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## Abstract

Wide-field-of-view (WFOV) radiometers have been flown as part of the Earth Radiation Budget instrument on the Nimbus 6 and 7 spacecraft and as part of the Earth Radiation Budget Experiment (ERBE) instruments aboard the ERBE spacecraft and also the NOAA 9 and 10 operational spacecraft. The measurement is the integral of the reflected solar flux distribution at the top of the earth-atmosphere system over the field-of-view of the radiometer. This paper develops the solution to this two-dimensional integral equation for the albedo distribution in terms of the measurements.

The assumption is made that the bidirectional function is known and is invariant with longitude. The resulting axial symmetry of the integral operator permits the separation of the two-dimensional integral equation into a set of uncoupled one-dimensional integral equations for the latitudinal functions. This permits a better understanding of the problem while also considerably reducing the computer resources required for the solution. The one-dimensional integral equations are each approximated by a matrix equation. The matrices are each ill-conditioned, due to the resolution of WFOV data. The solution is expressed in terms of observable and unobservable components. In order to produce acceptable albedo fields from WFOV measurements, it is necessary to use ancillary data for these unobservable components. The limits of resolution are also indicated.

## Abstract

Wide-field-of-view (WFOV) radiometers have been flown as part of the Earth Radiation Budget instrument on the Nimbus 6 and 7 spacecraft and as part of the Earth Radiation Budget Experiment (ERBE) instruments aboard the ERBE spacecraft and also the NOAA 9 and 10 operational spacecraft. The measurement is the integral of the reflected solar flux distribution at the top of the earth-atmosphere system over the field-of-view of the radiometer. This paper develops the solution to this two-dimensional integral equation for the albedo distribution in terms of the measurements.

The assumption is made that the bidirectional function is known and is invariant with longitude. The resulting axial symmetry of the integral operator permits the separation of the two-dimensional integral equation into a set of uncoupled one-dimensional integral equations for the latitudinal functions. This permits a better understanding of the problem while also considerably reducing the computer resources required for the solution. The one-dimensional integral equations are each approximated by a matrix equation. The matrices are each ill-conditioned, due to the resolution of WFOV data. The solution is expressed in terms of observable and unobservable components. In order to produce acceptable albedo fields from WFOV measurements, it is necessary to use ancillary data for these unobservable components. The limits of resolution are also indicated.

## Abstract

Data from the Earth Radiation Budget Experiment scanning radiometer aboard the *NOAA*-9 operational meteorological satellite are used to investigate the spatial variability of outgoing longwave radiation (OLR). Daily and monthly radiation maps at 2.5° latitude–longitude scale are used as a basis for the study. The regions of greatest variability are in the tropics and subtropics. Storm tracks such as the South Pacific convergence zone appear as regions of high OLR variability. Spatial spectra in longitude show two regimes of OLR. At large scales (wavenumbers less than 6), the spatial spectrum is flat. For wavenumbers greater than 10, the spectra decrease as wavenumber to the −3 power. The spatial spectrum of daily anomalies from the mean is a strong function of latitude and season, with interesting features. Correlations of daily anomalies from the monthly mean decrease exponentially in latitude but have a damped-wave structure in longitude. The spatial variability of the daily maps, as measured by degree variance, have 10 times the power at degree 24 than the monthly maps, but at scales between 1 and 10, the degree variance is practically the same for daily as for monthly.

## Abstract

Data from the Earth Radiation Budget Experiment scanning radiometer aboard the *NOAA*-9 operational meteorological satellite are used to investigate the spatial variability of outgoing longwave radiation (OLR). Daily and monthly radiation maps at 2.5° latitude–longitude scale are used as a basis for the study. The regions of greatest variability are in the tropics and subtropics. Storm tracks such as the South Pacific convergence zone appear as regions of high OLR variability. Spatial spectra in longitude show two regimes of OLR. At large scales (wavenumbers less than 6), the spatial spectrum is flat. For wavenumbers greater than 10, the spectra decrease as wavenumber to the −3 power. The spatial spectrum of daily anomalies from the mean is a strong function of latitude and season, with interesting features. Correlations of daily anomalies from the monthly mean decrease exponentially in latitude but have a damped-wave structure in longitude. The spatial variability of the daily maps, as measured by degree variance, have 10 times the power at degree 24 than the monthly maps, but at scales between 1 and 10, the degree variance is practically the same for daily as for monthly.

