements were conducted with a spacecraft prototype of the ITPR by viewing the sun as a function of air mass (solar zenith angle). As may be seen in figure 3-1, the adopted models yield transmission values which are generally within 1% of the observational data. 3.2 NEMS The atmospheric absorption of microwave radiation for clear atmospheric conditions is due to the molecular oxygen and water vapor constituents. Both absorption mechanisms have been treated by Van Vleck in 194-5 and comprise the basis for the NEMS transmission functions. The analytical expressions for the oxygen and water vapor transmission functions contained in the work of Barrett and Chung (1962) and Meeks and Lilley (1963) are employed in our calculations of those functions . 3.3 SCR This description of SCR transmittances is limited to the B channels, since the other channels were not considered in the joint ITPR/NEMS/SCR system. 1.0 U C O E CO C o 0.9 0.8 0.7 0.6 0.5 0.0L Jackass Flats, Nevada November 12, 1972 ITPR 11.0/im Transmission Model Observed 3.7fjLW Transmission Observed ll.O^tm Transmission ITPR 3.7 M m Transmission Model 1 i 12 3 4 5 6 Water Vapor Path Length (gm/cm 2 ) Fig. 3 - 1 22 In England, the SCR B channel transmittances were derived in two ways before launch of the satellite. These methods were (1) Use of the SCR unit as a detector in the measurement of transmission through a homogeneous path of CO2/N2 under laboratory conditions . The resulting homogeneous transmittances were extra- polated to the case of a vertical atmospheric path through the assumption of the Curtis-Godson approximation and a strong line absorp- tion model. (2) Calculation of vertical atmospheric and homogeneous transmittances by line-by-line integration across the spectrum. The process used experimental measurements of the infrared filter profile, and selected experimental data on the line parameters. It incorporated a mixed Doppler-Lorentz line shape and included the theoretical temperature dependence of the line strengths. It was intended that the calculation (2) should be corrected for imperfect knowledge of the magnitude of the line parameters employed (and hence of the absorption coefficient) by comparing the theoretical results with the experimental data (1). For example, if the homogeneous calculation gave a transmittance t (u) as a function of absorber amount given by x c (u) = exp (-K c u), (IB) then an absorption coefficient is defined by Kc = _1 In (t c ) . ( 19 ) u Similarly, an experimental absorption coefficient may be defined as Ke = _I In (r e ) (20) -m It was the intention to apply the correction factor a =1 -r— to all theoretically predicted absorption coefficients, which were then to be used as the basic method for deriving atmospheric transmittance curves. The bar in the expression for a indicates an RMS best fit in the sense that Q = I ( a Kc - Ke) 2 du (21) was minimized. 23 This approach was successfully employed for the SCR on Nimbus 4. The Nimbus 5 SCR B-channel transmittances derived from the two approaches, however, did not agree very well. The difference was interpreted as being due to errors in the measured profile of the multilayer filters, although it could also have been caused by imper- fect line parameter data Consequently, the measured filter shape was perturbed, by a process of successive approximation, such that the calculated transmittances agreed within 0.5% with those measured. The fact that all four B channels agree with calculations to this order of accuracy gives confidence in the approach, especially since it applies both to the homogeneous paths in the laboratory and to the transmittances of the CCU filter cells in the SCR unit. The joint ITPR/NEMS/SCR system does not employ the B channel radiances directly, since the corresponding weighting functions all overlap strongly with ITPR channel 6. Instead, the difference radiances B nm are employed, where B nm = A nm B n ~ ( A nm -D B m » B n , B m are the individual channel radiances (free of spectral leaks), and A nm is a weight composed of the cell transmittances x n and T m : A nm ~ T n/ ^n^m) (23) a If x n (P) is the combined atmospheric and CO2 cell transmitt- ance for channel n from a level at pressure p in the atmosphere, the difference radiances B nm is given by T nm (P) = (T n ^ p ) " ^ ^^ ^n " V (24) where the normalization is such that in the absence of atmospheric absorption, x^ m (P) = 1. The weighting functions derived at Oxford for Bj_2 and 6314 are shown in figure 3-2. They are labelled SCR 2 and SCR 1, and are respec- tively the highest and lowest difference weighting functions avail- able from the B channels. The intermediate difference channel, B23 was not used in the joint system. To establish confidence In the calculated functions, the weighting functions were calculated empirically from rocketsonde data. Two methods were used, the (6,y) approach and the radiance- temperature correlation approach. Both are described In section 3.4. Results from the two empirical approaches are shown in figure 3-2, and were derived from over 50 nearly simultaneous rocket/ satellite data sets. The criteria for near simultaneity were a lati- tude-longitude window of + 4 degrees and a time window of + 2 hours. -Q 5 E L. 10 D oo 0) 100 500- 1000 Weighting Function Fig. 3 - 2 25 The rocket temperature profiles were corrected for dynamical heating and other effects through a standard correction as a function of height. As a quality check on the data, measured radiances were plotted as a function of calculated radiances, where the calculated radiances were derived from the corrected rocket temperature and the current weighting function. Points which deviated from the best-fit straight line by more than a reasonable amount (judged by eye to be about 1.5 times the RMS of the main body of points) were removed from the sample. Weights were applied to the points remaining such that all measured radiances were approximately equally weighted in the final calculation. The empirically calculated functions of figure 3-2 agree well for the SCR 1 channel. Both prefer a slight lowering of the weighting function, with little change in shape. The (3,y) approach is very limited as far as shape changes are concerned, since such changes are contained in the single variable y. This is to be con- trasted with the correlation approach in which the shape changes contain many more independent variables. This difference between the two methods is illustrated in the results for the SCR 2 channel. The (3,y) approach prefers a lowered weighting function of similar shape to the original. The correlation approach prefers substantial change of shape with a smaller downward movement of the peak of the weighting function. Another reason for differences between the two approaches is the different sensitivity to noise in the measurements of radiance and of atmospheric temperature. This may account for a substantial part of the behavior of the solutions for SCR 2, since the noise level of the SCR 2 radiances is about twice that of SCR 1, and the rocket-measured temperature profile needs substantial correction above the 1-mb level. To establish which of the SCR 1, SCR 2 weighting functions are more appro- priate requires their comparison under operational conditions over time periods of at least several weeks. This has been done for the original as well as the (3,y) solutions, and the results are presented later in this report. 3.M- Empirical Adjustments to Transmittance Functions 3.4.1 General As a part of the Nimbus-5 data processing, "coincident" radiosonde and satellite observations have been collected and stored on a history tape. The matched observations serve not only to evaluate temperature determinations but also to obtain estimates of instrumental bias error and empirical transmission function adjustment factors, at least for the more transparent channels. Unfortunately, the limited altitude of radiosonde soundings precludes the use of the history tape 26 to determine adjustments to the more opaque channels '(e.g. SCR-1, SCR- 2, ITPR-5, ITPR-6, and NEMS-3). However, for these channels a limited sample of coincident radiosonde-rocketsonde and satellite observations has been obtained with the cooperation of the National Weather Service and Cooperative Meteorological Rocket Network. In order to determine empirical adjustments of theory, it is assumed that the true transmittance function t is given by x = x Y (25) where x is the theoretically estimated function, and y is an empirically derived constant. Furthermore, the true radiance is assumed to be given by R = R m - 3 (26) where P^ is the measured radiance with bias error 3. (The bias error 3 is presumed to exist because of uncertainties in the on-board calibration sources.) It follows that Rm = R (Y) + 3 (27) where R (y) is the radiance calculated with the true value of y. To solve for 3 and y it is assumed that R (y) can be expressed by a first order Taylor expansion about some initial estimate y ; R(Y) = R(Y ) + 8R(Y) (Y-Y ) (28) 3Y Substituting eq (28) into eq (27) yields Rm - R(y Q ) = 3 + (y-y ) 9R(Yq) (29) 3y From a sample of matched radiosonde and satellite observations the left-hand side of eq (29) is determined for each pair. Also, for each pair the derivative is approximated by aR(Y Q ) _ r(y + o.i Y ) - R(y - o.i y Q ) (30) 3Y 0.2y o Then from the sample it is straightforward to determine the constants 3 and (y-y ) by linear regression. The solution is iterated (i.e., the new value of y replaces y in eq (29) and eq (30) in order to account for the non-linearity between R and y until (Yn~Yn-l)/Y n _i < .001, where n refers to the nth iteration. 27 Matched satellite-radiosonde observations collected on the history tape are subject to three conditions: (a) The radiosonde must occur within a 2 degree latitude box about the Nimbus sounding location (the centroid of the clear area of an ITPR sounding grid). level or higher. Nimbus overpass. (b) The radiosonde must have reached the 100-mb (c) The radiosonde must be within six hours of the To be considered in a sample for adjusting the transmittance functions of the various sounding channels , somewhat stricter tolerances are imposed: (d) The radiosonde must have reached the 30-mb level or higher. (e) The sounding must be within three hours of the radiosonde launch. (f) The maximum temperature discrepancy between satellite determination and radiosonde must not exceed 15°C. (g) The sounding must have resulted from "clear- column" radiances. (h) The horizontal temperature gradient as measured by sub-grid (75 n. mi. scale) departures from the full grid (250 n. mi.) average retrieval must not exceed 2°C at any level up to 100 mb. (i) The difference between the satellite measured surface temperature and the radiosonde surface temperature must not exceed 10°C. (j) The difference between calculated and observed radiances for ITPR channels must not exceed 5 percent of the observed radiance. The collection of adequate data for correcting the trans- mittance functions of the stratospheric sounding channels was very difficult. After considerable effort a sample of slightly more than 50 coincident satellite, radiosonde/rocketsonde observations were ob- tained for the period January through April 1973. Since these were obtained manually, no specific spatial window was imposed but soundings in areas with large horizontal gradients were avoided unless the match- up was very close. Only those rocketsondes which agreed with and over- lapped the support rawinsonde and which attained an altitude of 0.3 mb 28 were considered. A generally accepted dynamic temperature correction was applied. Final quality control of the sample was achieved by plotting computed vs. observed radiances and subjectively excluding any pair which deviated markedly from the general trend. The quadrature calculation of a radiance from the radiosonde temperature profile as necessary for the left hand side of eq (29) requires that the profile extend to 0.2 mb. For the opaque channel sample this causes no difficulty. In those few cases when the highest level measured by the rocketsonde was 0.3 mb, the 0.2 mb value was extrapolated. For the tropospheric channel sample, however, additional temperature levels must be extrapolated from at least 10 mb and often 30 mb. These additional levels are computed by regression using as independent variables the highest three available mandatory level temperatures and the radiances measured by channels ITPR-5, ITPR-6, and SCR-1, SCR-2 (if available). The regression coefficients are determined from a standard set of 1200 radiosonde/rocketsonde temp- erature profiles (see appendix) with their computed radiances obtained from the standard transmittances adjusted by the factors obtained with the opaque channel sample. The procedure for obtaining the amalgamated set of transmittance adjustments