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Measurements in atmospheric science sometimes determine universal functions, but more commonly data are collected in the form of case studies. Models are conceptual constructs that can be used to make predictions about the outcomes of measurements. Hypotheses can be expressed in terms of model results, and the best use of measurements is to falsify such hypotheses. Tuning of models should be avoided because it interferes with falsification. Comparison of models with data would be easier if the minimum data requirements for testing some types of models could be standardized.
Measurements in atmospheric science sometimes determine universal functions, but more commonly data are collected in the form of case studies. Models are conceptual constructs that can be used to make predictions about the outcomes of measurements. Hypotheses can be expressed in terms of model results, and the best use of measurements is to falsify such hypotheses. Tuning of models should be avoided because it interferes with falsification. Comparison of models with data would be easier if the minimum data requirements for testing some types of models could be standardized.
Abstract
In this study we perform an error analysis for cloud-top pressure retrieval using the High-Resolution Infrared Radiometric Sounder (HIRS/2) 15-µm CO2 channels for the two-layer case of transmissive cirrus overlying an overcast, opaque stratiform cloud. This analysis includes standard deviation and bias error due to instrument noise and the presence of two cloud layers, the lower of which is opaque. Instantaneous cloud pressure retrieval errors are determined for a range of cloud amounts (0.1–1.0) and cloud-top pressures (850−250 mb). Large cloud-top pressure retrieval errors are found to occur when a lower opaque layer is present underneath an upper transmissive cloud layer in the satellite field of view (FOV). Errors tend to increase with decreasing upper-cloud elective cloud amount and with decreasing cloud height (increasing pressure). Errors in retrieved upper-cloud pressure result in corresponding errors in derived effective cloud amount. For the case in which a HIRS FOV has two distinct cloud layers, the difference between the retrieved and actual cloud-top pressure is positive in all casts, meaning that the retrieved upper-cloud height is lower than the actual upper-cloud height. In addition, errors in retrieved cloud pressure are found to depend upon the lapse rate between the low-level cloud top and the surface. We examined which sounder channel combinations would minimize the total errors in derived cirrus cloud height caused by instrument noise and by the presence of a lower-level cloud. We find that while the sounding channels that peak between 700 and 1000 mb minimize random errors, the sounding channels that peak at 300—500 mb minimize bias errors. For a cloud climatology, the bias errors are most critical.
Abstract
In this study we perform an error analysis for cloud-top pressure retrieval using the High-Resolution Infrared Radiometric Sounder (HIRS/2) 15-µm CO2 channels for the two-layer case of transmissive cirrus overlying an overcast, opaque stratiform cloud. This analysis includes standard deviation and bias error due to instrument noise and the presence of two cloud layers, the lower of which is opaque. Instantaneous cloud pressure retrieval errors are determined for a range of cloud amounts (0.1–1.0) and cloud-top pressures (850−250 mb). Large cloud-top pressure retrieval errors are found to occur when a lower opaque layer is present underneath an upper transmissive cloud layer in the satellite field of view (FOV). Errors tend to increase with decreasing upper-cloud elective cloud amount and with decreasing cloud height (increasing pressure). Errors in retrieved upper-cloud pressure result in corresponding errors in derived effective cloud amount. For the case in which a HIRS FOV has two distinct cloud layers, the difference between the retrieved and actual cloud-top pressure is positive in all casts, meaning that the retrieved upper-cloud height is lower than the actual upper-cloud height. In addition, errors in retrieved cloud pressure are found to depend upon the lapse rate between the low-level cloud top and the surface. We examined which sounder channel combinations would minimize the total errors in derived cirrus cloud height caused by instrument noise and by the presence of a lower-level cloud. We find that while the sounding channels that peak between 700 and 1000 mb minimize random errors, the sounding channels that peak at 300—500 mb minimize bias errors. For a cloud climatology, the bias errors are most critical.
