# Search Results

## You are looking at 1 - 10 of 24 items for

- Author or Editor: Fred G. Rose x

- All content x

## Abstract

Vertical profiles of shortwave and longwave irradiances computed with satellite-derived cloud properties and temperature and humidity profiles from reanalysis are used to estimate entropy production. Entropy production by shortwave radiation is computed by the absorbed irradiance within layers in the atmosphere and by the surface divided by their temperatures. Similarly, entropy production by longwave radiation is computed by emitted irradiance to space from layers in the atmosphere and surface divided by their temperatures. Global annual mean entropy production by shortwave absorption and longwave emission to space are, respectively, 0.852 and 0.928 W m^{−2} K^{−1}. With a steady-state assumption, entropy production by irreversible processes within the Earth system is estimated to be 0.076 W m^{−2} K^{−1} and by nonradiative irreversible processes to be 0.049 W m^{−2} K^{−1}. Both global annual mean entropy productions by shortwave absorption and longwave emission to space increase with increasing shortwave absorption (i.e., with decreasing the planetary albedo). The increase of entropy production by shortwave absorption is, however, larger than the increase of entropy production by longwave emission to space. The result implies that global annual mean entropy production by irreversible processes decreases with increasing shortwave absorption. Input and output temperatures derived by dividing the absorbed shortwave irradiance and emitted longwave irradiance to space by respective entropy production are, respectively, 282 and 259 K, which give the Carnot efficiency of the Earth system of 8.5%.

## Abstract

Vertical profiles of shortwave and longwave irradiances computed with satellite-derived cloud properties and temperature and humidity profiles from reanalysis are used to estimate entropy production. Entropy production by shortwave radiation is computed by the absorbed irradiance within layers in the atmosphere and by the surface divided by their temperatures. Similarly, entropy production by longwave radiation is computed by emitted irradiance to space from layers in the atmosphere and surface divided by their temperatures. Global annual mean entropy production by shortwave absorption and longwave emission to space are, respectively, 0.852 and 0.928 W m^{−2} K^{−1}. With a steady-state assumption, entropy production by irreversible processes within the Earth system is estimated to be 0.076 W m^{−2} K^{−1} and by nonradiative irreversible processes to be 0.049 W m^{−2} K^{−1}. Both global annual mean entropy productions by shortwave absorption and longwave emission to space increase with increasing shortwave absorption (i.e., with decreasing the planetary albedo). The increase of entropy production by shortwave absorption is, however, larger than the increase of entropy production by longwave emission to space. The result implies that global annual mean entropy production by irreversible processes decreases with increasing shortwave absorption. Input and output temperatures derived by dividing the absorbed shortwave irradiance and emitted longwave irradiance to space by respective entropy production are, respectively, 282 and 259 K, which give the Carnot efficiency of the Earth system of 8.5%.

## Abstract

A time filter that passes waves with periods in the 2.5-6.0 day band is applied to a six-winter record of the Nimbus-7 THIR/TOMS high cloudiness and the NMC 500-mb geopotential height in the northern extratropics. The strongest correlations between fluctuations in geopotential and high cloudiness are found in the baroclinic waveguides, where the fields of both geopotential and high cloudiness exhibit 1arge variabilities. Over many grid points in the waveguides, positive anomalies in high cloud areas are found to be approximately one-third of a wavelength to the east of negative anomalies in 500-mb heights (band-pass troughs), and negative anomalies in high cloud arms are found to be approximately one-sixth of a wavelength to the west. A map of the standardized anomalies in the cloud area associated with height fluctuations above the mean forms a simple negative of the map of the cloud anomalies associated with height fluctuations below the mean. The analysis presented here suggests that the high cloud structures of baroclinic waves are less spatially coherent than the internal geopotential height structures. Over the North Pacific, small-scale (latitudinal wavenumber 13-18) fluctuations in geopotential appear to play a greater role in forcing high cloudiness than do medium-wale (latitudinal wavenumber 7-12) fluctuations in geopotential.

