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- Author or Editor: David S. Crosby x
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Abstract
In many experiments where radiation emitted from the surface or lower atmosphere is to be measured, a fundamental difficulty is the presence of clouds. In this paper a technique is developed and described which uses a number of small fields-of-view to estimate the clear radiance. Specifically, it is assumed that some of these small fields-of-view are cloud-free and that the difference between the measured radiance from these cloud-free areas is due to instrument noise, which is normal with known standard deviation. Then the tail of the normal distribution is used to estimate the clear radiance. An example is provided.
Abstract
In many experiments where radiation emitted from the surface or lower atmosphere is to be measured, a fundamental difficulty is the presence of clouds. In this paper a technique is developed and described which uses a number of small fields-of-view to estimate the clear radiance. Specifically, it is assumed that some of these small fields-of-view are cloud-free and that the difference between the measured radiance from these cloud-free areas is due to instrument noise, which is normal with known standard deviation. Then the tail of the normal distribution is used to estimate the clear radiance. An example is provided.
Abstract
In interpreting radiation data from the Vertical Temperature Profile Radiometers aboard the NOAA satellites, the following problem arose: given a satellite retrieval of the atmospheric temperature profile and a measurement of radiance from the earth's atmosphere in a single spectral interval (535 cm−1) where water vapor is the principal optically active species, how can we estimate the atmospheric profile of water vapor mixing ratio? Our proposed solution has two steps. The first is to estimate the mixing-ratio profile by linear least-squares regression on the saturation mixing-ratio profile, the latter having been computed from the retrieved temperature profile. Associated with this estimate are residual errors. In the second step the measured radiance is used to reduce these errors, as follows: The covariance matrix of the errors is estimated and its principal eigenfunction is derived. The solution for the mixing-ratio profiles is assumed to be a linear combination of this eigenfunction and the regression estimate of the mixing-ratio profile. The unknown coefficient in this solution is determined through a solution of the radiative transfer equation by Newton's method. In simulation, this method produced accurate solutions for mixing-ratio profiles and total precipitable water; the absolute error in the latter averaging 13% of the true value. This number increased to 26% when a uniform 2 K bias was introduced into the estimates of the temperature profiles.
Abstract
In interpreting radiation data from the Vertical Temperature Profile Radiometers aboard the NOAA satellites, the following problem arose: given a satellite retrieval of the atmospheric temperature profile and a measurement of radiance from the earth's atmosphere in a single spectral interval (535 cm−1) where water vapor is the principal optically active species, how can we estimate the atmospheric profile of water vapor mixing ratio? Our proposed solution has two steps. The first is to estimate the mixing-ratio profile by linear least-squares regression on the saturation mixing-ratio profile, the latter having been computed from the retrieved temperature profile. Associated with this estimate are residual errors. In the second step the measured radiance is used to reduce these errors, as follows: The covariance matrix of the errors is estimated and its principal eigenfunction is derived. The solution for the mixing-ratio profiles is assumed to be a linear combination of this eigenfunction and the regression estimate of the mixing-ratio profile. The unknown coefficient in this solution is determined through a solution of the radiative transfer equation by Newton's method. In simulation, this method produced accurate solutions for mixing-ratio profiles and total precipitable water; the absolute error in the latter averaging 13% of the true value. This number increased to 26% when a uniform 2 K bias was introduced into the estimates of the temperature profiles.
Abstract
Measurements of infrared radiation from the National Oceanic and Atmospheric Administration series of satellites are used to retrieve atmospheric temperature, moisture, and ozone. It is well known that the measurements from the 4.3-μm channels of the High-Resolution Infrared Radiation Sounder (HIRS) are affected by solar radiation. These effects can have an important effect on retrieved parameters and have caused difficulties in the use of the higher-peaking shortwave channels for many applications. In the channels that respond to the upper atmosphere, this effect can reach 2 K for high solar angles. In this paper, a regression procedure is used on nighttime data to determine a relationship between these channels and the other channels of the HIRS and the Microwave Sounding Unit of the Television and Infrared Operation Satellite Operational Vertical Sounder. This regression then is applied to daytime data to study the effect of solar radiation on these channels. This paper provides a method for estimating and partially removing these effects.
Abstract
Measurements of infrared radiation from the National Oceanic and Atmospheric Administration series of satellites are used to retrieve atmospheric temperature, moisture, and ozone. It is well known that the measurements from the 4.3-μm channels of the High-Resolution Infrared Radiation Sounder (HIRS) are affected by solar radiation. These effects can have an important effect on retrieved parameters and have caused difficulties in the use of the higher-peaking shortwave channels for many applications. In the channels that respond to the upper atmosphere, this effect can reach 2 K for high solar angles. In this paper, a regression procedure is used on nighttime data to determine a relationship between these channels and the other channels of the HIRS and the Microwave Sounding Unit of the Television and Infrared Operation Satellite Operational Vertical Sounder. This regression then is applied to daytime data to study the effect of solar radiation on these channels. This paper provides a method for estimating and partially removing these effects.