Abstract
Reflected fluxes are calculated for broken cloudiness (i.e., nonplane parallel) as a function of cloud cover, cloud optical depth, solar zenith angle and surface albedo. These calculations extend previous results for broken cloud reflected fluxes over a black surface.
The present study demonstrates that not only radiances but also radiative fluxes over high albedo surfaces may be decreased by the presence of broken cloudiness. Conventional wisdom states that cloud radiances(brightnesses) are always greater than the background. While most cloud retrieval schemes are built around this assumption, it is incorrect for clouds over high albedo surfaces such as found in polar regions. However, the most startling and counterintuitive conclusion of this study is that nonabsorbing finite clouds over a highly reflecting surface will decrease the system albedo. As a result, surface absorption is increased, the result of multiple scattering between surface and cloud layer, controlled by cloud morphology and cloud optical thickness.
A simple parameterization of the effects of cloud contamination upon retrieved albedo is given in terms of solar zenith angle, cloud optical depth, surface albedo, cloud cover, and plane-parallel could albedo. In this way, the effects of broken cloudiness are modeled in terms of easily computed plane-parallel values.
Abstract
Reflected fluxes are calculated for broken cloudiness (i.e., nonplane parallel) as a function of cloud cover, cloud optical depth, solar zenith angle and surface albedo. These calculations extend previous results for broken cloud reflected fluxes over a black surface.
The present study demonstrates that not only radiances but also radiative fluxes over high albedo surfaces may be decreased by the presence of broken cloudiness. Conventional wisdom states that cloud radiances(brightnesses) are always greater than the background. While most cloud retrieval schemes are built around this assumption, it is incorrect for clouds over high albedo surfaces such as found in polar regions. However, the most startling and counterintuitive conclusion of this study is that nonabsorbing finite clouds over a highly reflecting surface will decrease the system albedo. As a result, surface absorption is increased, the result of multiple scattering between surface and cloud layer, controlled by cloud morphology and cloud optical thickness.
A simple parameterization of the effects of cloud contamination upon retrieved albedo is given in terms of solar zenith angle, cloud optical depth, surface albedo, cloud cover, and plane-parallel could albedo. In this way, the effects of broken cloudiness are modeled in terms of easily computed plane-parallel values.
Abstract
This paper examines the relative impacts on grid-averaged longwave flux transmittance (emittance) for marine boundary layer (MBL) cloud fields arising from horizontal variability of optical depth τ and cloud sides. First, using fields of Landsat-inferred τ and a Monte Carlo photon transport algorithm, it is demonstrated that mean all-sky transmittances for 3D variable MBL clouds can be computed accurately by the conventional method of linearly weighting clear and cloudy transmittances by their respective sky fractions. Then, the approximations of decoupling cloud and radiative properties and assuming independent columns are shown to be adequate for computation of mean flux transmittance.
Since real clouds have nonzero geometric thicknesses, cloud fractions  c presented to isotropic beams usually exceed the more familiar vertically projected cloud fractions A c . It is shown, however, that when A c ≲ 0.9, biases for all-sky transmittance stemming from use of A c as opposed to  c are roughly 2–5 times smaller than, and opposite in sign to, biases due to neglect of horizontal variability of τ. By neglecting variable τ, all-sky transmittances are underestimated often by more than 0.1 for A c near 0.75 and this translates into relative errors that can exceed 40% (corresponding errors for all-sky emittance are about 20% for most values of A c ). Thus, priority should be given to development of general circulation model (GCM) parameterizations that account for the effects of horizontal variations in unresolved τ; effects of cloud sides are of secondary importance.
On this note, an efficient stochastic model for computing grid-averaged cloudy-sky flux transmittances is furnished that assumes that distributions of τ, for regions comparable in size to GCM grid cells, can be described adequately by gamma distribution functions. While the plane-parallel, homogeneous model underestimates cloud transmittance by about an order of magnitude when 3D variable cloud transmittances are ≲ 0.2 and by ∼20% to 100% otherwise, the stochastic model reduces these biases often by more than 80%.
