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Abstract
A simple yet flexible and robust algorithm is described for fully partitioning an arbitrary dataset into compact, nonoverlapping groups or classes, sorted by size, based entirely on a pairwise similarity matrix and a user-specified similarity threshold. Unlike many clustering algorithms, there is no assumption that natural clusters exist in the dataset, although clusters, when present, may be preferentially assigned to one or more classes. The method also does not require data objects to be compared within any coordinate system but rather permits the user to define pairwise similarity using almost any conceivable criterion. The method therefore lends itself to certain geoscientific applications for which conventional clustering methods are unsuited, including two nontrivial and distinctly different datasets presented as examples. In addition to identifying large classes containing numerous similar dataset members, it is also well suited for isolating rare or anomalous members of a dataset. The method is inductive in that prototypes identified in representative subset of a larger dataset can be used to classify the remainder.
Abstract
A simple yet flexible and robust algorithm is described for fully partitioning an arbitrary dataset into compact, nonoverlapping groups or classes, sorted by size, based entirely on a pairwise similarity matrix and a user-specified similarity threshold. Unlike many clustering algorithms, there is no assumption that natural clusters exist in the dataset, although clusters, when present, may be preferentially assigned to one or more classes. The method also does not require data objects to be compared within any coordinate system but rather permits the user to define pairwise similarity using almost any conceivable criterion. The method therefore lends itself to certain geoscientific applications for which conventional clustering methods are unsuited, including two nontrivial and distinctly different datasets presented as examples. In addition to identifying large classes containing numerous similar dataset members, it is also well suited for isolating rare or anomalous members of a dataset. The method is inductive in that prototypes identified in representative subset of a larger dataset can be used to classify the remainder.
Abstract
Using stringent criteria pertaining to rain-cloud optical thickness and horizontal extent, 3203 multichannel microwave observations of heavy, widespread tropical precipitation over ocean were selected from 9 months of global Special Sensor Microwave Imager (SSM/I) data. These observations subsequently were found to be associated almost exclusively with stratiform rain areas in tropical cyclones. Because of the restrictions on optical thickness and spatial extent, the mean multichannel microwave brightness temperatures and their interchannel covariances are presumed to be determined primarily by the vertical microphysical structure of the rain clouds. The distribution of the above observations in seven-dimensional channel space is characterized concisely using principal component analysis. It is found that only three independent variables are sufficient to explain 97% of the variance in the correlation matrix. This result suggests that the radiometrically important microphysical properties of these rain clouds are strongly interdependent. The most significant eigenvector of the observation correlation matrix corresponds to variable scattering at high frequencies by ice aloft. Its spectral dependence is accurately given by ν 1.76, where ν is the microwave frequency. This empirical result constrains the effective mean sizes of ice particles responsible for observed passive microwave scattering in rain clouds and provides a plausible empirical basis for accurately predicting the magnitude of scattering effects by ice at non-SSM/I microwave frequencies. There are also qualitative indications that this mode of brightness temperature variability is poorly correlated with surface rain rate in this study sample. The empirical results presented herein are expected to be of value for the validation and improvement of microphysical assumptions and optical parameterizations in forward microwave radiative transfer models. Companion papers describe the actual retrieval of effective rain-cloud microphysical properties from the observed multichannel radiances.
Abstract
Using stringent criteria pertaining to rain-cloud optical thickness and horizontal extent, 3203 multichannel microwave observations of heavy, widespread tropical precipitation over ocean were selected from 9 months of global Special Sensor Microwave Imager (SSM/I) data. These observations subsequently were found to be associated almost exclusively with stratiform rain areas in tropical cyclones. Because of the restrictions on optical thickness and spatial extent, the mean multichannel microwave brightness temperatures and their interchannel covariances are presumed to be determined primarily by the vertical microphysical structure of the rain clouds. The distribution of the above observations in seven-dimensional channel space is characterized concisely using principal component analysis. It is found that only three independent variables are sufficient to explain 97% of the variance in the correlation matrix. This result suggests that the radiometrically important microphysical properties of these rain clouds are strongly interdependent. The most significant eigenvector of the observation correlation matrix corresponds to variable scattering at high frequencies by ice aloft. Its spectral dependence is accurately given by ν 1.76, where ν is the microwave frequency. This empirical result constrains the effective mean sizes of ice particles responsible for observed passive microwave scattering in rain clouds and provides a plausible empirical basis for accurately predicting the magnitude of scattering effects by ice at non-SSM/I microwave frequencies. There are also qualitative indications that this mode of brightness temperature variability is poorly correlated with surface rain rate in this study sample. The empirical results presented herein are expected to be of value for the validation and improvement of microphysical assumptions and optical parameterizations in forward microwave radiative transfer models. Companion papers describe the actual retrieval of effective rain-cloud microphysical properties from the observed multichannel radiances.