is shown schematically in figure 3-3. The final transmittance adjustments can be taken from the transparent channel sample (so that all channels are compatible) if it is assumed that the information of the opaque sample is passed through the regression temperature extrapolation. The adjustment factors determined from a radiosonde sample collected from January- April, 1973, are given in table 3-1. TABLE 3-1 January - April, 1973, Sample Adjustment Factors Channel Beta Gamma ITPR-3 0.03 0.993 ITPR-4 -0.88 0.986 ITPR-5 1.54 1.495 ITPR-6 3.36 1.024 ITPR-7 1.35 0.756 NEMS-1 3.15 1.236 NEMS-2 -2.52 1.183 NEMS-3 -4.83 1.253 SCR-1 -0.70 1.025 SCR-2 -2.04 0.779 Compute transmittance adjustment factors for ITPR-5, ITPR-6, NEMS-3, SCR-1, SCR-2 from Radiosonde/ Rocketsonde sample Compute regression coefficients to predict temperatures at high levels. Extend quadrature levels of Radiosonde sample by regression up to 0.2 mb. Compute transmittance adjustment factors for all channels from Radiosonde samples Fig. 3 - 3 30 One striking feature noted in the table is the large biases, 3, which occur with some of the channels when y is close to unity. For NEMS these are attributable to our use of antenna as opposed to brightness temperatures. (The conversion of antenna tempera- tures to brightness temperatures requries side lobe contribution corrections which are about the same magnitude of our derived 8 correc- tions.) For ITPR-6 the bias is unexplained. Extensive experimentation with the shape of the transmittance function has failed to remove the bias. This is discussed further in section 3.4.2. A second striking feature in the tables is the large departure of y from unity for several of the channels. Large deviations are basically undesirable since they imply one of the following: a) the theoretical transmittance function is seriously in error; b) the channel is measuring a layer insensitive to raising or lowering the transmittance function; c) the radiosonde/rocketsonde temperature measurements are not representative of the radiance measurement. For SCR 2 a strong case can be made for the latter especially as a consider- able portion of the transmittance function lies above the last quadrature level at 0.2 mb. For NEMS-3 and ITPR-5 the area of greatest suspicion is the second. Computations of the standard deviation and mean differ- ence between measured and calculated radiances as y is varied from 0.6 to 1.3 reveal that >f or NEMS-3 and especially ITPR-5, the minimum in the standard deviation (which essentially determines the correct y) is very ill-defined. This can be attributed to the fact that the channels are sensing on both sides of the tropopause so that raising or lowering the transmittance function does not materially affect the emitted energy. In summary, the y values derived here indicate that theoretical transmittance computations are accurate for all the ITPR CO2 channels, except for possibly channel 5. On the other hand the theoretical computations for the NEMS oxygen channels are systematically in error. The consistent y > 1 values indicate the theoretical compu- tations over estimate the transmission of the atmosphere in the 50-60 GHz region. By far the largest discrepancy (deviation of y from unity) exists for the ITPR 20-Mm H^O channel. The empirically derived y value indicates that atmospheric water vapor is considerably more transparent to 20-um radiation than is predictable from theoretical computations. This result has been independently verified by atmos- pheric transmission function estimates from vertical profile radiance measurements, conducted with a prototype ITPR aboard the NASA CV-990 air- craft, made beneath the Nimbus-5 satellite (Smith, Wydick, Howell, and Pellegrino, 1974- ). The error in the theoretical computations for this spectral region appears to be due to uncertainties of the continuum coefficients (the e-type and p-type) for this spectral region. 31 3.4.2 Adjustments to the ITPR Q Branch Channel 6 The original (pre-launch) weighting function for channel 6 is shown in figure 3-4. This function was derived by Davis (1972). As described earlier, his approach employs a combination of random and regular transmission functions to represent the transmission of homogeneous paths. The extrapolation to the condition of atmospheric near-vertical paths is through the Curtis-Godson approximation. The retrieved temperature profiles from the ITPR-NEMS- SCR system in the early months of 1973 showed significant disagreement with radiosonde and rocket measurements of the temperature profile in the range covered by the original weighting function. In addition, the channel 6 radiances conflicted with those of the SCR 1 channel, whose weighting function overlaps substantially with that of channel 6. The new weighting function (fig. 3-4) gives improved agreement with rocket-based measurements of temperature. The conflict with the SCR 1 radiance is substantially reduced, and should be further resolved with minor modification of the weighting function of either channel. The technique depends on the correlation between the radiance emitted through the top of the atmosphere with the atmospheric temperature at any pressure level in the atmosphere. A standard correlation function of atmospheric pressure, Q(p), was set up, corre- lating the measured radiance with rocketsonde observed temperatures for a set of nearly simultaneous satellite-rocket observations. Similar functions S n (P) were calculated for n models of the channel 6 atmos- pheric transmission function. The transmission function which produced the highest correlation between S n (P) and Q(P) was selected as the empirical best fit. The details of the method are as follows. A set of n atmospheric transmittance functions, T n (P) was calculated through line-by-line integration using the computer program of Drayson. Each transmittance function in the set was calculated from a channel 6 spectral profile within the range of experimental error of the spectral measurements . A set of m rocket-measured temperature profiles , T m (P), were collected. The corresponding satellite measurements of radiance, R m , were also noted. Let the correlation function between R m and T m (P) be Q(P). This function, at each pressure level P in the atmosphere, is the correlation coefficient between the measured (satellite) radiances and the measured (rocketsonde) temperatures. Similar functions, S n (P), were calculated for the correlation between calculated radiance (for each T n (P)) and measured (rocketsonde) tempera- ture . The calculated radiance is given by R Cm,n = [ B(v Q , T m (P)) dT n (P) dp (31) Jp s dp 0.1 0.5 1.0 D 5 10 50 - 100 - 500 1000 A A -A ~ *\ i i 1 1 1 — 5v 1 — \ \ • 0.9982 0.9990 ^N^ — Final yi - I _ — __ 1 1 l 1 I 1 = 0.0 Fig. 3 - 4 0.1 0.2 0.3 Weighting Function 0.4 33 where B represents the Planck function at the center v Q of the filter. P s represents surface pressure; the boundary term due to surface emission is zero for channel 6, since t(P s ) is zero. Equation (31) was approximated for the purposes of this calculation by a sum over the 25 standard ITPR pressure levels. The calculation was simplified by the fact that for channel 6 the T n (P) are virtually independent of temperature profile. The correlation coefficients x n were then found between Q(p) and S n (p). That x n '(p) which had maximum x n was selected as the best empirical transmittance function of the original set. To further improve the empirical fit, a set of 100 transmission functions was calculated from x n '.(p) by the addition of a perturbation term 2 At = a exp (-b p ) where a was random within a range ± a Q and log e (b) was random within a range £j_ to &2« This perturbation function has the same general shape as the original transmittance function T n '(p). The constants £]_ and %2 were chosen to be 0.0 and 5.0, which confines the main effect of the perturbation to the range 0.5 to 20 mb. a was initially ± .05. On selection of that T n "(p) from the range n" - 1 to 100 which gave the highest x n , a further set of 100 T n (p) was generated, with a Q multi- plied by the factor 0.7. A total of 4 similar iterations completed the optimization. Figure 3-4 shows the result for a relatively small sample of 28 atmospheric profiles. In figure 3-5, several weighting functions are shown together with the corresponding x n to illustrate the sensitivity of the method. Large departures from the best fit are readily detected, but there is not a high sensitivity (with this sample) to small changes from best fit. The result shown in figure 3-4 is dependent on the atmospheric profile sample size. A 56-sounding sample set analysis showed a more pronounced secondary peak in the 2- to 5-mb range than that of figure 3-4. The sample size dependence is pro- bably a result of the errors present in the temperature and radiance measurements, and the dependence should reduce as the sample size increases. Results will be presented in Part II of this report for a sample size of about 100 profiles. 0) IS! IS) 0) 500 - 1000 Weighting Function Fig. 3 - 5 35 4.0 Determination of Sounding Radiances 4.1 Surface Temperature and Clear-Column Radiance Computation Methods This section describes the procedure used to specify surface temperature and clear column radiances from the Nimbus- 5 ITPR measure- ments. Simultaneous 3.7-ym and 11 -urn window observations are utilized to filter erroneous clear -column radiance determinations due to varying cloud properties (i.e., heights, opacities, etc.) as well as to deter- mine the surface temperatures. Numerous "valid" determinations are averaged in order to reduce the cloud-induced noise to a tolerable level for accurate temperature retrievals down to the earth's surface. 4.1.1 Preliminary Data Processing 4.1.1.1 Angular Correction Model for ITPR Radiance Measurements The ITPR measures the spatial distribution of upwelling radiance by viewing 20 different nadir angles. Before the data can be used to compute atmospheric parameters, it is necessary to account for the radiance variations of the observations due solely to variations in the nadir angle of the observation. We desire corrections which will normalize the radiance observed at nadir angle 8 to the value which would have been ob- served at nadir angle 0°. The vector of corrections R'(9), in which each vector element denotes a different measurement frequency, is given by R'(e) = r(o) - R(e) = [£(o) - w(e)] • b = w*(e) b (33) where W'(0) is the matrix of transmittance (weighting) functions (an element for each frequency and level) and B is a vector of Planck radiances (an element for each level). Assuming a linear relationship between the B profile and the radiance measurements; i.e., B = A(6) • R(8) (34) where A(9) is a regression matrix. It then follows that R'(0) = W'(9) A(9) R(9) (35) or R'(0) = C(9) R(9). (36) Equation (36) states that the correction for angle can be estimated from a linear combination of the radiances. Consequently, given a statistical sample of radiances (in practice synthetic ones are used) the coefficients (i.e., the elements of C) can be estimated by linear regression. The final model for the angular correction to the radiance in the i "th spectral interval at the j— angle is R i,j = C i,J,o + X Cj. j k R jjk i=l,2,...,7 (37) j=l,2,...,20 36 where k denotes the radiance channel number. (In applying the coeffi- cients of equation (37), the radiances are normalized to the ITPR reference frequency of 714.8 cm - . ) For the ITPR window channels, the regression procedure is used to normalize the radiance values to the radiance observed for zero molecular absorption at nadir angle zero. Conse- quently, the derived regression equations are used to correct the window channel observations for all molecular -absorption as well as angular dependencies . The standard errors (mw/m -sr-cm~l) , explained variances, and coefficients determined from a statistical sample of 2040 atmospheres (120 different soundings in which clouds were assumed to exist at the 200- , 300- , 500- , and 700-mb levels in addition to the cloudless case) are given in table 7-2. The standard error of the radi- ance measurements was assumed to be 0.15 for channels 2-7 and 0.003 for channel 1 in generating the regression matrices. As may be seen, the standard error of the limb correction regression is well below the measurement noise level, even for the largest zenith angle of 42.5°. Finally, figures 4-1, 4-2, 4-3, and 4-4 show the angular corrections for the seven ITPR channels resulting from an application of the angular correction regression model to statistically independent tropical and polar model temperature profiles for cloudless and high cloud situations. As may be seen, the prediction of the vertically propagating radiance from off -nadir observations is near perfect in all cases. As a conse- quence, this approach is used to correct the 3. 