Abstract
This paper examines the relative impacts on grid-averaged longwave flux transmittance (emittance) for marine boundary layer (MBL) cloud fields arising from horizontal variability of optical depth τ and cloud sides. First, using fields of Landsat-inferred τ and a Monte Carlo photon transport algorithm, it is demonstrated that mean all-sky transmittances for 3D variable MBL clouds can be computed accurately by the conventional method of linearly weighting clear and cloudy transmittances by their respective sky fractions. Then, the approximations of decoupling cloud and radiative properties and assuming independent columns are shown to be adequate for computation of mean flux transmittance.
Since real clouds have nonzero geometric thicknesses, cloud fractions  c presented to isotropic beams usually exceed the more familiar vertically projected cloud fractions A c . It is shown, however, that when A c ≲ 0.9, biases for all-sky transmittance stemming from use of A c as opposed to  c are roughly 2–5 times smaller than, and opposite in sign to, biases due to neglect of horizontal variability of τ. By neglecting variable τ, all-sky transmittances are underestimated often by more than 0.1 for A c near 0.75 and this translates into relative errors that can exceed 40% (corresponding errors for all-sky emittance are about 20% for most values of A c ). Thus, priority should be given to development of general circulation model (GCM) parameterizations that account for the effects of horizontal variations in unresolved τ; effects of cloud sides are of secondary importance.
On this note, an efficient stochastic model for computing grid-averaged cloudy-sky flux transmittances is furnished that assumes that distributions of τ, for regions comparable in size to GCM grid cells, can be described adequately by gamma distribution functions. While the plane-parallel, homogeneous model underestimates cloud transmittance by about an order of magnitude when 3D variable cloud transmittances are ≲ 0.2 and by ∼20% to 100% otherwise, the stochastic model reduces these biases often by more than 80%.
Abstract
Derivation of top of atmosphere radiative fluxes requires the use of measured satellite radiances and assumptions about the anisotropy of the Earth's radiation field. The primary modification of the Earth's anisotropy is caused by variations in cloud properties. These variations occur rapidly in space and time and provide a challenge for the accurate derivation of radiative flux estimates. The present paper discusses the application of a maximum likelihood estimation (MLE) technique to the problem of cloud determination for coarse resolution broadband satellite data. This methodology is developed in concert with new empirical models of the angular dependence of radiance, and is tested against simulated satellite observations. It is argued that the new angular dependence models are a more complete description of the Earth's radiation field than any previously available models. When used to determine cloud conditions for the inversion of satellite-measured radiances to fluxes, simulations predict that the MLE approach gives substantial improvements over both a Lambertian Earth assumption and the clear/cloud threshold used in the inversion of Nimbus 3 and Nimbus 7 Earth Radiation Budget scanner data. The MLE methodology will be used in the operational processing of the Earth Radiation Budget Experiment (ERBE) scanner data. The present paper serves to document both the philosophy and the form of the MLE methodology. Validation studies using both ERBE and Nimbus 7 radiation budget data will be the subject of future papers by several ERBE Science Team investigators.
Abstract
Derivation of top of atmosphere radiative fluxes requires the use of measured satellite radiances and assumptions about the anisotropy of the Earth's radiation field. The primary modification of the Earth's anisotropy is caused by variations in cloud properties. These variations occur rapidly in space and time and provide a challenge for the accurate derivation of radiative flux estimates. The present paper discusses the application of a maximum likelihood estimation (MLE) technique to the problem of cloud determination for coarse resolution broadband satellite data. This methodology is developed in concert with new empirical models of the angular dependence of radiance, and is tested against simulated satellite observations. It is argued that the new angular dependence models are a more complete description of the Earth's radiation field than any previously available models. When used to determine cloud conditions for the inversion of satellite-measured radiances to fluxes, simulations predict that the MLE approach gives substantial improvements over both a Lambertian Earth assumption and the clear/cloud threshold used in the inversion of Nimbus 3 and Nimbus 7 Earth Radiation Budget scanner data. The MLE methodology will be used in the operational processing of the Earth Radiation Budget Experiment (ERBE) scanner data. The present paper serves to document both the philosophy and the form of the MLE methodology. Validation studies using both ERBE and Nimbus 7 radiation budget data will be the subject of future papers by several ERBE Science Team investigators.