## Abstract

A time filter that passes waves with periods in the 2.5-6.0 day band is applied to a six-winter record of the Nimbus-7 THIR/TOMS high cloudiness and the NMC 500-mb geopotential height in the northern extratropics. The strongest correlations between fluctuations in geopotential and high cloudiness are found in the baroclinic waveguides, where the fields of both geopotential and high cloudiness exhibit 1arge variabilities. Over many grid points in the waveguides, positive anomalies in high cloud areas are found to be approximately one-third of a wavelength to the east of negative anomalies in 500-mb heights (band-pass troughs), and negative anomalies in high cloud arms are found to be approximately one-sixth of a wavelength to the west. A map of the standardized anomalies in the cloud area associated with height fluctuations above the mean forms a simple negative of the map of the cloud anomalies associated with height fluctuations below the mean. The analysis presented here suggests that the high cloud structures of baroclinic waves are less spatially coherent than the internal geopotential height structures. Over the North Pacific, small-scale (latitudinal wavenumber 13-18) fluctuations in geopotential appear to play a greater role in forcing high cloudiness than do medium-wale (latitudinal wavenumber 7-12) fluctuations in geopotential.

## Abstract

The spatial and temporal relationships between fluctuations in geopotential height and high-cloud fractional area in low-pass (periods greater than 10 days) and intermediate-pass (10–30 days) time scales are investigated and compared with relationships in the fast-pass (2.5–6 days) time scale. NMC 500-hPa height and *Nimbus-7* THIR/TOMS high-cloud data are used for extended 6-month (October-March) winters (1979–85). Summary correlation maps describe the spatial phase relationships between the heights and the clouds over the full domain of the northern extratropics.

As we move from the slower low-pass and intermediate-pass regimes to the fast-pass regime, the temporal variance of the height field decreases, but the temporal variance of the high cloudiness increases. Surprisingly, the 500-hPa height and high-cloud fields are more strongly correlated in the slower time scales. The spatial phase relationships between the height and cloud fields are generally different in the low-pass and fast-pass regimes.

Over portions of the jet exit regions, one-half of the variance in the low-pass cloudiness can be explained by a correlation with the height fluctuations at nearby points. Over these areas, the low-pass height fluctuations are approximately equivalent barotropic, and the heights are correlated with clouds quite strongly downstream (to the east) but only weakly upstream (to the west). This contrasts with the spatial phase relationships found in the more baroclinic fast-pass regime, where fluctuations in height are correlated with clouds by about the same absolute magnitude either downstream or upstream. An analysis of the temporal evolution of intermediate-pass height and cloud fields reveals the cloud signal of two-dimensional Rossby wave dispersion over a small portion of the northern extratropics.

## Abstract

The spatial and temporal relationships between fluctuations in geopotential height and high-cloud fractional area in low-pass (periods greater than 10 days) and intermediate-pass (10–30 days) time scales are investigated and compared with relationships in the fast-pass (2.5–6 days) time scale. NMC 500-hPa height and *Nimbus-7* THIR/TOMS high-cloud data are used for extended 6-month (October-March) winters (1979–85). Summary correlation maps describe the spatial phase relationships between the heights and the clouds over the full domain of the northern extratropics.

As we move from the slower low-pass and intermediate-pass regimes to the fast-pass regime, the temporal variance of the height field decreases, but the temporal variance of the high cloudiness increases. Surprisingly, the 500-hPa height and high-cloud fields are more strongly correlated in the slower time scales. The spatial phase relationships between the height and cloud fields are generally different in the low-pass and fast-pass regimes.

Over portions of the jet exit regions, one-half of the variance in the low-pass cloudiness can be explained by a correlation with the height fluctuations at nearby points. Over these areas, the low-pass height fluctuations are approximately equivalent barotropic, and the heights are correlated with clouds quite strongly downstream (to the east) but only weakly upstream (to the west). This contrasts with the spatial phase relationships found in the more baroclinic fast-pass regime, where fluctuations in height are correlated with clouds by about the same absolute magnitude either downstream or upstream. An analysis of the temporal evolution of intermediate-pass height and cloud fields reveals the cloud signal of two-dimensional Rossby wave dispersion over a small portion of the northern extratropics.