7- urn and 11- ym channels for molecular absorption and to normalize all the ITPR radiance observa- tions with respect to zero nadir angle to facilitate accurate computations of clear-column radiance. 4.1.1.2 Modeling of Reflected Solar Radiation for ITPR Channel 1 (3.7-um Window) In the processing of ITPR 3.7-ym channel data, it is necessary to consider the limits of surface reflected solar radiation under a cloudless atmospheric condition. Neglecting atmos- pheric scattering processes, the solar radiation transfer can be summarized by the diagram below. ^ftfi 1 Local Vertical \ x O IT ^ F =n s RsCose T a (e ) CT' O - ift Q., Ch. 4 -e- ■© — Ch. 6 R(0) - R(0) O O O R (0) - R (0) 4 3 2 1 -1 1 -1 -2 - Ch. 7 . — Ch. 5 ^^ -©- &r ~ar -© - 0.15 - 0.10 - 0.05 I— 0.00 -e o— — & -©- -©- -» Ch. 6 — — R(0) -R(0) o O R(0) - R(0) 1.0 0.0 -1.0 -2.0 Ch. 7 -© © Q- © © © © 10 20 J I L 30 40 e Fig. 4 - 2 3 2 1 — i — r - Ch. 3 -0 Q - ^tp' ct < 1 -1 3 2 1 n — i — r~ 75N(July) Clear 1 1 1^ -e- -©- ^~ -q- - 3 Ch. 4 -e- 1 n=a^ _ Ch. 5 o— ©- — __Q Q q^ e -© R (0) - R(0) O O R (0) - R (0) Jlh. 6 -1 -2 -^ — o - - »gy — ff" Ch. 7 ^~ -Q- iD_ 10 20 30 40 9 Fig. 4 - 3 DC 0.5 0.0 -0.5 -1.0 1.0 0.0 -1.0 1.0 0.5 0.0 0.5 " 75N (July) >©- — ©- Ch. 3 G Cloudy (Cloud P. — © — ©- "1 \~ 300 mb) - — ©- O. --g -e- -e- "0- ■©■ -— ^.^ Ch. 4 Ch. 5 —.—.Q. „._.,_ — ©— — O o -e- -e- ■© — -©■ — __ ^Ch. 6 R(0)_R(£) O O O R (0) - R (0) 0.0 -0.1 0.2 -0.3 1.0 0.0 -1.0 2.0 "©- ©— —- ©— — ©i— .— — — -^— «-»— ^——r Ch. 7 !! 10 20 30 40 Fig. 4 - 4 :. - -- 41 where; fi s = solid angle subtended by sun x a = transmission of atmosphere G Q = solar zenith angle = local zenith angle of emerging ray r s = surface reflectivity F Q = flux of solar radiation reaching the earth's surface K R s = 'Direct solar radiance = \ cf> v B[v,T s (v)] d l\ v dv Jo 'Jo V = Spectral response function of the channel Assume; x(a) = exp < - K 1 +K 2 cos(lat) sec ai (38) where K, = optical depth of uniformly mixed gases (CO2 and N2O) K2 = optical depth of water vapor which is modelled as a function of the cosine of latitude Thus, the final reflected sunlight model takes the form I© = -2. n s Ct)exp i- K-l+KjcosCL) sec0 o +sec2 and 20 -ym H2O channels) the earth and cloud reflected sky and solar radiation is negligible compared to the infrared emission, and the earth's surface can be assumed to be a blackbody (i.e., e s (v)=1.0). Thus for the cloud components I u (v,p 0)=f "' B[v,T(p)] dT(v,0p) dp + B[v,T(p c )] e c (v)x(v,p c ,0), (43) Jo d P r c (v) I d (v,.p c ,0)x(v, Pc ,0) = 0, and (44) I u (v,p c ,p s ) = f : B[v,T(p)] dT(v,p c ,p) dp+B[v,T(p s )]x(v,p c ,p s ). (45) And for the clear components , l u (v,p s ,0)=( S B[v,T(p)] dT( ^°' p) dp+B[v,T(p s )]x(v,0,p s ), and (46) Jo P 43 r s (v) I d (v,p s ,0)T(v,p s ,0) = 0. For atmospheric window regions, the atmospheric trans- mittance is near unity. However, the reflected cloud and surface com- ponents of solar radiation for the short wavelength window regions A< 4.0 ym cannot be neglected. Also, at 11 ym the surface emissivity is near unity for most surfaces. Denoting short wavelength window regions as W s and long wavelength window regions as W^, then T(W s ,p 1 ,p 2 ) = T(W L , Pl ,p 2 ) = 1.0, (47) W B ,T(p fi ) W L ,T( Pc ) e c ( w s>P c )s £c ^L'Pc)' I u (W s ,p c ,0) = B I u (W L ,p c ,0) = B I d (W s ,p c ,0) = I Q (W S ) y Q i d (w L , Pc ,o) = , I u ( w s»Pc.Ps) = W Uo t c (W s )r s (W s ) + £s (W s ) B (w s ,T(p s ) , WPc>P s > = B [ W L^(Ps)] 5 I u (W s ,p s ,0) = £s (W s ) B [w s ,T(p s )J I u (W L ,p s ,0) = B W L,T(p s )] , I d (W S5 p s ,0) = I (W s ) y Q , I d (W L ,p s ,0) = 0, and (48) (49a) (49b) (50a) (50b) 5 (51a) (51b) (52a) (52b) (53a)' (53b) I (W) = B[W,T S ] (54) where T s is the brightness temperature of the sun, ft is the solid angle subtended by the sun, and y Q is cos(8), where is the solar zenith angle for < 90, and zero for night conditions (0 > 90). Substituting eq (48)-(51) into (41) and (42), equation (40) for the window regions becomes KW S ) = e s (W s ) B [w s ,T(p s )j + r s (W s )I o (W s )y +N | B [w s ,T(p c )] e c (W s ,p c ) + [r c (W s )r s (W s )] I Q (W s )y >] 1-t c (W s ) e s (W s ) B [w s ,T(p s )] + ^ (W s )r s (W s )I o (W s ) ^o}, and (55) 44 I(W L ) = B [w L ,T(p s )J + n{b ^W L ,T(p c )j e c (W L „p c ) (56) + [l-T c (W L )] B [w L ,T(p s )] } . 4.1.3 Surface Temperature Guess Generation The specification of clear-column radiances and con- sequent temperature and moisture profiles to the Earth's surface requires knowledge of the Earth's surface temperature. In the Nimbus-5 data processing an initial estimate of the surface temperature is obtained from the 24-hour old day or night NTMBUS-derived surface temperature analysis (see section 6). This surface temperature estimate, denoted as T (D(p s ), will be considered to be within an error a of the actual surface temperature, a is itself a function of temperature, varying from 2°C at 270°K or below, to 7°C at 330°K or above. In addition, within each NIMBUS data grid, as shown in figure 4-5, are sixty -four 11- urn window radiance maxima provided by the THIR 4 n. mi. resolution radiometer. A second estimate of the surface temperature T ^'(p s ) is derived from the average of all THIR radiances within a grid, which, after being corrected for molecular absorption, have associated brightness temperatures which are within 2.0°C of the maximum THIR brightness temperature observed within the grid. If T Q (2) (p s ) lT (1) (p s ) - a°C, then T Q (2) (p s ) is adopted as the final surface temperature guess, T (p s ) 5 and is assumed to be within an error 8, of +_ 2.0°C of the actual surface temperature at any location within the grid. If T ( 2 )(p s ) < T ^(p s ) - 4°C then T (Ps) i- s adopted as the final surface guess, T Q (p s ), and is assumed to be within an error, 3, of + a of the actual surface temperature at any location within the scan grid. 4.1.4 Surface Reflectivity, Surface Temperature and Clear Column Radiance Retrieval (From Sounder Data) Equations (a) Surface Reflectivity Equation Before the surface temperature can be retrieved from the 3.7-um and 11.0-ym window observations when broken clouds exist within the FOV, the surface reflectivity must be known. This, when possible, is obtained from any cloudless ITPR fields of view within the scan grid. It follows from (55) and (56) that, if no clouds exist within the field of view, I(W S ) = I c (W s ) = e s B [w s ,T(p s )J + r s (W s )I (W s )y , and (57) Radiance Measurement Distribution in Grids 1 thru 5 NIMBUS - E Orbitaj Track 135 Chan. B (6 per grid) (40 n.m.) Kti SCR F.O.V, - 2,3,4 ChaX.CD | (15 nm ' , < (16 per grid) ooooo ITPR F.O.V. (15 n.m (140 per grid - 1, 3, 5)j Fig. 4 - 5 i Locat on Range :i ^_ - • .| 4 , THIR F.O.V. (4 n.m.) (64/every grid ) i r • i J 2 NEMS FOV's (108n.m.) (2 per grid - 2, 3, 4) 46 I(W L ) = I C (W L ) = B [w L ,T(p s )J . (58) Thus, if the 11.0-ym window channel brightness temperature (after making appropriate molecular corrections) is greater than [T Q (p s ) - 3], then the FOV is assumed to be clear and the actual surface temperature, T(p s ), pertaining to that particular FOV will be assumed to be given by the ITPR 11.0-ym window channel brightness temperature. The surface is assumed to be a diffuse reflector so that £ s +r s = 1.0. Then the surface emissivity e s (W), is computed using eq (57) in the form e s (W s ) = Iq(W s )u q - I C (W S ) (5ga) W^o " B [W s ,T(p s )] and the surface reflectivity r s (W s ) = 1 - e s (W s ). (59b) (b) Surface Temperature Equation Assuming that a change of radiance from one FOV to a geographically adjacent FOV is due only to a change in cloud amount, it follows from eq (40) that *™L = fi cd .) In applying eq (68) and (69), the i h FOV is taken as that having the maximum longwave window channel radiance. Then using the long wavelength window channel to define Nv . 1 5 J 5 N^. = W - ^.j'V , (70) the clear -column radiance is obtained using eq (69) 4.1.5 Filtering Observation Pairs Having Different Cloud Properties The above solutions for surface temperature and clear- column radiance are valid only if the variation of radiance from one field of view to another is due to a variation in the fractional cloud coverage and not due to variations in the cloud properties (e.g., height, opacity, etc.). Such variations in cloud properties can be detected from an erroneous solution for the clear-column radiance of the shortwave window channel. It follows from eq (57) that , for a diffusely reflecting surface (r s = l-e s ), I C (W S ) = B [w s ,T(p s )j + r s {l (W s )u - B [w s ,T(p s )]| (71) 49 Therefore the maximum possible clear-column radiance, I max (W s ),is given by B W s ,T(p s ) + e +I»s I (W S ) I c max (W s ) = greatest of Iw s ,t( Ps ) + bJ W s ,T(p s )+6 k,T(p s )-Bj max mm B W s ,T(p s )+B +r s '" XI1 I o (W s )y -B W s ,T(p s ) + 6 max B K,T(p s )-3 +r s ' u ^ T (W R )y -B W s ,T(p s )- o v "s /H o ■] y -B W s ,T(p s )+8 y -B|w s , I mm [ W s»' W s ,T(p s )-eJ + r s "' xu I (W s )y - B |W s ,T(p s )- and the minimum possible clear column radiance, I c min (W s ) is given by I c min (W s ) = smallest of 72a - 73b . c Using eq (69) and (70) to compute 1^ -(W s ), the cloud properties are considered to be the same in elements l, and j, if • 2 oe c fr, -\ . T max/ IT n , 2 oe I c min - n^y * I i,j (w s ) * x c T (p R ) - the FOV is considered to be clear; if (b) B" 1 (l(W L )l < T (p s ) - 3 the FOV is considered to be overcast. If AT* > 3 p , the FOV is considered to be composed of broken or mixed clouds. During the day , I (W s )y > 0, we can solve for r using eq (59). If r S ( w s) < r s max (W s ) where r s max (W s ) is the maximum expected value of the surface reflec- tivity and if condition (78a) holds, the element is considered cloudless, During the day no differentiation between overcast and broken cloud conditions can be made for an individual FOV from only the window observations. (b) From Multi-FOV Observations From an array of observations, it is possible to determine whether or not a particular H2O or CO2 channel radiance is affected by any clouds within the FOV's making up the geographical observation array. I . If the channel is unaffected by cloud, then and or (1) Var ( 2 ) Var |l(u)]« + o_ [l(W)j >> a. + Or (3) I(W) * B W,T n (p s ) (77) (78a) (78b) (79) (80) (81) 51 where the bar denotes the average value and cr-p 2 is the expected variance due to surface or atmospheric temperature variations. II. If the channel is affected by cloud , then III. If and ( 1 ) Var (1) Var ( 2 ) Var I(v) » o P 2 + a Kv) * a 2 + a £ T [l(W)l * a 2 + a 2 £ T and (3) I(W) < B [ W ' T o ( Ps)] Then an overcast exists, but it cannot be said whether or not I(v) is affected by the cloud. 4.2 Computational Procedures for Nimbus-5 ITPR Data 4.2.1 Definition of Grid Values of T(p s ), r s (W s ),and e s (W s ) Steps: (1) Specify grid average surface temperatures, T Q (p ), from clear-column THIR window data as discussed above in Section 3. (2) Find the element for which the difference in brightness temperature between the 3.7-ym and 11.0-ym channels is minimum. If this minimum difference is greater than 15°K, then it is assumed that no clear FOV's exist. If the minimum difference is less than 15°K, proceed as follows. From all elements at which the 3.7 ~vim to 11. ~ym brightness temperature difference is no greater than the minimum difference plus 1°C, find the maximum 11.0-ym brightness temperature, Tmax. Then average all values ^ Tmax -4. If this grid average is greater than [T Q (p )-$] , replace the surface temperature estimate obtained in step (1) with this grid average clear -column ITPR 11.0 Mm window channel brightness temperature value. (3) Compute r s (W s ) and e s (W ) from the grid average clear -column 3.7-ym ITPR data, defined in step (2), using equations (59). Let r s max = r s + 0.10 r s and r s min =0. (82) (83) Options 52 (1) If no clear-column THIR data exist then we let T (p s ) be given by the day-old surface temperature analysis. (2) If no ITPR clear-columns exist we assume r_ = 0.02 and e = 0.98 o S 4.2.2 Definition of Spatial Radiance Sets for Clear-Column Radiance Computations The ITPR major grids are partitioned into 12 sub-grids, as shown in figure 4- 6a, for the purpose of calculating surface temperatures and clear-column radiances using spatially independent radiance observations. Figure 4-6b shows the configuration of the 36 spatially independent and adjacent ITPR observation sets to be used for the ITPR sub-grid computations. When the ITPR is in the nadir mode, each of 36 FOV's Is paired with one 10-FOV's removed along the sub-orbital track. This is the minimum separation that provides spatial independence. Also in figure 4-5 are shown the distribution of SCR and NEMS observations that correspond (in terms of time) with the ITPR grid data. The selection and sampling of SCR and NEMS data are described in sections 4.3 and 4.4, respectively. 