Abstract
Landsat Multispectral Scanner (MSS) and Thematic Mapper (TM) digital data are used to remotely sense fog properties. These include fog cell size distribution, cell aspect ratio (the ratio of the length of the major and minor axes of the cells), and cell orientation angle. The analysis is carried out for four fog scenes, three high-inversion radiation fogs in central California, and one advection fog in eastern South Dakota.
Results for these initial fog studies indicate that 1) fogs are stratocumulus in nature, being composed of individual cellular structures; 2) the reflectance properties vary strongly across the cells, suggesting considerable variation in liquid water content; 3) fogs often are patchy, often revealing surface features between fog cells; 4) the ratio of wavelength (λ) between cells and the height of the boundary layer (h) is λ/h ≈ 2–3, in agreement with values obtained for Benard cells and longitudinal rolls observed in cloud systems; 5) the typical horizontal aspect ratio of fog cells is about a factor of 2; and 6) observed quasi-periodic oscillations of measured fog variables may be caused by advection of the cellular structures across the observational site.
Abstract
Landsat Multispectral Scanner (MSS) and Thematic Mapper (TM) digital data are used to remotely sense fog properties. These include fog cell size distribution, cell aspect ratio (the ratio of the length of the major and minor axes of the cells), and cell orientation angle. The analysis is carried out for four fog scenes, three high-inversion radiation fogs in central California, and one advection fog in eastern South Dakota.
Results for these initial fog studies indicate that 1) fogs are stratocumulus in nature, being composed of individual cellular structures; 2) the reflectance properties vary strongly across the cells, suggesting considerable variation in liquid water content; 3) fogs often are patchy, often revealing surface features between fog cells; 4) the ratio of wavelength (λ) between cells and the height of the boundary layer (h) is λ/h ≈ 2–3, in agreement with values obtained for Benard cells and longitudinal rolls observed in cloud systems; 5) the typical horizontal aspect ratio of fog cells is about a factor of 2; and 6) observed quasi-periodic oscillations of measured fog variables may be caused by advection of the cellular structures across the observational site.
Abstract
Landsat Multispectral Scanner (MSS) digital data are used to remotely sense cumulus cloud properties such as cloud fraction and cloud reflectance, along with the distribution of cloud number and cloud fraction as a function of cloud size. The analysis is carried out for four cumulus fields covering regions approximately 150 km square. Results for these initial cloud fields indicate that: (i) the common intuitive model of clouds as nearly uniform reflecting surfaces is a poor representation of cumulus clouds, (ii) the cumulus clouds were often multicelled, even for clouds as small as 1 km in diameter, (iii) cloud fractional coverage derived using a simple reflectance threshold is sensitive to the chosen threshold even for 57-meter resolution Landsat data, (iv) the sensitivity of cloud fraction to changes in satellite sensor resolution is less sensitive than suggested theoretically, and (v) the Landsat derived cloud size distributions show encouraging similarities among the cloud fields examined.
Abstract
Landsat Multispectral Scanner (MSS) digital data are used to remotely sense cumulus cloud properties such as cloud fraction and cloud reflectance, along with the distribution of cloud number and cloud fraction as a function of cloud size. The analysis is carried out for four cumulus fields covering regions approximately 150 km square. Results for these initial cloud fields indicate that: (i) the common intuitive model of clouds as nearly uniform reflecting surfaces is a poor representation of cumulus clouds, (ii) the cumulus clouds were often multicelled, even for clouds as small as 1 km in diameter, (iii) cloud fractional coverage derived using a simple reflectance threshold is sensitive to the chosen threshold even for 57-meter resolution Landsat data, (iv) the sensitivity of cloud fraction to changes in satellite sensor resolution is less sensitive than suggested theoretically, and (v) the Landsat derived cloud size distributions show encouraging similarities among the cloud fields examined.