Abstract
It is generally assumed that atmospheric transmittance functions are known to an accuracy of no better than about five to ten percent. Consequently, one can expect a major impact of these errors on temperature retrieves based on the inversion of the radiative transfer equation, as opposed to regression methods that do not explicitly use transmittance functions. A numerical simulation study of the sensitivity of the retrieved temperature profiles to errors in transmittance is described. The study shows that most of the transmittance error is propagated into the retrieved profiles in the form of a bias error. A technique for removing this large bias component of the error is given. Furthermore, it is shown how the improper use of regularization transforms sonic of the bias error into an unremovable component of random error. Finally, we show results that indicate how well the bias-error removal technique works in practice using real data. It is found that, despite errors of measurement and errors in the transmittance functions, one can retrieve temperature profiles of good quality.
Abstract
It is generally assumed that atmospheric transmittance functions are known to an accuracy of no better than about five to ten percent. Consequently, one can expect a major impact of these errors on temperature retrieves based on the inversion of the radiative transfer equation, as opposed to regression methods that do not explicitly use transmittance functions. A numerical simulation study of the sensitivity of the retrieved temperature profiles to errors in transmittance is described. The study shows that most of the transmittance error is propagated into the retrieved profiles in the form of a bias error. A technique for removing this large bias component of the error is given. Furthermore, it is shown how the improper use of regularization transforms sonic of the bias error into an unremovable component of random error. Finally, we show results that indicate how well the bias-error removal technique works in practice using real data. It is found that, despite errors of measurement and errors in the transmittance functions, one can retrieve temperature profiles of good quality.
Abstract
Many methods for converting satellite radiances to temperatures require a comparison of observed radiances with radiances calculated from a first guess. Usually, measured values must be tuned to agree with theoretical calculations. A regression in which the calculated radiances are predicted from the observed ones is a method of making the adjustment, but results in unrealistic coefficients. Several modifications to standard regression are tried, and it is shown that rotated regression, a technique developed in this paper, provides the required accuracy with coefficients that satisfy the physical constraints.
Abstract
Many methods for converting satellite radiances to temperatures require a comparison of observed radiances with radiances calculated from a first guess. Usually, measured values must be tuned to agree with theoretical calculations. A regression in which the calculated radiances are predicted from the observed ones is a method of making the adjustment, but results in unrealistic coefficients. Several modifications to standard regression are tried, and it is shown that rotated regression, a technique developed in this paper, provides the required accuracy with coefficients that satisfy the physical constraints.
Abstract
The Advanced Microwave Sounding Unit-A (AMSU-A) is the first of a new generation of polar-orbiting cross-track microwave sounders operated by the National Oceanic and Atmospheric Administration. A feature of a cross-track sounder is that the measurements vary with scan angle because of the change in the optical pathlength between the earth and the satellite. This feature is called the limb effect and can be as much as 30 K. One approach to this problem is to limb adjust the measurements to a fixed view angle. This approach was used for the older series of Microwave Sounding Units. Limb adjusting is important for climate applications and regression retrieval algorithms. This paper describes and evaluates several limb adjustment procedures. The recommended procedure uses a combined physical and statistical technique. The limb adjusted measurements were compared with computed radiances from radiosondes and National Centers for Environmental Prediction models. The model error was found to be less than the instrument noise for most of the temperature sounding channels. The error in the window channels was small relative to the observed range of these channels. Limb adjusted fields appear to be smooth. Statistical tests of the distributions of the adjusted measurements at each scan angle show them to be very similar.
Abstract
The Advanced Microwave Sounding Unit-A (AMSU-A) is the first of a new generation of polar-orbiting cross-track microwave sounders operated by the National Oceanic and Atmospheric Administration. A feature of a cross-track sounder is that the measurements vary with scan angle because of the change in the optical pathlength between the earth and the satellite. This feature is called the limb effect and can be as much as 30 K. One approach to this problem is to limb adjust the measurements to a fixed view angle. This approach was used for the older series of Microwave Sounding Units. Limb adjusting is important for climate applications and regression retrieval algorithms. This paper describes and evaluates several limb adjustment procedures. The recommended procedure uses a combined physical and statistical technique. The limb adjusted measurements were compared with computed radiances from radiosondes and National Centers for Environmental Prediction models. The model error was found to be less than the instrument noise for most of the temperature sounding channels. The error in the window channels was small relative to the observed range of these channels. Limb adjusted fields appear to be smooth. Statistical tests of the distributions of the adjusted measurements at each scan angle show them to be very similar.