## Abstract

The classical picture of the influence of midlatitude troughs on cloud patterns is investigated in a general circulation model (GCM) and in satellite and National Meteorological Centre (NMC) data by comparing the cross correlation of the poleward component of the wind and the outgoing longwave radiation (OLR). The GCM stimulation is found to compare quite well with data for the bandpass (2.5- to 6-day) waves over the midlatitudes. Over the storm tracks, a significant portion of the variance of the OLR is explained by a correlation with the poleward component of the horizontal wind; this is forced, as expected, by stronger correlations with the vertical velocity through the cloud and humidity fields. The correlation of broadband OLR and tropospheric temperature is generally small over short time scales and more significant over land than over water. The GCM wind-OLR correlation is a maximum for bandpass waves of synoptic (spherical harmonic wavenumber 8–15) dimension, but it shows only a small variation with the temporal or spatial scale or with the height of the wind. Stratiform clouds are found to have a dominant impact on the model OLR fluctuations, even over much of the tropics.

## Abstract

The classical picture of the influence of midlatitude troughs on cloud patterns is investigated in a general circulation model (GCM) and in satellite and National Meteorological Centre (NMC) data by comparing the cross correlation of the poleward component of the wind and the outgoing longwave radiation (OLR). The GCM stimulation is found to compare quite well with data for the bandpass (2.5- to 6-day) waves over the midlatitudes. Over the storm tracks, a significant portion of the variance of the OLR is explained by a correlation with the poleward component of the horizontal wind; this is forced, as expected, by stronger correlations with the vertical velocity through the cloud and humidity fields. The correlation of broadband OLR and tropospheric temperature is generally small over short time scales and more significant over land than over water. The GCM wind-OLR correlation is a maximum for bandpass waves of synoptic (spherical harmonic wavenumber 8–15) dimension, but it shows only a small variation with the temporal or spatial scale or with the height of the wind. Stratiform clouds are found to have a dominant impact on the model OLR fluctuations, even over much of the tropics.

## Abstract

Because of the limitation of the spatial resolution of satellite sensors, satellite pixels identified as cloudy are often partly cloudy. For the first time, this study demonstrates the bias in shortwave (SW) broadband irradiances for partly cloudy pixels when the cloud optical depths are retrieved with an overcast and homogeneous assumption, and subsequently, the retrieved values are used for the irradiance computations. The sign of the SW irradiance bias is mainly a function of viewing geometry of the cloud retrieval. The bias in top-of-atmosphere (TOA) upward SW irradiances is positive for small viewing zenith angles (VZAs) <~60° and negative for large VZAs >~60°. For a given solar zenith angle and viewing geometry, the magnitude of the bias increases with the cloud optical depth and reaches a maximum at the cloud fraction between 0.2 and 0.8. The sign of the SW surface net irradiance bias is opposite of the sign of TOA upward irradiance bias, with a similar magnitude. As a result, the bias in absorbed SW irradiances by the atmosphere is smaller than the biases in both TOA and surface irradiances. The monthly mean biases in SW irradiances due to partly cloudy pixels are <1.5 W m^{−2} when cloud properties are derived from Moderate Resolution Imaging Spectroradiometer (MODIS) aboard *Aqua*.

## Abstract

Because of the limitation of the spatial resolution of satellite sensors, satellite pixels identified as cloudy are often partly cloudy. For the first time, this study demonstrates the bias in shortwave (SW) broadband irradiances for partly cloudy pixels when the cloud optical depths are retrieved with an overcast and homogeneous assumption, and subsequently, the retrieved values are used for the irradiance computations. The sign of the SW irradiance bias is mainly a function of viewing geometry of the cloud retrieval. The bias in top-of-atmosphere (TOA) upward SW irradiances is positive for small viewing zenith angles (VZAs) <~60° and negative for large VZAs >~60°. For a given solar zenith angle and viewing geometry, the magnitude of the bias increases with the cloud optical depth and reaches a maximum at the cloud fraction between 0.2 and 0.8. The sign of the SW surface net irradiance bias is opposite of the sign of TOA upward irradiance bias, with a similar magnitude. As a result, the bias in absorbed SW irradiances by the atmosphere is smaller than the biases in both TOA and surface irradiances. The monthly mean biases in SW irradiances due to partly cloudy pixels are <1.5 W m^{−2} when cloud properties are derived from Moderate Resolution Imaging Spectroradiometer (MODIS) aboard *Aqua*.