4.2.3 Specification of ITPR Sub-Grid Values of T(p s ), r s (W s ),and e s (W s ) Steps : (1) Average all THIR clear-column window data in sub-grid region which are greater than [T (p s )-3],where T Q (p s ) is the sub-grid average surface temperature estimate obtained from the day-old analysis. (2) Same procedure as employed for grid, 4.2.1 (2). (3) Compute sub-grid values of r s (W ) and e s (W s ) from clear-column ITPR 3.7-ym window data in sub-grid g using equations (59). Define r s min and r s max for the sub-grid as r s min = 0, r s max = r + 0.10 r s . Options (1) If no clear-column THIR data exist, then we let T (p s ) for the sub-grid be given by the day-old analysis. a Q -o © 3 0) c a c u E 3 O la o 0- I i I I 1 I I 00 00 99 00 6" o I I i § i e i O o O) c o E o u c o e 0) LU c & u o < c c a c o CO O) c 5 -° m en 55 (2) If no clear -column ITPR data exist, then we let r s (W s ) be given by the grid average values obtained in 4.2.1. 4.2.4 Computation of Surface Temperature and Clear-Column Radiances for ITPR Sub-Grid Steps: (1) ITPR channel 6 (the 15 -urn Q -branch channel) is assumed to be unaffected by clouds so its average value is taken as clear -column radiance. (2) Conditions (83) are used to determine whether the observations for a particular sub-grid are for an overcast condition. If conditions (83) are met (using 2a £ ^ + 2a T ^-, where a T is the expected variance due to temperature variations, as the actual criterion) then the average values are taken as "overcast cloud radiances" and no clear - column radiance or surface temperature computations are made for the sub-grid. (3) Conditions (81) are used to determine whether the observations for a particular channel are affected by cloud. If condi- tions (81) are met for a particular channel (using 2a £ + 2a T , as the actual criterion) then the average values are taken as the clear -column radiance for the channel. (4) For channels in which condition (82) holds, the clear-column radiance is computed, using equations (69) and (70) and the surface temperatures, using equation (65), from all radiance sets specified in 4.2.2 subject to condition (74) and the additional condition that N"j_ -: < 0.86. The sub-grid average value, I c (v), is then taken as the weighted average M E ig(v) [i-N* k ] T c (v)= 3s=i t i c M -| £ L i-n] k=l L J (84) where k denotes a particular I,j element combination. In addition, the standard deviation defined by / M [ Io(V) ] V If g i [lg-? e ] 2 (85) is obtained. All I] < (v) values which depart from I c (v) by more than 1.5 a(I c ) are filtered from the sample and a final weighted average is 56 obtained from the filtered data set. The standard deviation is again obtained and used to specify the expected error of the determination, e[I c (v)], assuming that [l c (v)j = lM , M The expected error, e[I c (v)], of the grid average value is assumed to be given by E ff A fesH r= 1 l=1 L Vn~ e m £ £=1 (86) N where cr(I c ) is for the filtered data set, and N is the product of the total number of spatially independent observations times the ratio of the final number of determinations over the total number possible. An analogous averaging procedure is used for the surface temperature determinations . (5) If neither conditions (81) or (82) hold, the radiance set corresponding to the maximum channel 2 radiance value is taken as "clearest broken cloud radiances" and no clear- column radiance or surface temperature computations are made for the sub-grid. (6) The ITPR grid average values, "I c (v) , are then ob- tained by L _ . E I c (v)*H.(v) _ 1=1 I c (v) = L » (87) E w £ (v) i=i where L is the number of sub-grid clear column radiances obtained, and the weight, W£(v), is defined by Mb. %( v ) = g_ -, • (88) (89) where N is for the entire grid. 57 4.3 Construction of Stratospheric Difference Channels for SCR As depicted in figure 4- 5, section 4.2.2, there are 16 SCR B-channel FOV's in the 64 seconds (four major frames) that correspond to an ITPR grid. At each of the 16 locations, two difference radiances are calculated (channels SI and S2) from the four B-channel radiances using the weighting procedure described in section 3.3. These 16 measurements are then averaged, and one-sigma filtering is performed to eliminate noise spikes. The resulting single "observation" (two radiance values) is then output along with the corresponding (in time) ITPR and NEMS data. These values are not used directly in the re- trieval of temperature profiles, but serve as input to a global objective analysis routine (see section 6). 4.4 Sampling of NEMS Observations Again referring to figure 4-5, section 4.1.3, we note that the four-major-frame ITPR grid structure encompasses 32 NEMS FOV's. Although simple averaging of all available FOV's in the four-major- frame ensemble has been found to be sufficient in the case of the SCR stratospheric difference channels (section 4.3), this procedure proved unsatisfactory with respect to NEMS. The ITPR sub-grids (section 4.2.2) are arranged in three rows of four each. Suppose that the clear-column radiance computations (section 4.2.4) yield reliable results for some, but not all, of the 12 sub-grids. Full-grid clear-column radiances are obtained by weighted averaging of the "good" sub-grids. If a straight average of NEMS measurements is amalgamated with such a radiance set in the temperature- retrieval process (section 5.1), the result may be degraded by incom- patibility between the two radiative estimates of atmospheric properties, since they are, in effect, sampling different (horizontal) regions. In order to obtain NEMS "observations" more nearly consistent, in the sense of spatial coverage, with ITPR full-grid clear-column radiance estimates, the following procedure was devised, and is successfully employed in routine processing. The 32 NEMS FOV's are divided into three groups, correspond- ing to the three rows of ITPR sub-grids. In each group, the measure- ments are averaged and screened with a one-sigma filter. In constructing the single "full-grid" observation, each group average is weighted by the number of "good" ITPR sub-grids in the corresponding row. Thus the NEMS and ITPR "sounding radiances" are nominally representative of the same horizontal region of the atmosphere. 58 b.O Retrieval Methods In this section, the procedures developed for determination of meteoro- logical parameters from the "sounding radiances" obtained using the techniques of section 4 are described. These parameters are the vertical temperature profile, T(p) - section 5.1; vertical profile of mixing ratio, w(p), total precipitable water, W, and liquid water, Q - section 5.2; the vertical distribution of cloud amount, A(p) - section 5.3; and total out- going longwave 5- to 25- urn radiation flux, F - section 5.4. 5 . 1 Temperature Profile i 5.1.1 Inversion Algorithm The algorithm employed in the inversion of the radiative transfer equation (RTE) to obtain atmospheric temperature from radiance measurements is a hybrid of regression and the minimum information solu- tions. The regression solution is used to specify a "first guess" for the minimum information retrieval. The mathematical basis for these techniques and their application to remote sounding have been discussed in considerable detail in the recent literature (e.g., Smith, Woolf, and Jacob, 1970; Smith, Woolf, and Fleming, 1972; and Fritz et. al., 1973). Therefore, only those aspects pertinent to the Nimbus- 5 amalgamation (of information from different sensors) problem need be presented here. As part of the linearization entailed in the development of the minimum information solution, it is necessary to normalize the radiative measurements. When the sensing channels are in a fairly narrow spectral region - such as the 15-ym CO2 band, as in the case of the SIRS-B experiment on Nimbus-4 - it is sufficient to normalize to a nominal frequency near the center of the band (Smith et. al., 1972). In the present Nimbus- 5 situation, we wish to combine infrared radiances (ITPR) with microwave brightness temperature (NEMS) measurements in vastly different spectral regions. Thus, a more complicated normali- zation procedure is required. Employing the first order Taylor expansion we define relative radiances, R-? , whose magnitudes are similar for all wavelengths. For the infrared, 1 — tj — tl L \ X i 9T °i ) and for the microwave (where Brightness Temp = Constant x Radiance) BT^ - BT°- N R j = V 3 = E (Ti,^) __ A Tij l and (91) 9B° BT D i=l C 2 v fB°exp(C 2 v /T°)"l ' T°2" Lexp (C 2 V /T°-l| 3T°/ T°2 Lexp (C 2 V /T°-l) " \vT/ P r °2 v " (92) 59 where K = C2/C1 = 120836.13; B is Planck radiance; BT is brightness temperature; subscript i denotes level, j channel; and the superscript zero denotes initial-guess quantities (generation of guess temperature profiles is described in section 5.1.2, following). In matrix form, R = <5T W , (93) where the elements W- • of W are W-h = JO At-- (infrared) (94a) I. 8T°. J 1 1 and W£j = gTj^ At^. (microwave) . (94b) The minimum information solution is then the "conditioned inverse" of eq (93)(see Smith et. al. , 1972), 6T = (W T W + y I)" 1 W T R (95a) or 6T = C R , (95b) where I is the identity matrix and y is a vector Lagrangian multiplier. — • T The "error matrix" y I serves to condition the matrix W W for inversion. y - ae z (5Ti) (96) 2 where ae ( ) is the expected error of the particular quantity. ae(R. ) = 11 1_ (infrared) (97a) and ] h CJF (BT • ) ae(R.) = L_ (microwave) (97b) J BTj ae(ST ± ) = 5o c # (97c) 60 The above formulation is particularly convenient when various combinations of radiative measurements are employed. (See section 5.1.4). In determining the coefficient matrix j3,eq 95, , we can readily zero the coefficient for any channel simply by speci- fying a very large "error" for that channel. A value of 10^, for example, for any diagonal element insures a value of zero in the corresponding diagonal element of the inverse matrix, and therefore in the elements of C for that channel. 5.1.2 First Guess The first guess temperature profile for the minimum information solution is obtained by applying to the sounding radiances a set of regression coefficients appropriate to the particular combina- tion of channels being employed. These regression coefficients are obtained through radiance synthesis, using a fixed data base of radio- sonde/rocketsonde temperature profiles (see Appendix, Section 7.1). Infrared radiances and microwave brightness temperatures are calculated from these profiles - 400 in each of three latitude bands (60-90 N and S, 30-60 N and S, 30N-30S) spanning all seasons - by radiative transfer, using the transmittance functions described in section 3. Normally distributed errors , with RMS levels equal to the nominal noise equiva- lent radiance in each channel, are applied to simulate expected instru- mental deviations. Infrared radiances are converted to brightness temperatures, to render them spectrally compatible with the microwave data. Then, multiple linear regression is performed with the "observed" brightness temperatures as predictors (x) and the original in situ atmospheric temperatures as predictands (y). In matrix notation, y = x A , (98) where x is a vector of brightness temperatures, and y the corresponding temperature-profile vector; extending eq (98) to the ensemble of data (400 samples in a latitude ban" 1 ) yields the matrix relationship Y = X A (99) where X is an nxm matrix of n observations in m channels, Y is an nx& matrix of n observations at % levels, and A is the desired mxi coefficient matrix. The least-squares solution to eq (99) is straight- forward, being A = (X T X) _1 X T Y . (100a) 61 Now the matrix of radiance observations X are expressed in terms of their true values plus a random error component, as X = x + E ^ ^> ^ Substituting eq (100b) into eq (100a) , noting the fact that the errors of radiance are uncorrelated with the temperature profiles (i.e., E T Y=0) fields A = (X T X + E T E) _1 X T Y . Applying the reasonable constraint that errors be uncorrelated between channels ( X' s), than E T E is a diagonal matrix, E T £ = k I where k- A = a c 2 [BT-] and I is the identity matrix, such that 11 e 1 -* J A = (X T X + kl)" 1 X T Y Equation (lOOd) is identical (in matrix form) to eq (95a). We use this feature in much the same way: namely, to zero the coefficients of various channels, simply by making the appropriate element (s) of k very large, say 10^. 