Abstract
A highly simplified, yet meteorologically realistic and flexible, parametric model is described for generating hydrometeor profiles and other environmental properties relevant to microwave radiative transfer calculations in quasi-stratiform rain clouds. With this model, it is possible, via 19 adjustable parameters, to vary cloud and environmental properties, including hydrometeor size distributions and densities, in a continuous, yet self-consistent, fashion and to assess the impact of these changes on computed multichannel microwave brightness radiances. It is also possible to utilize gradient descent methods to find plausible combinations of cloud properties that explain observed multichannel microwave radiances in rain clouds. Potential applications of the above model include 1) gaining insight into effective microphysical properties, for microwave radiative transfer purposes, of actual precipitating cloud systems and 2) accurate extrapolation of observed microwave multichannel radiances in rain clouds to the frequencies and viewing angles of new microwave sensors.
Abstract
A highly simplified, yet meteorologically realistic and flexible, parametric model is described for generating hydrometeor profiles and other environmental properties relevant to microwave radiative transfer calculations in quasi-stratiform rain clouds. With this model, it is possible, via 19 adjustable parameters, to vary cloud and environmental properties, including hydrometeor size distributions and densities, in a continuous, yet self-consistent, fashion and to assess the impact of these changes on computed multichannel microwave brightness radiances. It is also possible to utilize gradient descent methods to find plausible combinations of cloud properties that explain observed multichannel microwave radiances in rain clouds. Potential applications of the above model include 1) gaining insight into effective microphysical properties, for microwave radiative transfer purposes, of actual precipitating cloud systems and 2) accurate extrapolation of observed microwave multichannel radiances in rain clouds to the frequencies and viewing angles of new microwave sensors.
Abstract
A new conceptual and computational basis is described for renormalizing the single-scatter and extinction properties (optical depth, single-scatter albedo, and scattering phase function or asymmetry parameter) of a three-dimensionally inhomogeneous cloud volume or layer so as to describe a radiatively equivalent homogeneous volume or layer. The renormalization may allow area-averaged fluxes and intensities to be efficiently computed for some inhomogeneous cloud fields using standard homogeneous (e.g., plane parallel) radiative transfer codes.
In the Independently Scattering Cloudlet (ISC) model, macroscopic “cloudlets” distributed randomly throughout a volume are treated as discrete scatterers, analogous to individual cloud droplets but with modified single-scatter properties due to internal multiple scattering. If a volume encompasses only cloudlets that are optically thin, the renormalized single-scatter properties for the volume revert to the intrinsic values and the homogeneous case is recovered.
Although the ISC approach is based on a highly idealized, and therefore unrealistic, geometric model of inhomogeneous cloud structure, comparisons with accurate Monte Carlo flux calculations for more realistic random structures reveal surprising accuracy in its reproduction of the relationship between area-averaged albedo, direct transmittance, diffuse transmittance, and in-cloud absorptance. In particular, it describes the approximate functional dependence of these characteristics on the intrinsic single-scatter albedo when all other parameters are held constant. Moreover, it reproduces the relationship between renormalized single-scatter albedo and renormalized optical thickness derived independently, via a perturbative analysis, by other authors. Finally, the ISC model offers a reasonably intuitive physical interpretation of how cloud inhomogeneities influence area-averaged solar radiative transfer, including the significant enhancement of in-cloud absorption under certain conditions.
Abstract
A new conceptual and computational basis is described for renormalizing the single-scatter and extinction properties (optical depth, single-scatter albedo, and scattering phase function or asymmetry parameter) of a three-dimensionally inhomogeneous cloud volume or layer so as to describe a radiatively equivalent homogeneous volume or layer. The renormalization may allow area-averaged fluxes and intensities to be efficiently computed for some inhomogeneous cloud fields using standard homogeneous (e.g., plane parallel) radiative transfer codes.