## Abstract

The respective errors caused by the gamma-weighted two-stream approximation and the effective thickness approximation for computing the domain-averaged broadband shortwave irradiance are evaluated using cloud optical thicknesses derived from 1 h of radiance measurements by the Moderate Resolution Imaging Spectrometer (MODIS) over footprints of Clouds and the Earth’s Radiant Energy System (CERES) instruments. Domains are CERES footprints of which dimension varies approximately from 20 to 70 km, depending on the viewing zenith angle of the instruments. The average error in the top-of-atmosphere irradiance at a 30° solar zenith angle caused by the gamma-weighted two-stream approximation is 6.1 W m^{−2} (0.005 albedo bias) with a one-layer overcast cloud where a positive value indicates an overestimate by the approximation compared with the irradiance computed using the independent column approximation. Approximately one-half of the error is due to deviations of optical thickness distributions from a gamma distribution and the other half of the error is due to other approximations in the model. The error increases to 14.7 W m^{−2} (0.012 albedo bias) when the computational layer dividing the cloud layer is increased to four. The increase is because of difficulties in treating the correlation of cloud properties in the vertical direction. Because the optical thickness under partly cloudy conditions, which contribute two-thirds of cloudy footprints, is smaller, the error is smaller than under overcast conditions; the average error for partly cloudy condition is −2.4 W m^{−2} (−0.002 albedo bias) at a 30° solar zenith angle. The corresponding average error caused by the effective thickness approximation is 0.5 W m^{−2} for overcast conditions and −21.5 W m^{−2} (−0.018 albedo bias) for partly cloudy conditions. Although the error caused by the effective thickness approximation depends strongly on the optical thickness, its average error under overcast conditions is smaller than the error caused by the gamma-weighted two-stream approximation because the errors at small and large optical thicknesses cancel each other. Based on these error analyses, the daily average error caused by the gamma-weighted two-stream and effective thickness approximations is less than 2 W m^{−2}.

## Abstract

The respective errors caused by the gamma-weighted two-stream approximation and the effective thickness approximation for computing the domain-averaged broadband shortwave irradiance are evaluated using cloud optical thicknesses derived from 1 h of radiance measurements by the Moderate Resolution Imaging Spectrometer (MODIS) over footprints of Clouds and the Earth’s Radiant Energy System (CERES) instruments. Domains are CERES footprints of which dimension varies approximately from 20 to 70 km, depending on the viewing zenith angle of the instruments. The average error in the top-of-atmosphere irradiance at a 30° solar zenith angle caused by the gamma-weighted two-stream approximation is 6.1 W m^{−2} (0.005 albedo bias) with a one-layer overcast cloud where a positive value indicates an overestimate by the approximation compared with the irradiance computed using the independent column approximation. Approximately one-half of the error is due to deviations of optical thickness distributions from a gamma distribution and the other half of the error is due to other approximations in the model. The error increases to 14.7 W m^{−2} (0.012 albedo bias) when the computational layer dividing the cloud layer is increased to four. The increase is because of difficulties in treating the correlation of cloud properties in the vertical direction. Because the optical thickness under partly cloudy conditions, which contribute two-thirds of cloudy footprints, is smaller, the error is smaller than under overcast conditions; the average error for partly cloudy condition is −2.4 W m^{−2} (−0.002 albedo bias) at a 30° solar zenith angle. The corresponding average error caused by the effective thickness approximation is 0.5 W m^{−2} for overcast conditions and −21.5 W m^{−2} (−0.018 albedo bias) for partly cloudy conditions. Although the error caused by the effective thickness approximation depends strongly on the optical thickness, its average error under overcast conditions is smaller than the error caused by the gamma-weighted two-stream approximation because the errors at small and large optical thicknesses cancel each other. Based on these error analyses, the daily average error caused by the gamma-weighted two-stream and effective thickness approximations is less than 2 W m^{−2}.