## Abstract

Lapse rate, moist adiabatic lapse rate and the critical lapse rate for baroclinic adjustment are calculated as was done by Stone and Carlson using a different data set covering both hemispheres. Results show very good agreement in low latitudes, where temperature lapse rate can be approximated by the moist adiabatic lapse rate. In midlatitudes of the Northern Hemisphere, the lapse rate agrees with the critical lapse rate for baroclinic adjustment. In midlatitudes of the Southern Hemisphere, the lapse rate follows the critical lapse rate for baroclinic adjustment with a 15° lag.

## Abstract

Lapse rate, moist adiabatic lapse rate and the critical lapse rate for baroclinic adjustment are calculated as was done by Stone and Carlson using a different data set covering both hemispheres. Results show very good agreement in low latitudes, where temperature lapse rate can be approximated by the moist adiabatic lapse rate. In midlatitudes of the Northern Hemisphere, the lapse rate agrees with the critical lapse rate for baroclinic adjustment. In midlatitudes of the Southern Hemisphere, the lapse rate follows the critical lapse rate for baroclinic adjustment with a 15° lag.

## Abstract

The shape factor technique is routinely used to invert wide-angle radiometric measurements at satellite altitude to flux at the top of the atmosphere. The derivation of a shortwave shape factor requires assumptions on both the viewed radiation field and the angular distribution of the radiance. This paper describes the effect on the shape factor of assuming a constant flux field, a constant albedo field, and a variable albedo field. In addition, three assumptions on the angular distributions are investigated: Lambertian, an analytic model, and the Earth Radiation Budget Experiment (ERBE) bidirectional models.

The accuracies and resolutions of the shape factor flux estimates arising from these assumptions are determined by simulating the shape factor inversion technique with ERBE scanner data. First, the scanner data are summed at satellite altitude to simulate the wide-angle radiometric measurements. Radiant flux at the top of the atmosphere is then estimated from these simulated wide-angle measurements with the various shape factors and compared to the original scanner flux field. The resulting biases and variances are given for both the ERBE medium-field-of-view and wide-field-of-view radiometers.

## Abstract

The shape factor technique is routinely used to invert wide-angle radiometric measurements at satellite altitude to flux at the top of the atmosphere. The derivation of a shortwave shape factor requires assumptions on both the viewed radiation field and the angular distribution of the radiance. This paper describes the effect on the shape factor of assuming a constant flux field, a constant albedo field, and a variable albedo field. In addition, three assumptions on the angular distributions are investigated: Lambertian, an analytic model, and the Earth Radiation Budget Experiment (ERBE) bidirectional models.

The accuracies and resolutions of the shape factor flux estimates arising from these assumptions are determined by simulating the shape factor inversion technique with ERBE scanner data. First, the scanner data are summed at satellite altitude to simulate the wide-angle radiometric measurements. Radiant flux at the top of the atmosphere is then estimated from these simulated wide-angle measurements with the various shape factors and compared to the original scanner flux field. The resulting biases and variances are given for both the ERBE medium-field-of-view and wide-field-of-view radiometers.

## Abstract

Monthly averaged, resolution enhanced global distributions of the Earth's emitted radiation, as measured by the Nimbus-6 Earth Radiation Budget (ERB) wide field of view radiometers, have been analyzed for 1 year of data from July 1975 to June 1976. These distributions am expressed in terms of spherical harmonic coefficients, and time and space variability of the emitted radiation field is studied in terms of these coefficients. The average annual distribution amounts for 78% of the space-time power, and the annual cycle accounts for 17% of the power. Spatial variations over the globe are described in terms of degree variance, and longitudinal variations are described in terms of spectral power as a function of latitude. The longitudinal spectra were found to vary strongly with lime.