Abstract
Adopting procedures often applied to model the earth's climate, we use zonal fields from the control run of a general circulation climate model (GCM) (Wetherald and Manabe, 1975) to construct parameterizations of the energy budget components for use in. a simple Budyko-Sellers energy balance climate model (EBM) (North, 1975). Comparing the results of the GCM and the EBM for changes in solar constant, we find that with these parameterizations changes in the surface temperature calculated with the EBM are substantially larger than those calculated with the GCM. Furthermore, when the meridional energy transport in the EBM is held constant so that it simulates the transport in the GCM, the results of the two models diverge hopelessly. On the other hand, with the parameterizations of the EBM modified to simulate the behavior of the GCM fields, the results of the two models agree fairly well. This exercise illustrates the weakness of current methods used to extract parameterizations for EBMs from observations of the present climate.
Abstract
Adopting procedures often applied to model the earth's climate, we use zonal fields from the control run of a general circulation climate model (GCM) (Wetherald and Manabe, 1975) to construct parameterizations of the energy budget components for use in. a simple Budyko-Sellers energy balance climate model (EBM) (North, 1975). Comparing the results of the GCM and the EBM for changes in solar constant, we find that with these parameterizations changes in the surface temperature calculated with the EBM are substantially larger than those calculated with the GCM. Furthermore, when the meridional energy transport in the EBM is held constant so that it simulates the transport in the GCM, the results of the two models diverge hopelessly. On the other hand, with the parameterizations of the EBM modified to simulate the behavior of the GCM fields, the results of the two models agree fairly well. This exercise illustrates the weakness of current methods used to extract parameterizations for EBMs from observations of the present climate.
Abstract
An error analysis is presented for cloud-top pressure and cloud-amount retrieval using infrared sounder data. Rms and bias errors are determined for instrument noise (typical of the HIRS-2 instrument on TIROS-N) and for uncertainties in the temperature profiles and water vapor profiles used to estimate clear-sky radiances. Errors are determined for a range of test cloud amounts (0.1–1.0) and cloud-top pressures (920–100 mb). Rms errors vary by an order of magnitude depending on the cloud height and cloud amount within the satellite's field of view. Large bias errors are found for low-altitude clouds. These bias errors are shown to result from physical constraints placed on retrieved cloud properties, i.e., cloud amounts between 0.0 and 1.0 and cloud-top pressures between the ground and tropopause levels. Middle-level and high-level clouds (above 3–4 km) are retrieved with low bias and rms errors. For instrument noise the 4.3 μm channels provide the smallest errors. For temperature profile and water vapor profile uncertainties the 15 μm channels generally give smaller errors. Errors due to rms temperature profile uncertainties of 2.0°C are found to be larger than errors due to instrument noise, independent of the sounding channels used.
Abstract
An error analysis is presented for cloud-top pressure and cloud-amount retrieval using infrared sounder data. Rms and bias errors are determined for instrument noise (typical of the HIRS-2 instrument on TIROS-N) and for uncertainties in the temperature profiles and water vapor profiles used to estimate clear-sky radiances. Errors are determined for a range of test cloud amounts (0.1–1.0) and cloud-top pressures (920–100 mb). Rms errors vary by an order of magnitude depending on the cloud height and cloud amount within the satellite's field of view. Large bias errors are found for low-altitude clouds. These bias errors are shown to result from physical constraints placed on retrieved cloud properties, i.e., cloud amounts between 0.0 and 1.0 and cloud-top pressures between the ground and tropopause levels. Middle-level and high-level clouds (above 3–4 km) are retrieved with low bias and rms errors. For instrument noise the 4.3 μm channels provide the smallest errors. For temperature profile and water vapor profile uncertainties the 15 μm channels generally give smaller errors. Errors due to rms temperature profile uncertainties of 2.0°C are found to be larger than errors due to instrument noise, independent of the sounding channels used.