## Abstract

Shortwave irradiance biases due to two- and four-stream approximations have been studied for the last couple of decades, but biases in estimating Earth’s radiation budget have not been examined in earlier studies. To quantify biases in diurnally averaged irradiances, we integrate the two- and four-stream biases using realistic diurnal variations of cloud properties from Clouds and the Earth’s Radiant Energy System (CERES) synoptic (SYN) hourly product. Three approximations are examined in this study: delta-two-stream-Eddington (D2strEdd), delta-two-stream-quadrature (D2strQuad), and delta-four-stream-quadrature (D4strQuad). Irradiances computed by the Discrete Ordinate Radiative Transfer model (DISORT) and Monte Carlo (MC) methods are used as references. The MC noises are further examined by comparing with DISORT results. When the biases are integrated with one day of solar zenith angle variation, regional biases of D2strEdd and D2strQuad reach up to 8 W m^{−2}, while biases of D4strQuad reach up to 2 W m^{−2}. When the biases are further averaged monthly or annually, regional biases of D2strEdd and D2strQuad can reach −1.5 W m^{−2} in SW top-of-atmosphere (TOA) upward irradiances and +3 W m^{−2} in surface downward irradiances. In contrast, regional biases of D4strQuad are within +0.9 for TOA irradiances and −1.2 W m^{−2} for surface irradiances. Except for polar regions, monthly and annual global mean biases are similar, suggesting that the biases are nearly independent to season. Biases in SW heating rate profiles are up to −0.008 K day^{−1} for D2strEdd and −0.016 K day^{−1} for D2strQuad, while the biases of the D4strQuad method are negligible.

## Abstract

Shortwave irradiance biases due to two- and four-stream approximations have been studied for the last couple of decades, but biases in estimating Earth’s radiation budget have not been examined in earlier studies. To quantify biases in diurnally averaged irradiances, we integrate the two- and four-stream biases using realistic diurnal variations of cloud properties from Clouds and the Earth’s Radiant Energy System (CERES) synoptic (SYN) hourly product. Three approximations are examined in this study: delta-two-stream-Eddington (D2strEdd), delta-two-stream-quadrature (D2strQuad), and delta-four-stream-quadrature (D4strQuad). Irradiances computed by the Discrete Ordinate Radiative Transfer model (DISORT) and Monte Carlo (MC) methods are used as references. The MC noises are further examined by comparing with DISORT results. When the biases are integrated with one day of solar zenith angle variation, regional biases of D2strEdd and D2strQuad reach up to 8 W m^{−2}, while biases of D4strQuad reach up to 2 W m^{−2}. When the biases are further averaged monthly or annually, regional biases of D2strEdd and D2strQuad can reach −1.5 W m^{−2} in SW top-of-atmosphere (TOA) upward irradiances and +3 W m^{−2} in surface downward irradiances. In contrast, regional biases of D4strQuad are within +0.9 for TOA irradiances and −1.2 W m^{−2} for surface irradiances. Except for polar regions, monthly and annual global mean biases are similar, suggesting that the biases are nearly independent to season. Biases in SW heating rate profiles are up to −0.008 K day^{−1} for D2strEdd and −0.016 K day^{−1} for D2strQuad, while the biases of the D4strQuad method are negligible.

## Abstract

The relationship between low frequency variations in extratropical fields of outgoing longwave radiation (OLR) and geopotential teleconnection patterns as determined by rotated principal components (RPC) analysis of the NMC 500-mb heights is investigated in the Northern Hemisphere. The monthly broadband OLR is obtained from the Nimbus-6 and Nimbus-7 Wide-Field-Of-View (WFOV) radiometer record.