5.1.3 Terrain Effects Implicit in the retrieval model is the assumption that the base of the atmosphere is at the 1000-mb level. Over regions of the earth where the terrain intrudes appreciably into the atmos- phere, this assumption no longer holds, and it is necessary to account for the reduced vertical extent of the atmosphere in performing the requisite radiative transfer calculations. An auxiliary data set, consisting of the elevations above sea level of the earth's surface on a one-degree latitude by one-degree longitude grid, is used to specify the surface pressure for the retrieval program. If the retrieval location is found to have a non-zero elevation, the surface pressure is estimated by the hydro- static equation; (100b) (100c) (lOOd) -Z p sfc = 1000 exp sfc/ Ki sfc< (101) where Z s f c is the terrain elevation, ^ s f c is the surface (skin) temp- erature obtained in the course of clear-column radiance determination, R is the gas constant, and g is the acceleration due to gravity. If P s f c > 1000 mb, the terrain is ignored (i.e., P s f c is assumed equal to 1000 mb); otherwise, P s fc i- s replaced by the nearest retrieval model level (e.g., 920 mb, 850 mb, or 700 mb).- 62 In all subsequent radiative transfer calculations relating to this location, the downward integration of the RTE is terminated at P s fcj an< 3 the boundary term, Ig, is changed from I B = B(T sfc ,v) • t(0, Po ) (102a) to Z B = B ^ T sfc' v) * ^O'Psfc) > where B is Planck radiance (infrared) or brightness temperature (microwave), and x(0,p) is the total transmission from the "top" of the atmosphere (p=0) to pressure p. 5.1.4 Solutions for "Non Clear- Column Radiance" Conditions For situations where no reliable "clear-column" radiances could be derived (which are flagged as being "overcast" or "unreliable") , an attempt is made to correct the radiances for cloud effects using the established procedures used for SIRS-A and SIRS-B data processing (Smith, Woolf, and Jacob, 1970). In this case, the clear-column radiance is given by the relation (102b) I c (v)=l (v)+A B(T s )x(p )-B(T c )T(p c ) S B(T>££Ei d p]. (103) where the c subscript denotes the cloud level and A is the amount of cloudiness. The quantity in brackets must be evaluated using a "guess" temperature profile which is usually obtained from regression relations employing the surface temperature and the cloud unaffected radiances from stratospheric channels 5 and 6. If NEMS data are available, the regression solution obtained from the NEMS oxygen channel radiances and surface temperature is used to compute the cloud correction term. The cloud pressure, p c , and amount, A, are specified by the technique given in section 5.3. Having corrected the radiances for cloud contami- nation, the temperature (and moisture) retrieval proceeds as described earlier for the clear-column radiance case. However, since it is known that the retrieval below the cloud level is heavily biased towards the initial guess as a result of this cloud correction procedure (Smith, Woolf, and Fleming, 1972), the profiles are set equal to "missing" flag values at all levels below the inferred cloud level. 5.1.5 Channel Combinations There are three basic channel combinations employed in the retrieval of temperature profiles in the Nimbus- 5 sounding system: 63 (1) ITPR + SCR; (2) NEMS + SCR; and (3) ITPR + NEMS + SCR. There are several variations on this basic "theme" which bring the number of combinations in use to a total of twelve. Note that SCR is considered "present" in all three basic sets; this is by virtue of the objective analysis applied to the SCR difference channels, providing global grid-point fields of stratospheric radiance. However, when the SCR is in calibration, no data can be provided to the analysis routine, and grid-points in the vicinity of the calibration region will be unchanged in value from the 24-hour old "guess"field. Therefore, SCR is considered unavailable when in calibration; this constraint raises the number of "basic" channel combinations to six. The six additional sets involve various reductions in the number of ITPR channels used, based on considerations of the reli- ability of clear-column radiance determinations. For example: if the ITPR grid is deemed overcast, only the stratospheric channels (5 and 6) are employed with the surface temperature to generate the "first guess" profile. Note that all channels are still used in the subsequent "minimum information" solution. When the ITPR is scanning to the left or right of the orbital track, or when the NEMS is in calibration, the latter is not available, and only channel combination (1), or a variation of the type described in the immediately preceding paragraph, is employed. Otherwise (ITPR center grid or nadir mode), the three basic combina- tions, or variations thereof, are utilized. However, if either solution (1) or solution (2) fails any of the consistency checks described in the next section, solution (3) is not attempted. 5.1.6 Consistency Checks Several internal consistency checks are applied in the course of obtaining temperature profiles. If any of the following conditions are met, the retrieval is tagged unsatisfactory: (1) Difference between retrieved 1000-mb temperature and surface temperature greater than 5 degrees (this eliminates retrievals over hot land surfaces , where our handling of boundary effects is of uncertain reliability); (2) Difference between the regression solution and the subsequent minimum information retrieval greater than 5 degrees at any level up to 100 mb$ 64 (3) Difference between the observed brightness temperature in NEMS channel 3 (53.65 GHz), and that computed from the ITPR + SCR (or ITPR only) solution, greater than 3 degrees. (This test is not applied over elevated terrain, since that NEMS channel becomes sensitive to surface emissivity); (4) RMS deviation between observed radiances and those calculated from the retrieved profile greater than the expected instrumental noise, for the channels actually employed in the parti- cular solution; or (5) Retrieved profile superadiabatic between any two levels up to 100 mb. As mentioned in the preceding section, failure of any consistency check for a type one (ITPR + SCR or ITPR) or type two (NEMS + SCR or NEMS) solution precludes any attempt at the type three retrieval (ITPR + NEMS + SCR or ITPR + NEMS) for that set of radiances . 5.1.7 ITPR Sub-Grid As described in section 4.2.4, surface temperatures and clear-column radiances are obtained on a so-called sub-grid scale from ITPR observations. Temperature profiles up to the 100-mb level are retrieved from these data, using minor modifications of the full- grid retrieval procedure. The minimum information solution is applied directly. The full-grid clear-column radiances and the temperature profiles obtained from them are taken as "guess" values. The selection of channels used for clear-column cases is in accordance with the following criteria: Let Al(v) = |l(v) - I(v)|; then full sub (i) if AI(899) < 5, use all four C0 2 channels; (ii) if AI(899) ^ 5, but AI(747) < 4, use the 714, 690, and 668 cm-1 channels; (iii) if AK899) > 5, Al(747) ^ 4, but AI(714) < 3, use the 690 and 668 cm - - 1 - channels; (iv) if AI(899) > 5, AI(747) > 4, and AI(714) ^ 3, do not attempt a sub-grid retrieval. 65 The purpose of the above criteria is to eliminate sub-grid retrievals for cases when noisey sub-grid radiances exist. Sub-grid retrievals are output in the form of 5T(p), the direct result of the solution. In order to obtain the temperature profile at a sub-grid location, the full grid retrieval is employed as a "guess", to which the 6T's are added at each level. The above applies only to sub-grids for which clear- column radiances have been obtained. For sub-grids in which the radiances have been flagged as overcast or unreliable, the following "reclamation" process is attempted. Provided either (a) the ITPR full grid radiances are clear, or (b) a full grid retrieval has been made with the use of NEMS data (so that the full grid solution can be assumed to be free of cloud contamination), an algorithm similar to that described in section 5.1.4 is applied to correct sub-grid radiances for cloud contamination. The temperature retrieval then proceeds as described previously. As in the non clear-column radiance full grid case the sub-grid profile is set equal to the "missing" flag values at all levels below the inferred cloud level. 5.2 Atmospheric Water Substance 5.2.1 From ITPR The retrieval of atmospheric water vapor information from full grid ITPR clear-column radiances is performed in two steps . First, a guess profile of mixing ratio from 1000 to 150 mb is obtained by application of regression equations, which are generated in the same manner as those for specifying temperature (section 5.1.2). This regression solution employs all ITPR channels except the 3.7_um window. Next , an initial guess radiance is calculated for the 20 -ym water vapor channel, using the guess mixing ratio profile in the radiative transfer model. Then, the total water vapor mass is adjusted through an iterative solution (Smith, 1970) in which the difference between observed and calculated 20 ym radiance is reduced to the nominal noise level. The iterative solution is ji+lt n \ - „n u n+± (p) = u"(p) 1 + I(v) - I n (v) 's 3t( p ) 3B , ' (1° 4 > L J o u n (p) — ^ tL dp 9 u n (p) 3p where it is assumed that the ratio of the actual path length profile u(p) to the initial profile u'(p) is a constant. The superscript denotes the iterative step. 66 The shape of the mixing ratio profile w(p) = g 9u ^ /3p remains essentially as specified in the initial regression solution. The final value of the total precipitable water, W(=u(p s )), is output along with the mixing ratio profile. 5.2.2 Determination of Atmospheric Water Content From Nimbus- 5 NEMS Measurements The brightness temperature, Tg(v), measured by NEMS is related to the surface temperature, T s , surface emissivity, e s (v), and atmospheric transmittance, x(v), by the approximate radiative transfer solution (Grody, 1974). a-Bx 2 (l-e s )l (105) T B (v) = T a =0.860 +0.270T -0.134x 2 Bx 2 =0.023 -0.020x +0.999T 2 a =0.845 +0.304X -0.151x 2 Bx 2 =0.020 -O.Ollx +0.990x 2 v = 22.235 GHz v = 31.40 GHz where the RMS deviations in a and Bx 2 are within 0.5 percent of the exact radiative transfer solution for x >0.35. These values were obtained using a total of 330 simulations, which included one clear and four cloudy atmospheric models. The cloud models consist of two types of nimbo-stratus with water densities of 0.15 and 0.30 g/m extending from 900 to 650 mb . and two cumulonimbus clouds having water densities of 0.45 and 0.60 g/m^ extending from 850 to 450 mb. In general, the transmittance is written as the pro- duct of the cloud liquid water, x c ]_(v), water vapor, x^ o^ v -*' an< ^ oxygen, T 02(v), transmittances : x(v) = t c1 (v) • t H2 q(v) • x 02 (v) , where the bracketed term has a NEMS frequency dependence given by x H20 (31) • Xq 2 (31) =0.6753 +0.3120 x H2 q(22) • x 02 (22) (107) which was determined using atmospheric simulations and found to be accurate to within 1 percent (RMS). The frequency dispersion associated with the cloud transmittance is given in the Rayleigh limit, x cl (v) = e-kv 2 Q , (108) (106) 67 Here where v is the frequency in GHz, Q is the cloud liquid water in g/cm 2 and k is a parameter which depends on the mean cloud temperature, T c j_. K = 1.11 x 10 0.0122(291-T cl ) - 3 . (109) An approximately linear relationship exists between the precipitable water content, W, and the water vapor transmittance at 22.235 GHz: W(g/cm 2 ) = 18.114 fl-1.042TH 2 o(22) • t 02 (22)~| , (110) where the above equation was obtained using atmospheric simulations and found to result in less than a 10 percent RMS error. Before applying equations (105) - (110) for computing liquid and precipitable water from brightness temperature measurements, it is necessary to have knowledge of the surface temperature, emissivity and mean cloud temperature. Since the determination of transmittance from brightness temperatures is most accurate for low emissivity sur- faces (see eq 105), the procedure is applied only to measurements over sea surfaces, as opposed to higher emissivity land surfaces. The sea surface temperature is obtained from Nimbus- 5 ITPR measurements and the emissivity is approximately given by the equations for a smooth sea surface: e s (31) • T s = 130. 5°K e s (22) • T s = 121. 