Abstract
A method for deriving a water vapor index is presented. An important feature of the index is the fact that it does not rely on radiosondes. Thus, it is not influenced by problems associated with radiosondes and the extent to which the horizontal variability of moisture invalidates the extrapolations from radiosonde measurements to satellite measurements. The index is derived by using channels that are insensitive to changes in moisture to predict a brightness temperature for one of the moisture channels and then by subtracting this predicted value from the observation. The predicted value represents the moisture value expected for the given temperature profile, and the difference between the predicted and measured values is the index. The subtraction removes the variability due to changes in atmospheric temperature from the moisture signal. This separation greatly enhances the ability to monitor atmospheric moisture patterns, especially near the ground and at high latitudes where some alternative methods have difficulties. The ability of the indices to display moisture patterns at all levels and latitudes is demonstrated.
Abstract
A method for deriving a water vapor index is presented. An important feature of the index is the fact that it does not rely on radiosondes. Thus, it is not influenced by problems associated with radiosondes and the extent to which the horizontal variability of moisture invalidates the extrapolations from radiosonde measurements to satellite measurements. The index is derived by using channels that are insensitive to changes in moisture to predict a brightness temperature for one of the moisture channels and then by subtracting this predicted value from the observation. The predicted value represents the moisture value expected for the given temperature profile, and the difference between the predicted and measured values is the index. The subtraction removes the variability due to changes in atmospheric temperature from the moisture signal. This separation greatly enhances the ability to monitor atmospheric moisture patterns, especially near the ground and at high latitudes where some alternative methods have difficulties. The ability of the indices to display moisture patterns at all levels and latitudes is demonstrated.
Abstract
Layer-mean virtual temperatures retrieved from satellite measurements are more accurate than retrievals at specific pressure not only because an averaging process is involved, but also because of advantages in the retrieval process. In this note, a “retrieval efficiency” is derived to express this advantage over simple averaging as a function of layer thickness. The efficiency is examined for two common cases of retrieval initial guess: a statistical sample mean and a forecast profile obtained from a numerical prediction model. The advantage of the layer-mean retrieval clearly is demonstrated in both cases.
Abstract
Layer-mean virtual temperatures retrieved from satellite measurements are more accurate than retrievals at specific pressure not only because an averaging process is involved, but also because of advantages in the retrieval process. In this note, a “retrieval efficiency” is derived to express this advantage over simple averaging as a function of layer thickness. The efficiency is examined for two common cases of retrieval initial guess: a statistical sample mean and a forecast profile obtained from a numerical prediction model. The advantage of the layer-mean retrieval clearly is demonstrated in both cases.
Abstract
The SSM/I has been used successfully to estimate precipitation and to determine the fields of view (FOV) that contain precipitating clouds. The use of multivariate logistic regression with the SSM/I brightness temperatures to estimate the probability that it is raining in an FOV is examined. The predictors used in this study are those that have been evaluated by other investigators to estimate rain events using other procedures. The logistic regression technique is applied to a matched set of SSM/I and radar data for a limited area from June to August 1989. For this limited dataset the results are quite good. In one example, if the predicted probability is less than 0.1, the radar data shows only 2 of 340 FOVs have precipitation. If the predicted probability is greater than 0.9, the radar data shows precipitation in 748 of 774 FOVS. These probabilities can be used for both instantaneous and climate timescale retrievals.
Abstract
The SSM/I has been used successfully to estimate precipitation and to determine the fields of view (FOV) that contain precipitating clouds. The use of multivariate logistic regression with the SSM/I brightness temperatures to estimate the probability that it is raining in an FOV is examined. The predictors used in this study are those that have been evaluated by other investigators to estimate rain events using other procedures. The logistic regression technique is applied to a matched set of SSM/I and radar data for a limited area from June to August 1989. For this limited dataset the results are quite good. In one example, if the predicted probability is less than 0.1, the radar data shows only 2 of 340 FOVs have precipitation. If the predicted probability is greater than 0.9, the radar data shows precipitation in 748 of 774 FOVS. These probabilities can be used for both instantaneous and climate timescale retrievals.
Abstract
Total ozone amounts are determined from atmospheric radiances measured by the TIROS Operational Vertical Sounder (TOVS). The retrieval procedure is one of linear regression where total ozone amounts derived from Dobson spectrophotometer measurements are regressed against “clear” radiances that are measured in three of the TOVS spectral channels and converted to brightness temperatures. This paper discusses the retrieval technique, the accuracy of the ozone data products compared to an independent set of Dobson measurements used for validation, and comparisons with zonal-averaged total ozone data derived from the Nimbus-7 Solar Backscatter Ultraviolet (SBUV) instrument.
Abstract
Total ozone amounts are determined from atmospheric radiances measured by the TIROS Operational Vertical Sounder (TOVS). The retrieval procedure is one of linear regression where total ozone amounts derived from Dobson spectrophotometer measurements are regressed against “clear” radiances that are measured in three of the TOVS spectral channels and converted to brightness temperatures. This paper discusses the retrieval technique, the accuracy of the ozone data products compared to an independent set of Dobson measurements used for validation, and comparisons with zonal-averaged total ozone data derived from the Nimbus-7 Solar Backscatter Ultraviolet (SBUV) instrument.