Abstract
A technique is developed that uses a multispectral, multiresolution (MSMR) method to improve the overall retrieval of mid-to high-level cloud properties by combining HIRS sounding channel data with higher spatial resolution AVHRR radiometric data collocated with the HIRS footprint. Cirrus cloud radiative and physical properties are determined using satellite data, surface-based measurements provided by rawinsondes and lidar, and aircraft-based lidar data collected during the First ISCCP (International Satellite Cloud Climatology Program) Regional Experiment (FIRE) in Wisconsin during the months of October and November 1986. HIRS cloud-height retrievals are compared to ground-based lidar and aircraft lidar when possible. Retrieved cloud heights are found to have close agreement with lidar for thin cloud, but are higher than lidar for optically thick cloud. The fact that the retrieved cloud height is higher than lidar for optically thick cloud is probably due to the attenuation of the lidar signal before the signal reaches through the cloud, while the satellite is viewing the cloud from above. AVHRR visible (0.63-μm) and infrared (11-μm) radiances are analyzed to determine the cloud emittances and reflectances collocated with each HIRS pixel. The bidirectional reflectances from the AVHRR visible-channel data are corrected for solar direct and diffuse surface reflection to isolate the cloud reflectance. The individual AVHRR pixel emittances are calculated using the cloud-top temperature derived from the HIRS cloud-retrieval analysis. The results of the reflectance-emittance relationships derived in this fashion are compared to theoretical scattering model results for both water-droplet spheres and randomly oriented hexagonal ice crystals. It is found that the assumption of 10-μm water droplets is inadequate to describe the reflectance-emittance relationship for the ice clouds seen here. Use of this assumption would lead to lower cloud heights using the ISCCP approach. The theoretical results show that use of hexagonal ice-crystal phase functions could lead to much improved results for cloud retrieval algorithms using a bispectral approach.
Abstract
A technique is developed that uses a multispectral, multiresolution (MSMR) method to improve the overall retrieval of mid-to high-level cloud properties by combining HIRS sounding channel data with higher spatial resolution AVHRR radiometric data collocated with the HIRS footprint. Cirrus cloud radiative and physical properties are determined using satellite data, surface-based measurements provided by rawinsondes and lidar, and aircraft-based lidar data collected during the First ISCCP (International Satellite Cloud Climatology Program) Regional Experiment (FIRE) in Wisconsin during the months of October and November 1986. HIRS cloud-height retrievals are compared to ground-based lidar and aircraft lidar when possible. Retrieved cloud heights are found to have close agreement with lidar for thin cloud, but are higher than lidar for optically thick cloud. The fact that the retrieved cloud height is higher than lidar for optically thick cloud is probably due to the attenuation of the lidar signal before the signal reaches through the cloud, while the satellite is viewing the cloud from above. AVHRR visible (0.63-μm) and infrared (11-μm) radiances are analyzed to determine the cloud emittances and reflectances collocated with each HIRS pixel. The bidirectional reflectances from the AVHRR visible-channel data are corrected for solar direct and diffuse surface reflection to isolate the cloud reflectance. The individual AVHRR pixel emittances are calculated using the cloud-top temperature derived from the HIRS cloud-retrieval analysis. The results of the reflectance-emittance relationships derived in this fashion are compared to theoretical scattering model results for both water-droplet spheres and randomly oriented hexagonal ice crystals. It is found that the assumption of 10-μm water droplets is inadequate to describe the reflectance-emittance relationship for the ice clouds seen here. Use of this assumption would lead to lower cloud heights using the ISCCP approach. The theoretical results show that use of hexagonal ice-crystal phase functions could lead to much improved results for cloud retrieval algorithms using a bispectral approach.