## Abstract

Monthly averaged, resolution enhanced global distributions of the Earth's emitted radiation, as measured by the Nimbus-6 Earth Radiation Budget (ERB) wide field of view radiometers, have been analyzed for 1 year of data from July 1975 to June 1976. These distributions am expressed in terms of spherical harmonic coefficients, and time and space variability of the emitted radiation field is studied in terms of these coefficients. The average annual distribution amounts for 78% of the space-time power, and the annual cycle accounts for 17% of the power. Spatial variations over the globe are described in terms of degree variance, and longitudinal variations are described in terms of spectral power as a function of latitude. The longitudinal spectra were found to vary strongly with lime.

## Abstract

The problem of relating satellite measurements from wide field-of-view (WFOV) radiometers to the radiant exitance emitted from the top of the atmosphere is treated. The problem is formulated as an integral equation to be solved for the radiant exitance distribution in terms of the measurements. An analytical solution to this integral equation in terms of spherical harmonies is presented for the case in which the directional dependence of the outgoing radiation is a function of zenith angle only. It is shown that the resolution which can be obtained under real conditions is limited.

The sensitivity of the derived radiant exitance distribution to the directional dependence of the out-going radiation is studied, and results are presented for WFOV flat-plate and spherical radiometers and for restricted field-of-view flat-plate radiometers. It is demonstrated that this sensitivity is a function of the scale of spatial resolution; thus higher resolutions in the radiant exitance distribution are more sensitive to variations in the directional dependence.

The technique is applied to measurements of earth-emitted radiation from the Nimbus 6 ERB (Earth Radiation Budget) experiment WFOV radiometer to produce a resolution enhanced map of emitted radiation for the month of August 1975. For this case, the limit of resolution appeared to be spherical harmonies of degree 15. Comparison with results from the ERB scanning radiometer shows very good agreement.

## Abstract

The problem of relating satellite measurements from wide field-of-view (WFOV) radiometers to the radiant exitance emitted from the top of the atmosphere is treated. The problem is formulated as an integral equation to be solved for the radiant exitance distribution in terms of the measurements. An analytical solution to this integral equation in terms of spherical harmonies is presented for the case in which the directional dependence of the outgoing radiation is a function of zenith angle only. It is shown that the resolution which can be obtained under real conditions is limited.

The sensitivity of the derived radiant exitance distribution to the directional dependence of the out-going radiation is studied, and results are presented for WFOV flat-plate and spherical radiometers and for restricted field-of-view flat-plate radiometers. It is demonstrated that this sensitivity is a function of the scale of spatial resolution; thus higher resolutions in the radiant exitance distribution are more sensitive to variations in the directional dependence.

The technique is applied to measurements of earth-emitted radiation from the Nimbus 6 ERB (Earth Radiation Budget) experiment WFOV radiometer to produce a resolution enhanced map of emitted radiation for the month of August 1975. For this case, the limit of resolution appeared to be spherical harmonies of degree 15. Comparison with results from the ERB scanning radiometer shows very good agreement.

## Abstract

The effects of the earth’s oblateness on computation of its radiation budget from satellite measurements are evaluated. For the Clouds and the Earth’s Radiant Energy System (CERES) data processing, geolocations of the measurements are computed in terms of the geodetic coordinate system. Using this system accounts for oblateness in the computed solar zenith angle and length of day. The geodetic and geocentric latitudes are equal at the equator and poles but differ by a maximum of 0.2° at 45° latitude. The area of each region and zone is affected by oblateness as compared to geocentric coordinates, decreasing from zero at the equator to 1.5% at the poles. The global area receiving solar radiation is calculated using the equatorial and polar axes. This area varies with solar declination by 0.0005. For radiation budget computations, the earth oblateness effects are shown to be small compared to error sources of measuring or modeling.