Each of the main 500-mb teleconnection patterns has a characteristic signal in the OLR field for the month in which the 500-mb pattern occurs. The OLR signals mark cloud and diabatic heating events that are associated with the Reconnection patterns. Our demonstration of correlation between extratropical monthly OLR and geopotential height, coupled with the expected tropospheric response to radiation on monthly time scales, stresses the importance of the radiation simulation in model studies of the low frequency variability of atmospheric circulation.

The extratropical OLR does not appear to be a useful predictor for the 500-mb teleconnection patterns on a monthly time scale.

## Abstract

The relationship between low frequency variations in extratropical fields of outgoing longwave radiation (OLR) and geopotential teleconnection patterns as determined by rotated principal components (RPC) analysis of the NMC 500-mb heights is investigated in the Northern Hemisphere. The monthly broadband OLR is obtained from the Nimbus-6 and Nimbus-7 Wide-Field-Of-View (WFOV) radiometer record.

Each of the main 500-mb teleconnection patterns has a characteristic signal in the OLR field for the month in which the 500-mb pattern occurs. The OLR signals mark cloud and diabatic heating events that are associated with the Reconnection patterns. Our demonstration of correlation between extratropical monthly OLR and geopotential height, coupled with the expected tropospheric response to radiation on monthly time scales, stresses the importance of the radiation simulation in model studies of the low frequency variability of atmospheric circulation.

The extratropical OLR does not appear to be a useful predictor for the 500-mb teleconnection patterns on a monthly time scale.

## Abstract

A surface, atmospheric, and cloud (fraction, height, optical thickness, and particle size) property anomaly retrieval from highly averaged longwave spectral radiances is simulated using 28 years of reanalysis. Instantaneous nadir-view spectral radiances observed from an instrument on a 90° inclination polar orbit are computed. Spectral radiance changes caused by surface, atmospheric, and cloud property perturbations are also computed and used for the retrieval. This study’s objectives are 1) to investigate whether or not separating clear sky from cloudy sky reduces the retrieval error and 2) to estimate the error in a trend of retrieved properties. This simulation differs from earlier studies in that annual 10° latitude zonal cloud and atmospheric property anomalies defined as the deviation from 28-yr climatological means are retrieved instead of the difference of these properties from two time periods. The root-mean-square (RMS) difference of temperature and humidity anomalies retrieved from all-sky radiance anomalies is similar to the RMS difference derived from clear-sky radiance anomalies computed by removing clouds. This indicates that the cloud property anomaly retrieval error does not affect the retrieved temperature and humidity anomalies. When retrieval errors are nearly random, the error in the trend of retrieved properties is small. Approximately 30% of 10° latitude zones meet conditions that the true temperature and water vapor amount trends are within a 95% confidence interval of retrieved trends, and that the standard deviation of retrieved anomalies *σ*
_{ret} is within 20% of the standard deviation of true anomalies *σ*
_{n}. If *σ*
_{ret}/*σ*
_{n} − 1 is within ±0.2, 91% of the true trends fall within the 95% confidence interval of the corresponding retrieved trend.

## Abstract

A surface, atmospheric, and cloud (fraction, height, optical thickness, and particle size) property anomaly retrieval from highly averaged longwave spectral radiances is simulated using 28 years of reanalysis. Instantaneous nadir-view spectral radiances observed from an instrument on a 90° inclination polar orbit are computed. Spectral radiance changes caused by surface, atmospheric, and cloud property perturbations are also computed and used for the retrieval. This study’s objectives are 1) to investigate whether or not separating clear sky from cloudy sky reduces the retrieval error and 2) to estimate the error in a trend of retrieved properties. This simulation differs from earlier studies in that annual 10° latitude zonal cloud and atmospheric property anomalies defined as the deviation from 28-yr climatological means are retrieved instead of the difference of these properties from two time periods. The root-mean-square (RMS) difference of temperature and humidity anomalies retrieved from all-sky radiance anomalies is similar to the RMS difference derived from clear-sky radiance anomalies computed by removing clouds. This indicates that the cloud property anomaly retrieval error does not affect the retrieved temperature and humidity anomalies. When retrieval errors are nearly random, the error in the trend of retrieved properties is small. Approximately 30% of 10° latitude zones meet conditions that the true temperature and water vapor amount trends are within a 95% confidence interval of retrieved trends, and that the standard deviation of retrieved anomalies *σ*
_{ret} is within 20% of the standard deviation of true anomalies *σ*
_{n}. If *σ*
_{ret}/*σ*
_{n} − 1 is within ±0.2, 91% of the true trends fall within the 95% confidence interval of the corresponding retrieved trend.