5°K where equation (ill) is a reasonable approximation for winds less than 10 m/sec. In the liquid water computations we consider a mean cloud temperature of about 260°K,so that k^ 2.5 x 10-3 ( eq 109). The computations proceed as follows : (1) From brightness temperatures at 22.235 and 31.40 GHz, together with the ITPR-derived surface temperature, we compute the total atmospheric transmittance at the two frequencies using equations (105) and (111). (2) Applying equations (106), (107), and (108 ^the liquid water and water vapor-oxygen transmittance terms are computed from the total transmittances. (3) Employing the relationships (108), (109), and (110), the precipitable and liquid water contents are computed using the results of step (2). (Ill) 68 5.3 Cloud Height Distribution 5.3.1 Theory The radiance measured over a partly cloudy air column is given by I = NI cd + (1-N) I c , (112) where I is the measured radiance, I cd is the radiance from the cloud covered portion, I c is the radiance from the clear portion, and N is the fractional cloud coverage. The cloud radiance is given by led = £ lBcd + (1" £ ) 1 c > (113 > where e is the emissivity of the cloud and ^(Pc)t(Pc) ■ ^ ° B(p) ~&- dp (1W) i I c = B(p ) T (p ) - ( ° B(p) d lM dp . (115) Substituting eq (113), (114), and (115) into (112) yields after inte- gration by parts viBcd = f° T(p) W 1 dp (116) and I - I c = N« [ X Bcd - X c] We consider two frequencies, v^_ and Vo, where the radiances are sensitive to cloud and the cloud emissivity can be assumed to be equal (e.g., the 714 cm~l and 747 cm~l C0„ channels). It follows from eq (116) and (117) that Observed Calculated ' P ° T/ v dB(v-,,p) C*0 \ T (v l5 p) I(v 1 )-I c (v 1 ) Jp» dp 2 ° 2 f° T( V2tp) d B(v 2 ,p) (118) 69 Thus, given the temperature profile, R(vj, V2,p c ' ) can be calculated. The cloud pressure for any given ITPR grid element is then given by that p c ' value in which | y ( Vt 9 \>2 ) - R(v-| ,Vp,p ' ) | = Minimum. (119) The effective cloud amount A(=Ne) can be obtained using the highly transparent CO2 channel in equation (117), i.e., A = W - Hv c ) (120) I c (v n ) - It^ (v c ,p c ) where v c = 747 cm •*-, 5.3.2 Computational Procedure After the full-grid temperature profile has been retrieved, clear-air radiances (I c ), "black-cloud" radiances (Ib C( j)» and the ratios R(v2,V2,p c ') for two channel cmbinations (v-j_,V2 = 714, 747 cm -1 ; V]_,v 2 = 747, 899 cm -1 ) are calculated. For each of the 140 ITPR scan elements, the quantities y( v ]_s v 2) ~ "t ne left hand side of eq (118) - are computed for the two channel combinations using observed radiances. If I(899)> [I c (899)-2], then the element is assumed to be clear. Otherwise, a search for a "minimum" (eq 119) is performed, using the upper pair of channels (714, 747) first. If a level o_ minimum is found, and the associated cloud amount (eq 120) is reasonable (between and 1), the cloud determination is accepted if p c < 700 mb (i.e., the cloud is higher in altitude than the 700 mb level). Should p c be greater than 700 mb the search-for-minimum is performed again, using y and R for the lower pair of channels (747, 899). If p c > 700 mb then the result of this second pass is accepted; however, if the lower pair of channels yields p c < 700, then the result obtained in the first pass is retained. If an acceptable minimum is not found on either pass, the scan element is flagged as having "non- determinable" cloud pressure and amount. When this process has been applied to all 140 scan elements, the results are summarized in the form of a histogram, giving the grid-average percent cloud cover at each pressure level: J(pi) mpi) = 1 x; 1 Aj( Pi ) , (121) where J(p-j_) is the number of elements with cloud at pressure p^, and M is the total number of "good" elements (M < 140). The 1000-mb level is used to accumulate the total percent determined to be clear. A sample distribution is shown below: 70 Pressure = 1000 920 850 700 500 400 300 250 200 150 100 Amount =25 5 20 5 25 15 5 This distribution is interpreted as follows; the ITPR grid area has a total cloud cover of 75% (i.e., 25% clear) with 30% middle clouds whose tops are near 500 mb and 40% high cloud with tops in the vicinity of 200 mb. 5.4 Total Outgoing Long-Wave Flux Winston et al. (1972) demonstrated the feasibility of specifying, to a high degree of relative accuracy, the total out- going longwave (5-25 ym) radiative flux by statistical regression from infrared sounder data. The 15 ym CO2 and 11 ym window channels of the Nimbus-3 SIRS-A instrument (Wark and Hilleary, 1969) were employed in that study. The same procedure has been applied to Nimbus- 5, using the 11 ym window, 15 ym CO2, and 20 ym H2O channels of ITPR. Radiances in these channels were calculated by radiative transfer from 100 radiosonde profiles for which flux computations have been made (Wark et. al. , 1962). Clouds were treated as blackbodies in both the flux and radiance computations. Stepwise multiple regression analysis was then performed on the data, treating the calculated radiances as predictors and longwave flux as the predict and. Individual correlations of the ITPR radiances with longwave flux are as follows : Channel No. 2 3 4 5 6 7 v(cm-l) 899 747 713.8 689.5 668.3 507.4 r 0.986 0.994 0.945 0.028 0.257 0.967 As pointed out by Winston et al. , tropospheric temperature, water vapor, and clouds are the primary modulators of the total out- going flux; this accounts for the high correlations exhibited by channels 2, 3, 4, and 7. Channel 5 has maximum sensitivity near the tropopause, and therefore has little relation, in a statistical sense, to the flux. The stratospheric channel (6) has a relatively low, but nevertheless significant, correlation. The results of the stepwise regression analysis are given in Table 5-1, which is self-explanatory. The values of C Q and SE for step zero are the sample mean and standard deviation, respectively, of longwave flux. Step No, 71 TABLE 5-1 Results of Stepwise Multiple Regression Analysis ITPR Channel Coefficients Cj C, SE EV 482.7 84.0 1 61.1 5.49 9.3 98.7 2 105.4 1.04 3.94 8.1 99.1 3 65.9 1.17 3.75 0.91 6.8 99.3 4 36.4 1.67 1.93 0.92 1, .35 6.1 99.5 5 38.8 1.69 1.82 0.42 .41 1, .38 6.0 99.5 6 24.3 2.03 0.61 0.92 0.13 .47 1, .77 5.9 99.5 SE = Standard Error, &y/day EV = Explained Variance , percent Values of total outgoing longwave flux are calculated routinely on the ITPR full-grid scale by means of the equation F = C o + S i=2 i » where F is flux in £y/day, C Q - Cy are the values obtained for step 6 (Table 5-1), and I2 - I 7 are grid averaged values of observed (not derived clear-column) radiance in standard units (mw/m^ - sr-cm~lXi 72 6.0 Objective Analysis 6.1 Introduction An objective analysis system was designed as an integral part of the Nimbus-5 processing system to provide analyzed fields on a spherical grid with a horizontal resolution meeting the GARP specifications (5 degree longitude wide x 4 degree latitude). Analyses listed below are provided for three purposes: (1) Surface temperature analyses are used to aid in the discrimination of cloud free areas and clear column radiances for the ITPR. Two global analyses are processed to provide local noon or local midnite estimates of the temperature. (2) Radiance analyses are used to estimate the radiance which would be obtained by the SCR instrument at the off -nadir posi- tions where no SCR measurements are made. The analysis values for the SCR 1 and SCR 2 radiances are used with the measured ITPR radiance in determining the temperature structure. (3) Constant pressure temperature analysis are performed at twenty pressure levels (1000 to 1 mb) to aid in quality control of the temperature determinations as well as to provide a "level 3" data archive of the Nimbus-5 measurements. The analysis program was designed to be flexible enough to be readily adaptable to the three purposes stated above. It is basically a Successive Approximation Technique (SAT) whereby the gridpoints of an initial guess field are modified by the neighboring data in M- scans over the field. This system can be used for computing grid -point values for any initially specified meteorological quantity with observations, but it has been specifically tailored to temperature observations as obtained by a polar-orbiting satellite. A brief summary of the theory and numerical techniques is given in section 6.2. The computer programs and their use are described in section 6.3. A generalized flow diagram of the modules comprising the system is included. The actual programs are listed in section 6.3. Results obtained with the program are given in Part II of this report. 6.2 Numerical Techniques 6.2.1 Neighboring Report Discrimination The basic vehicle for changing the initial estimate at a gridpoint is a discrepancy indicated by neighboring observation. It 73 is therefore necessary to know which observations influence each gridpoints. Because the SAT technique involves 4 scans over the entire field, it is economical to pre-process and save the neighbors for each gridpoint. To do this an observation subscript array is ordered from northernmost to southernmost. Then for each gridpoint, a search is made among those reports between the limits of five grid- lengths north or south of the gridpoint. Of these, all that are not more than five gridlengths (20 degree latitude) in total distance from the gridpoint are ordered from closest to furthest. Finally, up to 5 neighbors are selected according to the following rules: (1) The nearest in each quadrant about the gridpoint is selected. (2) The nearest of the remaining irrespective of quadrant is selected. (These rules are designed to promote isotropy in the corrections to the initial gridpoint estimates, since experiments have shown that isotropy is important in reducing aliasing. ) For ready access during the analysis, the subscripts of the neighbors for each gridpoint are packed into a single work and stored in an array of the same size as the grid. 6.2.2 Weighting Factor Determination The degree to which a neighboring observation is per- mitted to influence a gridpoint is determined by the separating distance and the degree to which all stations on that latitude zone fit the initial estimate (or the result of a previous scan). Basically, if all observations indicate that the estimate is a close fit to the data, there is little reason to change the estimate, and the weighting factor should be small. Also, empirical studies (e.g. Bengtsson and Gustavssen) show that the autocorrelation of error in forecasts (initial estimates) falls off rapidly with distance, so a weighting factor should likewise fall off rapidly. A number of experiments were conducted with real temperature data and real forecasts to determine empirical curves re- lating autocorrelation to distance and to forecast error. It was discovered that these could be fairly represented by the expression W = 1 - S-D 1/2 (122) where W is the autocorrelation, S is the standard deviation of the forecast error in the latitude and D is the distance in hundreds of kilometers. This expression was adopted directly for a weighting function with the limitations W > 0; S < 5. 74 There are 5 latitude zones in each hemisphere which are used to determine standard deviations of the data from the current estimate. These are bounded by: 90-74; 74-58; 58-42; 42-26; 26-0 degrees . 6.2.3 Report Quality Control In common with most objective analysis systems the validity of data is determined by comparison with the initial estimate for previous scan and with nearby data. In this analysis system there are two levels at which data can be rejected on each scan. First they are subject to fixed tolerances and secondly they are tested against the standard error for their latitude zone, which is determined from the data passing the gross tolerance tests. (1) To determine if data are to be rejected from fixed tolerances, it is first asked if a value deviates from the current estimate by more than 10°C. If so, it is then asked if this deviation exceeds the deviation of the nearest neighboring data by more than a fixed amount. If so, the value is rejected for the current scan. The fixed amount Is a function of scan, decreasing as the scans proceed. Limits imposed in this system are 5, 3, 2, and 1.5°C for the four scans respectively. (2) To determine if data are to be rejected at the second level, the correction which is indicated by each station at its closest neighboring gridpoint is evaluated against the corrections im- plied by other neighboring reports which influence that gridpoint. The individual correlations are given by Ci = Wi (0 i - F i ) 9 (123) where W is the weighting function, is the observed value, and F is the value interpolated from the gridpoint estimates. If 2 or less corrections are influencing the gridpoint, the report in question is rejected if its indicated correction exceeds twice the standard error of the latitude zone. If 3 or more corrections are influencing the gridpoint, the report in question is evaluated against an average of all the corrections. The average is formed, subject to the condition that none of the corrections deviate from the average by more than the standard error of the latitude zone. However, if any correction does, it is eliminated from the average. If that correction happens to be for the report in question, the report is rejected. If the number comprising the average falls below 3 the testing reverts to the procedure for 2 or less influencing reports. Report quality control can be bypassed by a sense switch option. The quality of radiance data has been found to be sufficiently good to obviate the need for quality control during the radiance analyses. 