## Abstract

The effects of the earth’s oblateness on computation of its radiation budget from satellite measurements are evaluated. For the Clouds and the Earth’s Radiant Energy System (CERES) data processing, geolocations of the measurements are computed in terms of the geodetic coordinate system. Using this system accounts for oblateness in the computed solar zenith angle and length of day. The geodetic and geocentric latitudes are equal at the equator and poles but differ by a maximum of 0.2° at 45° latitude. The area of each region and zone is affected by oblateness as compared to geocentric coordinates, decreasing from zero at the equator to 1.5% at the poles. The global area receiving solar radiation is calculated using the equatorial and polar axes. This area varies with solar declination by 0.0005. For radiation budget computations, the earth oblateness effects are shown to be small compared to error sources of measuring or modeling.

## Abstract

Eighteen months of wide field-of-view (WFOV) outgoing longwave radiation (OLR) measurements from the Earth Radiation Budget Experiment (ERBE) *NOAA-9* and *NOAA-10* spacecraft have been deconvolved to produce resolution-enhanced flux maps at the top of the atmosphere. *NOAA-9* had a 0230 LST equator-crossing time, and *NOAA-10* a 0730 LST equator-crossing time. Intercomparison of these results with ERBE scanner and numerical filtered WFOV results is made. Results have also been compared with corresponding months of deconvolved results from the *Nimbus-7* spacecraft (1200 LST equator crossing). Comparisons have been made of zonal profile plots of OLR for the different sensors and of contour maps of differences in OLR between sensors. In general *Nimbus-7* OLR results show reasonable agreement with *NOAA-9* and *NOAA-10* over most regions of the globe. The largest differences occur over the extratropies, noticeably over land and especially over deserts. This study suggests that long-term monitoring of OLR with WFOV sensors is feasible for globally averaged trends to an accuracy of less than 1 W m^{−2}, for the global absolute mean to within 3 W m^{−2}, and for regional monthly means to within 8 W m^{−2} for most of the globe. Global averages for numerical filtered and deconvolved *NOAA-9* WFOV results are consistently higher than *Nimbus-7* deconvolved results because *NOAA-9* results over land and deserts are higher. However, the ERBE *NOAA-9* scanner gives smaller values of OLR over most regions ofthe globe than either the *NOAA-9* WFOV numerical filtered or WFOV deconvolved results.

## Abstract

Eighteen months of wide field-of-view (WFOV) outgoing longwave radiation (OLR) measurements from the Earth Radiation Budget Experiment (ERBE) *NOAA-9* and *NOAA-10* spacecraft have been deconvolved to produce resolution-enhanced flux maps at the top of the atmosphere. *NOAA-9* had a 0230 LST equator-crossing time, and *NOAA-10* a 0730 LST equator-crossing time. Intercomparison of these results with ERBE scanner and numerical filtered WFOV results is made. Results have also been compared with corresponding months of deconvolved results from the *Nimbus-7* spacecraft (1200 LST equator crossing). Comparisons have been made of zonal profile plots of OLR for the different sensors and of contour maps of differences in OLR between sensors. In general *Nimbus-7* OLR results show reasonable agreement with *NOAA-9* and *NOAA-10* over most regions of the globe. The largest differences occur over the extratropies, noticeably over land and especially over deserts. This study suggests that long-term monitoring of OLR with WFOV sensors is feasible for globally averaged trends to an accuracy of less than 1 W m^{−2}, for the global absolute mean to within 3 W m^{−2}, and for regional monthly means to within 8 W m^{−2} for most of the globe. Global averages for numerical filtered and deconvolved *NOAA-9* WFOV results are consistently higher than *Nimbus-7* deconvolved results because *NOAA-9* results over land and deserts are higher. However, the ERBE *NOAA-9* scanner gives smaller values of OLR over most regions ofthe globe than either the *NOAA-9* WFOV numerical filtered or WFOV deconvolved results.