In the Independently Scattering Cloudlet (ISC) model, macroscopic “cloudlets” distributed randomly throughout a volume are treated as discrete scatterers, analogous to individual cloud droplets but with modified single-scatter properties due to internal multiple scattering. If a volume encompasses only cloudlets that are optically thin, the renormalized single-scatter properties for the volume revert to the intrinsic values and the homogeneous case is recovered.
Although the ISC approach is based on a highly idealized, and therefore unrealistic, geometric model of inhomogeneous cloud structure, comparisons with accurate Monte Carlo flux calculations for more realistic random structures reveal surprising accuracy in its reproduction of the relationship between area-averaged albedo, direct transmittance, diffuse transmittance, and in-cloud absorptance. In particular, it describes the approximate functional dependence of these characteristics on the intrinsic single-scatter albedo when all other parameters are held constant. Moreover, it reproduces the relationship between renormalized single-scatter albedo and renormalized optical thickness derived independently, via a perturbative analysis, by other authors. Finally, the ISC model offers a reasonably intuitive physical interpretation of how cloud inhomogeneities influence area-averaged solar radiative transfer, including the significant enhancement of in-cloud absorption under certain conditions.
On Some Shortcomings of Shannon Entropy as a Measure of Information Content in Indirect Measurements of Continuous VariablesAbstract
Shannon entropy has long been accepted as a primary basis for assessing the information content of sensor channels used for the remote sensing of atmospheric variables. It is not widely appreciated, however, that Shannon information content (SIC) can be misleading in retrieval problems involving nonlinear mappings between direct observations and retrieved variables and/or non-Gaussian prior and posterior PDFs. The potentially severe shortcomings of SIC are illustrated with simple experiments that reveal, for example, that a measurement can be judged to provide negative information even in cases in which the postretrieval PDF is undeniably improved over an informed prior based on climatology. Following previous authors’ writing mainly in the data assimilation and climate analysis literature, the Kullback–Leibler (KL) divergence, also commonly known as relative entropy, is shown to suffer from fewer obvious defects in this particular context. Yet, even KL divergence is blind to the expected magnitude of errors as typically measured by the error variance or root-mean-square error. Thus, neither information metric can necessarily be counted on to respond in a predictable way to changes in the precision or quality of a retrieved quantity.
Abstract
Shannon entropy has long been accepted as a primary basis for assessing the information content of sensor channels used for the remote sensing of atmospheric variables. It is not widely appreciated, however, that Shannon information content (SIC) can be misleading in retrieval problems involving nonlinear mappings between direct observations and retrieved variables and/or non-Gaussian prior and posterior PDFs. The potentially severe shortcomings of SIC are illustrated with simple experiments that reveal, for example, that a measurement can be judged to provide negative information even in cases in which the postretrieval PDF is undeniably improved over an informed prior based on climatology. Following previous authors’ writing mainly in the data assimilation and climate analysis literature, the Kullback–Leibler (KL) divergence, also commonly known as relative entropy, is shown to suffer from fewer obvious defects in this particular context. Yet, even KL divergence is blind to the expected magnitude of errors as typically measured by the error variance or root-mean-square error. Thus, neither information metric can necessarily be counted on to respond in a predictable way to changes in the precision or quality of a retrieved quantity.
Ship reports of present weather obtained from the Comprehensive Ocean–Atmosphere Data Set are analyzed for the period 1958–91 in orderto elucidate regional and seasonal variations in the climatological frequency, phase, intensity, and character of oceanic precipitation. Specific findings of note include the following:
The results of this study suggest that many current satellite rainfall estimation techniques may substantially underestimate the fractional coverage or frequency of precipitation poleward of 50° latitude and in the subtropical dry zones. They also draw attention to the need to carefully account for regional differences in the physical and spatial properties of rainfall when developing calibration relationships for satellite algorithms.
Ship reports of present weather obtained from the Comprehensive Ocean–Atmosphere Data Set are analyzed for the period 1958–91 in orderto elucidate regional and seasonal variations in the climatological frequency, phase, intensity, and character of oceanic precipitation. Specific findings of note include the following:
The results of this study suggest that many current satellite rainfall estimation techniques may substantially underestimate the fractional coverage or frequency of precipitation poleward of 50° latitude and in the subtropical dry zones. They also draw attention to the need to carefully account for regional differences in the physical and spatial properties of rainfall when developing calibration relationships for satellite algorithms.