75 6.2.4 Gridpoint Correction The correction applied to each gridpoint on the first two scans is a simple average of the individual corrections as ob- tained from 6.2.3 (2). For the final two scans a modification is made to increase the correction with emphasis on the nearest reports. The procedure is to sum the corrections ordered by distance until the total sum of the weights reaches 0.8. At that point the remaining corrections are added but with diminished weight according to: w k = fo.8 - x; W- + W k j (124) where W^ is the new weight of the kth report. This modification was added when the ITPR scan mechanism failed since reports from rather distant but adjacent orbits appeared to be having too much influence on gridpoints close to the sub-orbital path. In the scanning mode reports from distant adjacent orbits are not usually selected as neighbors to a gridpoint. This modification has also been found useful for analyzing radiosonde reports. Either or both of the initial two scans may be skipped if the average of the standard error of all latitude zones is less than a pre-determ-ined number, 3.1 and 2.2, respectively. This criteria is frequently met during the summer at stratospheric levels in both hemispheres. 6 . 3 Computer Programs All of the analysis programs are done in three sections. The initial section obtains the gridpoint initial estimates from an archive tape and writes them on disc. The second section reads in data and initial estimates, performs the analysis, and writes the final gridded fields on disc. The final section adds the final fields to the archive tape and establishes disc files for use with other programs in the retrieval package. A schematic of the basic steps is as follows SECTION 1 GETGUES PRELIMINARY STEPS A - Read data flag and file skip number B - Flag o Skip designated number of files on input tape =o Do nothing I 76 FOR N INITIAL ESTIMATES A - Read 664 sixty-bit word record B - Unpack 5:1 to 3320 word record (72 x 43 + 8 word of identification ) C - Write words 1657-3312 (Southern Hemisphere) into ECS D - Encode level and date into words 1657 and 1658 E - Write words 1-1658 (Northern Hemisphere) as disc record I FOR N INITIAL ESTIMATES A - Read Southern Hemisphere from ECS B - Invert field to orient like Northern Hemisphere C - Write Southern Hemisphere as disc record SECTION 2 ANALYSIS PRELIMINARY STEPS A - Set constants B - Read sense switches for rejections, output print options ! REPORTS READ IN DATA A - Read 505 word retrieval record of five 101 word retrievals B - From first record extract date and time for return to analysis 77 SAVE DATA A - Loop through 5 retrievals; from latitude/longitude set up grid indices to store B - Store data sequentially in 900 word buffers for N fields, Northern Hemisphere; N fields, Southern Hemisphere C - Read next record and repeat A and B until end of data STORE DATA I A - Write 900 word buffers into ECS, grid indices (I and J) followed by levels , northern then southern hemisphere B - Print sample of data C - Return number of reports for each hemisphere 1000 BEGIN ANALYSIS FOR EACH HEMISPHERE A - Read locations from ECS and increment address pointer B - Order a subscript array in increasing values of J (pole to equator) C - Find number of stations in each of 5 latitude zones \ 73 SORT FIND NEIGHBORS FOR EACH GRIDPOINT A - Find beginning and end points in ordered subscript array for stations within 20 degree latitude. B - Store distance and subscript number of all stations also within longi- tude limit C - Sort eligible station by distance D - Beginning with closest station find quadrant about gridpoint and save if quadrant is not represented or no quadrant has been represented twice E - After finding 5 neighbors or exhausting eligible stations, pack 5 neighbors' subscripts into 1 word and store in array dimen- sioned 72x23 in position appro- priate to gridpoint F - Return to A until all gridpoints finished I FIND GRIDPOINT NEAREST EACH STATION A - Store in array the linear gridpoint subscript of the gridpoint nearest each station 100 DO ALL FIELDS FOR HEMISPHERE A - Read initial estimate from disc B - Read data from ECS and increment address pointer C - Test option to print contoured polar stereographic display of guess \ 79 ANALYZE FIELD 1 * POLSIER FORM POLSIER STEROGRAPHIC ARRAY A - Convert from 72x23 geographic grid to 53x57 polar stereographic f PRTW PRINT CONTROLLED MAP ANALYSER DO 4 SCANS OF GRIDPOINT CORRECTIONS A - Calculate array of values inter- polated on gridpoint field to location of each report B - Test reports against fixed criteria for rejection (if rejection option on). Print rejected reports C - Compute and print standard error for 5 latitude zones from retained reports D - Test average standard error to stop scan E - If rejection option on, for each test its influence on closest gridpoint as compared with influence of neighbors. Reject according to standard error of latitude zone, using maximum of 5, minimum of 0.9 F - For each gridpoint (except pole row) compute correction from retained reports and weighting function G - Add corrections to each gridpoint except pole row H - Assign average value of row next to pole to pole point. i 80 APPLY LIGHT SMOOTHER SUMMARIZE FIT A - Calculate array of values inter- polated in final grid/point field to location of reports B - Test reports for final rejection against fixed criteria C - Compute and print final standard error for 5 latitude zones D - Print all reports which deviate by more than 2 standard errors FIVE PT DO THREE PASSES WITH LIGHT 5-P0INT SMOOTHER PREPARE OUTPUT OUT WRITE OUTPUT FIELD A - If northern hemisphere save 1656 gridpoint field in ECS and return B - If southern hemisphere invert so pole row is last and store in second half of 3312 array C - Read northern hemisphere from ECS into first half of 3312 array, store identification at end of array D - Pack 5:1 into 664 word array E - Write record on disc 81 TEST OPTION FOR PRINT OF ANALYZED FIELD J 10O»-RETURN FOR NEXT FIELD OR PRINT REPORT COVERAGE 100O*-RETURN FOR SOUTHERN HEMISPHERE OR STOP POLSTER PRTW POUT PRINT POLAR STEREOGRAPHIC MAP OF REPORT LOCATIONS ON SAME BASE AS CONTOURED MAPS SECTION 3 SYSTEM HARDWARE AND UTILITY ROUTINES COPY OUTPUT FROM DISC TO ARCHIVE TAPE FOR ALL LEVELS i COPY OUTPUT ONTO PERMANENT DISC FILE FOR USE WITH OTHER PROGRAMS 92 7.0 Appendix 7.1 Regression Data Base Regression coefficients are employed heavily in the Nimbus-5 sounding data processing system: to correct ITPR radiances for angular (limb darkening) effects (section 4.1.1); to specify total outgoing long-wave infrared flux from ITPR measurements (section 5.4); to extrapolate soundings to high altitude for the transmittance adjustment calculations (section 3.4); and, most important, to specify first-guess retrieval profiles from various combinations of ITPR, SCR, and NEMS sounding radiances (section 5.1.2). As stated in the descriptions of these procedures, the regression coefficient sets are generated through radiance synthesis. The long-wave flux calculations employ a set of 100 soundings for which the complex, time-consuming computations of flux have previously been made (Wark et. al., 1962). The limb-darkening and retrieval regressions are generated from a set of soundings assembled especially for this purpose with the aid of personnel of the Upper Air Branch of NCAA's National Meteorological Center. The soundings consist of composite radiosonde/rocketsonde temp- erature profiles from the surface to 0.2 mb, and the corresponding (radiosonde) mixing ratio profiles from the surface to 100 mb. The original specifications for the data set called for 100 soundings, distributed as uniformly as possible in time of year, In each of six latitude bands: 90N-60N, 60N-30N, 30N-Eq, Eq-30S, 30S-60S, 60S-90S. Because of the relative scarcity of rocketsonde observations in the Southern Hemisphere, it was necessary to "mirror", by six months, several Northern Hemisphere soundings. The actual distribution of soundings by month and observation site in each latitude zone is given in the accom- panying table 7-1. Because of range safety constraints on the launching of small meteorological rockets, the associated radiosondes tend to be biased toward fair weather conditions - light winds, small amounts of cloudiness in the troposphere. Time-series analysis by the Upper Air Branch of a small sample of data indicated that most rocket firings took place at the beginning of a period of fine weather. To lessen the obvious fair- weather bias of the original data set, each rocket sounding was mated to another radiosonde, from either the launch site itself or a nearby regular upper-air station, taken one to two days before the rocket ob- servation. Since upper-stratospheric temperature changes are generally slow, this "doubling" of soundings did not induce any significant "smearing" of high-level thermal structure. In those few situations where rapid changes were occurring, such as in December 1967 at West Geirinish, Scotland, the soundings were not doubled. Some independent additions were made, and the data set was finalized at 1200 soundings. After some initial experimentation, the latitudinal stratification was broadened: the 90-60, 60-30, and 30-0 degree bands in both hemispheres were combined, giving three zones of 400 soundings each. 83 TABLE 7-1. Source and Distribution of Soundings in Regression Data Base Oct Nov Dec Jan Feb Mar Total Apr' May Jun Jul Aug Sep Total SAMPLE A Heiss Is. 81N 57E 1 3 3 5 5 3 20 Thule 77N 69W 4 2 1 3 2 12 F . Greely 64N 146W 14 4 4 7 3 3 25 Churchill 59N 94W 4 3 4 6 3 3 23 W. Geirinish 57N 7W 1 2 6 4 5 2 20 100 SAMPLE B F. Greely 64N 146W 1 1 1 3 2 1 9 Churchill 59N <34W 2 1 2 4 1 1 11 W. Geirinish 57N 7W 1 1 5 2 1 1 11 Primrose 55N HOW 1 2 2 1 1 7 Volgagrad 49N 45E 2 2 2 2 2 2 12 Wallops Is. 38N 75W 4 2 3 3 3 4 19 Pt . Mugu 34N 119W 3 3 3 2 2 2 15 W. Sands 32N 106W 3 3 2 2 3 3 16 100 SAMPLE C C. Kennedy 28N 81W 3 3 3 3 3 3 18 B. Sands 22N 160W 3 3 3 3 3 3 18 Antigua 17N 62W 2 3 3 3 3 2 16 Eniwetok UN 162E 1 1 Kwajalein 9N 167E 1 1 Ft. Sherman 9N 80W i+ 3 4 3 3 3 20 Thumba 9N 77E 2 2 Ascension Is .8S 14W 4 4 4 5 3 4 24 100 SAMPLE D C. Kennedy 28N 81W 3 4 4 4 3 2 20 B. Sands 22N 160W 2 4 5 5 5 3 24 Antigua 17N 62W 3 3 4 2 3 1 16 Ft . Sherman 9N 80W 4 4 3 4 15 Ascension Is . 8S 14W 4 4 5 5 2 2 22 Natal 6S 35W 1 1 1 3 100 SAMPLE E F. Greely 64N 146W 2 2 4 1 3 12 Churchill 59N 94W 6 1 4 4 3 18 Primrose 55N now 4 3 1 8 Wallops Is. 38N 75W 1 3 3 4 3 2 16 Pt. Mugu 34N 119W 2 3 4 3 3 2 17 W. Sands 32N 106W 1 6 1 4 4 3 19 Ship 30-60S 1 4 5 Chamical 30S 66W 1 1 Mar Chi quit a 38S 57W 1 2 1 4 100 SAMPLE F Thule 77N 69W 6 7 6 6 6 2 33 F. Greely 64N 146W 8 6 6 2 7 1 30 Churchill 59N 94W 8 3 5 6 4 26 Molodeznaia 68S 46E 4 3 2 9 McMurdo 78S 167E 2 2 100 8*t The retrieval regressions for generating guess profiles of temperature and mixing ratio are determined in the three zones, using the full sample. Limb-darkening and radiosonde extrapolation regres- sions are constructed from a global set of 120 soundings , 40 in each latitude band. Statistics concerning the limb corrections are presented in table 7-2. Figure 7-1 presents the standard error of estimate (square root of the unexplained variance) as a function of pressure for the temperature-retrieval regressions , in the three latitude zones described above, for the three principal sensor /channel combinations described in section 5.1.5. 7.2 System Data Flow The overall flow of data through the Nimbus -5 Sounding Data Software System is depicted in figure 7-2, in which the rectangles denote major software modules and the circles, rotating storage devices - magnetic tape and/or disk. The various processing steps have been des- cribed in detail in the main body of this report. The double arrow from surface analysis to sounding radiance, identified as "on-line, one-day delayed," indicates that "today's" analysis will be employed as the first guess for "tomorrow's" processing. The "as necessary" in the definition of the broken line occurs when there are significant changes in the transmittance-adjustment parameters B and y. As the system evolved at NOAA/NESS, data were processed in one-day batches of (usually) 12 orbits; hence the origin of the word "day" in the legend of the flow diagram. The system has been implemented at GISS, with a basic processing unit of three orbits; while there have been major modifications to the software, the fundamental data flow remains essentially the same. Thus the word "run" may be substituted for "day". The meteorological output of the Nimbus- 5 sounding system is summarized in table 7-3. 85 TABLE 7-2. ITPR Angular Correction Statistics ZENITH ANGLE * 1.06 DEGREES CHANNEL STANDARD ERROR EXPLAINED VARIANCE 1 .1028E-01 .699? 