## Abstract

NASA’s Clouds and the Earth’s Radiant Energy System (CERES) project is responsible for operation and data processing of observations from scanning radiometers on board the Tropical Rainfall Measuring Mission (TRMM), *Terra*, *Aqua*, and Suomi National Polar-Orbiting Partnership (NPP) satellites. The clouds and radiative swath (CRS) CERES data product contains irradiances computed using a radiative transfer model for nearly all CERES footprints in addition to top-of-atmosphere (TOA) irradiances derived from observed radiances by CERES instruments. This paper describes a method to constrain computed irradiances by CERES-derived TOA irradiances using Lagrangian multipliers. Radiative transfer model inputs include profiles of atmospheric temperature, humidity, aerosols and ozone, surface temperature and albedo, and up to two sets of cloud properties for a CERES footprint. Those inputs are adjusted depending on predefined uncertainties to match computed TOA and CERES-derived TOA irradiance. Because CERES instantaneous irradiances for an individual footprint also include uncertainties, primarily due to the conversion of radiance to irradiance using anisotropic directional models, the degree of the constraint depends on CERES-derived TOA irradiance as well. As a result of adjustment, TOA computed-minus-observed standard deviations are reduced from 8 to 4 W m^{−2} for longwave irradiance and from 15 to 6 W m^{−2} for shortwave irradiance. While agreement of computed TOA with CERES-derived irradiances improves, comparisons with surface observations show that model constrainment to the TOA does not reduce computation bias error at the surface. After constrainment, shortwave down at the surface has an increased bias (standard deviation) of 1% (0.5%) and longwave increases by 0.2% (0.1%). Clear-sky changes are negligible.

## Abstract

NASA’s Clouds and the Earth’s Radiant Energy System (CERES) project is responsible for operation and data processing of observations from scanning radiometers on board the Tropical Rainfall Measuring Mission (TRMM), *Terra*, *Aqua*, and Suomi National Polar-Orbiting Partnership (NPP) satellites. The clouds and radiative swath (CRS) CERES data product contains irradiances computed using a radiative transfer model for nearly all CERES footprints in addition to top-of-atmosphere (TOA) irradiances derived from observed radiances by CERES instruments. This paper describes a method to constrain computed irradiances by CERES-derived TOA irradiances using Lagrangian multipliers. Radiative transfer model inputs include profiles of atmospheric temperature, humidity, aerosols and ozone, surface temperature and albedo, and up to two sets of cloud properties for a CERES footprint. Those inputs are adjusted depending on predefined uncertainties to match computed TOA and CERES-derived TOA irradiance. Because CERES instantaneous irradiances for an individual footprint also include uncertainties, primarily due to the conversion of radiance to irradiance using anisotropic directional models, the degree of the constraint depends on CERES-derived TOA irradiance as well. As a result of adjustment, TOA computed-minus-observed standard deviations are reduced from 8 to 4 W m^{−2} for longwave irradiance and from 15 to 6 W m^{−2} for shortwave irradiance. While agreement of computed TOA with CERES-derived irradiances improves, comparisons with surface observations show that model constrainment to the TOA does not reduce computation bias error at the surface. After constrainment, shortwave down at the surface has an increased bias (standard deviation) of 1% (0.5%) and longwave increases by 0.2% (0.1%). Clear-sky changes are negligible.