## Abstract

The diurnal cycle of outgoing longwave radiation (OLR) from the earth is analyzed by decomposing satellite observations into a set of empirical orthogonal functions (EOFs). The observations are from the Earth Radiation Budget Experiment (ERBE) scanning radiometer aboard the *Earth Radiation Budget Satellite,* which had a precessing orbit with 57° inclination. The diurnal cycles of land and ocean differ considerably. The first EOF for land accounts for 73% to 85% of the variance, whereas the first EOF for ocean accounts for only 16% to 20% of the variance, depending on season. The diurnal cycle for land is surprisingly symmetric about local noon for the first EOF, which is approximately a half-sine during day and flat at night. The second EOF describes lead–lag effects due to surface heating and cloud formation. For the ocean, the first EOF and second EOF are similar to that of land, except for spring, when the first ocean EOF is a semidiurnal cycle and the second ocean EOF is the half-sine. The first EOF for land has a daytime peak of about 50 W m^{−2}, whereas the first ocean EOF peaks at about 25 W m^{−2}. The geographical and seasonal patterns of OLR diurnal cycle provide insights into the interaction of radiation with the atmosphere and surface and are useful for validating and upgrading circulation models.

## Abstract

The diurnal cycle of outgoing longwave radiation (OLR) from the earth is analyzed by decomposing satellite observations into a set of empirical orthogonal functions (EOFs). The observations are from the Earth Radiation Budget Experiment (ERBE) scanning radiometer aboard the *Earth Radiation Budget Satellite,* which had a precessing orbit with 57° inclination. The diurnal cycles of land and ocean differ considerably. The first EOF for land accounts for 73% to 85% of the variance, whereas the first EOF for ocean accounts for only 16% to 20% of the variance, depending on season. The diurnal cycle for land is surprisingly symmetric about local noon for the first EOF, which is approximately a half-sine during day and flat at night. The second EOF describes lead–lag effects due to surface heating and cloud formation. For the ocean, the first EOF and second EOF are similar to that of land, except for spring, when the first ocean EOF is a semidiurnal cycle and the second ocean EOF is the half-sine. The first EOF for land has a daytime peak of about 50 W m^{−2}, whereas the first ocean EOF peaks at about 25 W m^{−2}. The geographical and seasonal patterns of OLR diurnal cycle provide insights into the interaction of radiation with the atmosphere and surface and are useful for validating and upgrading circulation models.

## Abstract

During January and August 1985, the scanning radiometers of the Earth Radiation Budget Experiment (F-RBE) aboard the Earth Radiation Budget Satellite (ERBS) and the *NOAA-9* satellite were operated in along- track scanning modes. Along-track scanning permits the study of many measurement problems. It provides the data for developing a limb-darkening model for a single site over a short period of time and also permits the identification of the scene from data taken at small nadir angles. The earth-emitted radiation measured by the scanners has been analyzed to produce limb-darkening models for a variety of scene types. Limb-darkening models relate the radiance in any given direction to the radiant flux. The scene types were computed using measurements within 1O° of zenith. The models have values near zenith of 1.02–1.09. The typical zenith values of the model are 1.06 for both day and night for FRBS, and for *NOAA-9*, 1.06 for day and 1.05 for night. Mean models are formed for the ERBS and *NOAA-9* results and are found to differ less than 1%, the ERBS results being the higher. The models vary about 1% with latitude near zenith and agree with earlier models that were used to analyze ERBE data typically to 2%.

## Abstract

During January and August 1985, the scanning radiometers of the Earth Radiation Budget Experiment (F-RBE) aboard the Earth Radiation Budget Satellite (ERBS) and the *NOAA-9* satellite were operated in along- track scanning modes. Along-track scanning permits the study of many measurement problems. It provides the data for developing a limb-darkening model for a single site over a short period of time and also permits the identification of the scene from data taken at small nadir angles. The earth-emitted radiation measured by the scanners has been analyzed to produce limb-darkening models for a variety of scene types. Limb-darkening models relate the radiance in any given direction to the radiant flux. The scene types were computed using measurements within 1O° of zenith. The models have values near zenith of 1.02–1.09. The typical zenith values of the model are 1.06 for both day and night for FRBS, and for *NOAA-9*, 1.06 for day and 1.05 for night. Mean models are formed for the ERBS and *NOAA-9* results and are found to differ less than 1%, the ERBS results being the higher. The models vary about 1% with latitude near zenith and agree with earlier models that were used to analyze ERBE data typically to 2%.