2 .1170E+01 .7008 3 .4364E-04 .9955 4 .2706E-04 .9985 5 .5396E-04 .9499 6 .7349E-04 .9864 7 .7&68E-04 .9651 REGRESSION COEFFICIENTS CHANNEL CO C2 C3 C4 C5 C6 C7 1 -.2590E-01 .2218F-02-.1920E-02 .4477E-02- . 2458E-02 .7093E-03- .2678E-02 2 -.2329E+01 .1572E+00 .7219E-01 .3599E*00- . 1 662E+00 .2099E-0 1-.3940E *00 3 -.2284E-03 .3399F-04 .2007E-04- .3694E-04 . 7062E-05- .2309E-05- . 1 748E-04 4 -.B581E-04-.9971E-05 . 7673E-0<+- . 3194E-04- .2308E-04-. 1 325E-06-.8561E-05 5 .4^08E-03 .1616E-04-.5883E-04 .841 0E-04- .8473E-05- .41 01E-Q4 .4333E-05 6 .3572E-03-.88A4E-05 . 3038E-0^- . 3351 E-04 .2222E-03- .2053E-03- .3493E-05 7 -.1604E-03-.3120E-0S .9630E-04- .8351E-04 .2470E-04-.9054E-06- .3220E-04 ZENITH ANGLE = 3.17 DEGREES CHANNEL STANDARD ERROR EXPLAINED VARIANCE 1 .1027E-01 .7008 2 .1168E*01 .7026 3 .3940E-03 .9955 4 .2394E-03 .9986 5 .4733E-03 .9525 6 .6547E-03 .9867 7 .6848E-03 .9657 REGRESSION COEFFICIENTS CHANNEL CO C2 C3 C4 C5 C6 C7 1 -.2848E-01 .???OE-0?-.1907E-02 .4522E-02- .2376E-02 .6624E-03- .2706E-02 2 -.2627E + 01 .1612E + 00 .6391E-01 .36700 3 -.1891E-01 .2833E-0? . 1465E-02- .2916E-02 .5639E-03- . 1 889E-03-. 1 390E-02 4 -.7750E-02-.8156F-03 .6274E-Q2" .2649E-02- . 1872E-02 .6723E-05- .6848E-03 5 .3677E-01 .1385E-0^-.5003E-02 . 7009E-02- .7762E-03- . 3323E-02 .3929E-03 6 .2716E-01-.6304E-03 .2192E-02- .2536E-02 . 1 788E-0 1- . 1 654E-0 1-.2252E-03 7 -.1438E-01-.29Q7E-03 . 7996E-02-.6952E-02 .21 21E-02-.9487E-04- .2648E-02 ZENITH ANGLE = 11.63 DEGREES CHANNEL STANDARD ERROR REGRESSION COEFFICIENTS CHANNEL CO C2 .1050E-01 .1194E+01 .5381E-02 .3260E-02 .6438E-02 .8966E-02 .9276E-02 EXPLAINED VARIANCE .6960 .6977 .9954 .9986 .9518 .9866 .9659 C7 .2723E-02 .3954E*00 .2180E-02 .1053E-02 .6252E-03 .7376E-03 .4010E-02 88 ZENITH ANGLE = 13.76 DEGREES CHANNEL STANDARD ERROR EXPLAINED VARIANCE ) .1064E-01 .6918 2 .1209E*01 .6935 3 .7534E-02 .9955 4 .4556E-0? .9986 5 .9201E-02 .9498 6 .1267E-01 .9865 7 .1315E-01 .9652 REGRESSION COEFFICIENTS CHANNEL CO C2 C3 C4 C5 C6 C7 1 -.2513E-01 .2206E-0?- e ]781E-O2 . 4338E-02- .2583E-02 .8207E-03- .2745E-02 2 -.2346E*01 .1594000 .7953E-01 . 3545E*00- . 1 81 1E*00 . 3400E-0 1- . 3993E+00 3 -.3920E-01 .5909E-0? . 3205E-02- .6251 E-02 . 1 157E-02- .3470E-03-.2928E-02 4 -.1674E-01-.1701E-0? .1320E-01-.5522E-02-.3968E-02 .251 1E-Q4-. 1476E-02 5 .7730E-01 .2806E-02-.1026E-01 . 1449E-01 - . 1 660E-02- .6878E-02 .8287E-03 6 .6041E-01-.1762E-02 .5873E-02- .6163E-02 .3754E-0 1 - .3453E-0 1- .7422E-03 7 -.3040E-01-.4029E-03 . 1623E-0 1 - . 141 8E-01 .4368E-02- .2296E-03-.5497E-02 ZENITH ANGLE = 15.89 DEGREES CHANNEL STANDARD ERROR EXPLAINED VARIANCE 1 .1070E-01 .6937 2 .1216E*01 .6945 3 .1016E-01 .9954 4 .6238E-02 .9986 5 .1215E-01 .9509 6 .1713E-01 .9862 7 .1753E-01 .9655 REGRESSION COEFFICIENTS CHANNEL CO C2 C3 C4 C5 C6 C7 1 -.2641E-01 .2263E-02-.1950E-02 .4533E-02-.2673E-02 .8804E-03-.2727E-02 2 -.?395E*01 .1619E*00 .7424E-01 . 3604E*00-. 1920E*00 .4246E-01-.4003E *00 3 -.5193E-01 .8043E-02 . 3903E-02- .8072E-02 . 1483E-02- .4854E-03- .3873E-02 4 -.2095E-01-.2361E-0? . 1 790E-0 1 - .7493E-02- .5297E-02 . 1530E-04-.2046E-02 5 .9889E-01 .4022E-0?-.1449E-01 . 1990E-0 1- .2252E-02-.9240E-02 .1277E-02 6 .8549E-01-.2396E-0? .3012E-02- .8335E-02 .4951E-0 1- .4564E-01- . 1 040E-02 7 -.3546E-01-.8974E-03 .2273E-0 1- . 1963E-01 .5836E-02- .2205E-03-.7569E-02 89 ZENITH ANGLE = 1ft. 03 DEGpEES CHANNEL STANDARD ERROR REGRESSION COEFFICIENTS CHANNEL CO C2 .1094E-01 .1237E+01 .1304E-01 .7953E-02 .1599E-01 .2082E-01 .2251E-01 C3 EXPLAINED VARIANCE .6853 .6890 .9955 .9986 .9488 .9879 .9659 C4 C5 C6 C7 _.?484E-01 .2102E-0?-.1365E-02 .4 1 31E-02- .2545E-02 .8480E-03- .2883E-02 -.2302E+01 .1444E+00 .1380E+00 . 31 66E*00- . 1 754E*00 .3698E-01- .4165E *00 -.6631E-01 .1027F-01 .5425E-02- . 1 067E-0 1 .2054E-02- .6870E-03- .5097E-02 -.2751E-01-.2835F-0 2 . 2261E-0 1 - .94 1 1 E-02-.6816E-02-.5329E-04-.2546E-02 .1299E+00 .4726E-02-.1742E-01 .2480E-0 1- .2974E-02-. 1 168E-0 1 .1450E-02 .1027E*00-.2932F-0 2 . 1 01 6E-0 1 - . 1 053E-0 1 .6401 E-01- .5889E-0 1-. 1460E-02 -.4625E-01-.7032F-03 .2828E-0 1 - .2482E-01 .7715E-02-.4996E-03-.9596Er02 ZENITH ANGLE = 20.17 OEGPEES CHANNEL STANDARD ERROR EXPLAINED VARIANCE 1 .1093E-01 .6922 2 .1241E*01 .6927 3 .1638E-01 .9955 4 .1001E-01 .9985 5 .2001E-01 .9489 6 .2645E-01 .9877 7 .2881E-01 .9647 REGRESSION COEFFICIENTS CHANNEL 1 2 3 4 5 6 7 CO C2 C3 C4 C5 C6 C7 -.2899E-01 .2317F-02-.2095E-02 .4862E-02- .2650E-02 .7707E-03- .2786E-02 -.2691E+01 ,172ftE*00 .4551E-01 .4040E*00~. 1 880E*00 .2816E-01- .4044E *00 -.8285E-01 .1293E-01 .671 7E-02- . 1 3^6E-0 1 .2455E-02-. 7338E-03-.6339E-02 -.3257E-01-.3662E-02 . 2883E-0 1- . 121 7E-0 1-.8660E-02 .8737E-04- . 3303E-02 .1634E+00 .6025E-02-.2226E-01 .3 l<*9E-0 1 -. 3854E-02-. 1469E-01 .1933E-02 . 1249E*00-.354ftE-02 . 1 224E-0 1- . 1 267E-01 .7949E-01 - .7322E-0 1~. 1 786E-02 -.6023E-01-.5245E-0 3 . 3450F-0 1 - . 3050E-0 1 .9384E-02-.471 3E-0 3-. 1 189E-01 90 ZENITH ANGLE = 22.3? DEGREES CHANNEL STANDARD ERROR EXPLAINED VARIANCE 1 .U25E-01 .6807 2 ,1271E*01 .6845 ) .2032E-01 .9954 4 .12066-01 .9986 5 .2458E-01 .9488 h .3269E-01 .9877 7 .3458E-01 .9664 REGRESSION COEFFICIENTS CHANNEL CO C? C3 C4 C5 C6 C7 1 -.2508E-01 .2229F-02-.1699E-02 .4449E-02- . 2707E-02 .8784E-03- .2859E-02 2 -.2247E*01 .]592E*0n .9941E-01 .3527E*00- . 1 962E + 00 .4331E-0 1 - .4148E ♦OO 3 -.1045£*00 .1577E-01 .8690E-02- . 1669E-0 1 .3078E-02- .8852E-03- . 7971E-02 4 -.4085E-01-.4562E-0? . 3583E-0 1 - . 1541 E-0 1 - . 1 056E-0 1 . 1 798E-03-.41 08E-02 5 .2022E+00 .7477E-02-.2761E-01 .3889E-0 1 - .5035E-02- . 1 789E-0 1 .2476E-02 6 .lf35E*00-.4920E-0? . 1626E-0 1 - . 1579E-0 1 .9692E-01 - .8924E-0 1" .2442E-02 7 -.7388E-01-.1206E-0? .4431E-0 1" . 3905E-0 1 . 1 207E-0 1 - .5726E-03- . 1499E-01 ZENITH ANGLE = 24.49 DEGREES CHANNEL STANDARD ERROR EXPLAINED VARIANCE 1 .1134E-01 .6825 2 .1281E+01 .6860 3 .2488E-01 .9953 4 .1477E-01 .9986 5 .2954E-01 .9491 6 .3863E-01 .9883 7 .4213E-01 .9660 REGRESSION COEFFICIENTS CHANNEL CO C2 C3 C4 C5 C6 C7 1 -.2747^-01 .2102F-02-.1269E-02 .41 73E-02-.2779F-02 . 1 01 1E-02- .2953E-02 2 -.2558E*01 .1509E»00 .1306E+00 .3371E+00- .2031E*00 .5382E-0 1- .4237E *00 3 -.1253E*00 .1959F-01 .9076E-02- . 1 948E-01 . 3606E-02- . 1 096E-02-.9296E-02 4 -.4898E-01-.5196E-0? .431 OE-0 1- . 1848E-01 - . 1274E-01 . 1471E-03-.4953E-02 5 .2409E*00 .K816E-0?-.3305E-01 .4691 E-01- .6350E-02- .21 36E-0 1 .3066E-02 6 .1793E*00-.550?E-0? . 1886E-0 1- . 1859E-0 1 . 1 158E + 00-. 1 067E»00-. 3026E-02 7 -.3657E-01-.9452E-03 .5235E-0 1 - .4652E-0 1 . 1469E-0 1 -.8991 E-03- . 1798E-0 1 91 ZENITH ANGLE = 26.66 DEGPEES CHANNEL STANDARD ERROP EXPLAINED VARIANCE 1 .1150E-01 .6828 2 ,1305E*01 .6824 3 .2964E-01 .9953 4 .1724E-01 .9986 5 .3S34E-01 .9484 6 .4622E-01 .9883 7 .5088E-01 .9651 REGRESSION COEFFICIENTS CHANNEL CO C? C3 C4 C5 C6 C7 1 -.2916E-01 .2422E-0?-.?324E-02 .5221E-02- .2805E-02 .7659E-03- .2843E-02 2 -.2759E+01 .1826E+00 .2949E-01 .4349E*00- .204 1 E*00 . 3055E-0 1-.41 28E *00 3 -.1530E*00 .2316E-01 . 1 1 26E-0 1- .2314E-0 1 .4300E-02-. 1366E-02-. 1 126E-0 1 4 -.6459E-01-.6506E-02 .5 1 96E-0 1" .2235E-0 1 - . 1 493E-0 1 .7650E-04- .6126E-02 5 .?953E*00 .1081E-01-.4046E-01 .5633E-0 1 - . 8546E-02- .2 O- 0.1 0.2 0.3 0.5 0.7 1 2 3 5 7 10 20 30 50 70 100 200 300 500 - 700 : 1000 1 1 1 - 1 1 1 1 f ITPR+NEMS+SCR -- NEMS+SCR+T ITPR+SCR Standard Error (°C Fig. 7 - 1 NIMBUS 5 SOUNDING DATA PROCESSING SYSTEM ON-LINE, SAME DAY OFF-UNE, AS NECESSARY > ON-UNE. ONE-DAY-DELAYEO REGRESSION LiMB-DARKENING CORRECTION (ITPR) INGEST REGRESSION LONG-WAVE FLUX SPECIFICATION (ITPR) REGRESSION T(p) vs R(j/) ITPR, SCR+NEMS W(p) vs R(y) ITPR SOUNDING RADIANCE GLOBAL SURFACE TEMPERATURE ANALYSIS GLOBAL STRATOSPHERIC RADIANCE ANALYSIS SATELLITE/ RADIOSONDE MATCH TRANSMITTANCE/ RADIANCE TUNER I _ VERIF. STAT. GLOBAL MULTI-LEVEL TEMPERATURE ANALYSIS © Fig. 7- 2 97 TABLE 7-3 Meteorological Output of Nimbus- 5 System .rameter Source Hor izontal Scale (km) T(p) 15 ym C0 2 , 0.5cm 2 400, 150 q(p) 20 ym H 2 400 Wrp 20 ym H 2 0, 22 + 31 GHz 400 T s fc 3.7-ym, 11-ym windows 400, 150 P C ,N 15 ym, 11 ym 400 Fi 11 - 18 ym 400 98 REFERENCES Barrett, A. H. , and Chung, V. K. , "A Method for the Determination of High-Altitude Water-Vapor Abundance from Ground-Based Microwave Observations," Journal of Geophysical Research, Vol. 67, No. 11, 1962, pp. 4259-426B. Bengtsson, L. , and Gustavsson, N. , "An Experiment in the Assimilation of Data in Dynamical Analysis," Tellus, 23, 1971, pp. 328-336. Davis, P. A., "Universal Transmittance Representations for Application to ITPR Measurements," Final Report prepared for NOAA/NESS, Contract 2 - 35136, St anford Research Institute, Menlo Park, California, May 1972, 45 pp. Fritz, S., Wark, D. Q., Fleming, H. E., Smith, W. L., Jacobowitz, H. , Hilleary, D. 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F. , "On the Shape of Collision Broadened Lines," Reviews of Modern Physics , Vol. 17, Nos. 2 and 3, 1945, pp. 227-236. Wark, D. Q. , Yamamoto, G. and Lienesch, J., "Infrared Flux and Surface Temperature Determinations From TIROS Radiometer Measurements," M.S.L. Report No. 10, U. S. Dept. of Commerce, Wash. D.C., Aug. 1962 84 pp. Wark, D. Q. , and Hilleary D. , ESSA, "Atmospheric Temperature: Successful Test of Remote Probing," Science , 165, Sept. 1969, pp. 1256-1258. Winston, J. S., Smith, W. L. , and Woolf, H. M. , "The Global Distri- bution of Outgoing Long-Wave Radiation Derived From SIRS Radiance Measurements," Proceedings of the Conference on Atmospheric Radiation , Fort Collins, Colorado, Aug. 7-9, 1972, pp. 221-227. (Continued from inside front cover) NESS 33 Use of Satellite Data in East Coast Snowstorm Forecasting. Frances C. Parmenter, February 1972. (COM-72-10482) NESS 34 Chromium Dioxide Recording—Its Characteristics and Potential for Telemetry. Florence Nesh, March 1972. (COM-72-10644) NESS 35 Modified Version of the Improved TIROS Operational Satellite (ITOS D-G). A. Schwalb, April 1972. (COM-72-10547) NESS 36 A Technique for the Analysis and Forecasting of Tropical Cyclone Intensities From Satellite Pictures. Vernon F. Dvorak, June 1972. (COM-72-10840) NESS 37 Some Preliminary Results of 1971 Aircraft Microwave Measurements of Ice in the Beaufort Sea. Richard J. DeRycke and Alan E. Strong, June 1972. (COM-72-10847) NESS 38 Publications and Final Reports on Contracts and Grants, 1971--NESS. June 1972. (COM-72-11115) NESS 39 Operational Procedures for Estimating Wind Vectors From Geostationary Satellite Data. Mi- chael T. Young, Russell C. Doolittle, and Lee M. Mace, July 1972. (COM-72-10910) NESS 40 Convective Clouds as Tracers of Air Motion. Lester F. Hubert and Andrew Timchalk, August 1972. (COM-72-11421) NESS 41 Effect of Orbital Inclination and Spin Axis Attitude on Wind Estimates From Photographs by Geosynchronous Satellites. Linwood F. Whitney, Jr., September 1972. (COM-72-11499) NESS 42 Evaluation of a Technique for the Analysis and Forecasting of Tropical Cyclone Intensities From Satellite Pictures. Carl 0. Erickson, September 1972. (COM-72-11472) NESS 43 Cloud Motions in Baroclinic Zones. Linwood F. Whitney, Jr., October 1972. (COM-73-10029) NESS 44 Estimation of Average Daily Rainfall From Satellite Cloud Photographs. Walton A. Follansbee, January 1973. (COM- 7 3- 105 39) NESS 45 A Technique for the Analysis and Forecasting of Tropical Cyclone Intensities From Satellite Pictures. (Revision of NESS 36) Vernon F. Dvorak, February 1973. (COM-73-10675) NESS 46 Publications and Final Reports on Contracts and Grants, 1972--NESS. April 1973. NESS 47 Stratospheric Photochemistry of Ozone and SST Pollution: An Introduction and Survey of Se- lected Developments Since 1965. Martin S. Longmire, March 1973. (COM-73-10786) NESS 48 Review of Satellite Measurements of Albedo and Outgoing Long-Wave Radiation. Arnold Gruber, July 1973. (COM-73-11443) NESS 49 Operational Processing of Solar Proton Monitor Data. Louis Rubin, Henry L. Phillips, and Stanley R. Brown, August 1973. (C0M-73-11647-AS) NESS 50 An Examination of Tropical Cloud Clusters Using Simultaneously Observed Brightness and High Resolution Infrared Data From Satellites. Arnold Gruber, September 1973. (C0M-73-11941/4AS) NESS 51 SKYLAB Earth Resources Experiment Package Experiments in Oceanography and Marine Science. A. L. Grabham and John W. Sherman, III, September 1973. NESS 52 Operational Products From ITOS Scanning Radiometer Data. Edward F. Conlan, October 1973. (COM-74-10040) NESS 53 Catalog of Operational Satellite Products. Eugene R. Hoppe and Abraham L. Ruiz (Editors). In press, 1974. NESS 54 A Method of Converting the SMS/GOES WEFAX Frequency (1691 MHz) to the Existing APT/WEFAX Fre- quency (137 MHz). John J. Nagle, April 1974. NESS 55 Publications and Final Reports on Contracts and Grants, 1973 - NESS. April, 1974. NESS 56 What Are You Looking at When You Say This Area Is a Suspect Area for Severe Weather? Arthur H. Smith, Jr., in press, 1974. PENN STATE UNIVERSITY LIBRARIES HIIIIHIIIII