Abstract
Land and ship surface synoptic reports of nondrizzle intensity precipitation in progress were matched with 3596 nearly coincident full disk 4-km resolution infrared images from the GMS-5 geostationary satellite, covering 18 calendar months, in order to derive regional and seasonal estimates of the contribution of relatively warm-topped clouds to the total time in precipitation.
Minimum infrared temperatures of 273 K or warmer were found to be associated with 20%–40% of the surface reports of nondrizzle precipitation over much of the ocean east of Australia during all four seasons. Similar or even larger fractions were found during December–March over parts of Indochina, southern China, and the adjacent South China Sea. Although reports of precipitation of moderate or heavy intensity were found to be associated more often with colder cloud tops, there were still regions for which a substantial fraction of these reports were associated with relatively warm clouds. These results suggest at least a potential for significant regional and seasonal biases in satellite infrared or passive microwave scattering based estimates of global precipitation.
Abstract
Land and ship surface synoptic reports of nondrizzle intensity precipitation in progress were matched with 3596 nearly coincident full disk 4-km resolution infrared images from the GMS-5 geostationary satellite, covering 18 calendar months, in order to derive regional and seasonal estimates of the contribution of relatively warm-topped clouds to the total time in precipitation.
Minimum infrared temperatures of 273 K or warmer were found to be associated with 20%–40% of the surface reports of nondrizzle precipitation over much of the ocean east of Australia during all four seasons. Similar or even larger fractions were found during December–March over parts of Indochina, southern China, and the adjacent South China Sea. Although reports of precipitation of moderate or heavy intensity were found to be associated more often with colder cloud tops, there were still regions for which a substantial fraction of these reports were associated with relatively warm clouds. These results suggest at least a potential for significant regional and seasonal biases in satellite infrared or passive microwave scattering based estimates of global precipitation.
Abstract
Four spiraliform polar lows, two over the Sea of Japan and two over the Nordic Seas, were simulated with the Weather Research and Forecasting (WRF) model. Five mixed-phase bulk microphysics schemes (BMS) provided with WRF were run respectively in order to compare their performance in polar low simulations. The observed cloud-top temperatures (CTTs) were compared with the model simulations. Precipitation rates estimated by the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) and gauge-calibrated surface radar precipitation estimates around Japan were also used for validation. Although definitive validation is not possible with the available data, results from the WRF Single-Moment 6-class (WSM6) scheme appear to reproduce the cloud and precipitation processes most realistically. The model produced precipitation intensities comparable to validation products over the Sea of Japan. However, in the Nordic Seas cases, all five schemes produced significantly more precipitation than the AMSR-E estimates even though the latter estimates are known to average slightly high in the same region when validated against monthly totals measured at Jan Mayen Island (Norway).
Abstract
Four spiraliform polar lows, two over the Sea of Japan and two over the Nordic Seas, were simulated with the Weather Research and Forecasting (WRF) model. Five mixed-phase bulk microphysics schemes (BMS) provided with WRF were run respectively in order to compare their performance in polar low simulations. The observed cloud-top temperatures (CTTs) were compared with the model simulations. Precipitation rates estimated by the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) and gauge-calibrated surface radar precipitation estimates around Japan were also used for validation. Although definitive validation is not possible with the available data, results from the WRF Single-Moment 6-class (WSM6) scheme appear to reproduce the cloud and precipitation processes most realistically. The model produced precipitation intensities comparable to validation products over the Sea of Japan. However, in the Nordic Seas cases, all five schemes produced significantly more precipitation than the AMSR-E estimates even though the latter estimates are known to average slightly high in the same region when validated against monthly totals measured at Jan Mayen Island (Norway).
Abstract
Coincident satellite passive microwave (SSM/I) observations and 48-h numerical simulations of 23 intensifying extratropical cyclones located over the North Atlantic or North Pacific Oceans during a single cold season are examined in order to identify systematic differences in the moist processes of storms exhibiting rapid and ordinary intensification rates. Analysis of the observations and simulations focus on the 24-h period of most rapid intensification for each case as determined from European Centre for Medium-Range Weather Forecasts 12-h mean sea level pressure analyses.
SSM/I observations of area-averaged precipitation and an index that responds to cold-cloud (convective) precipitation to the northeast of surface cyclone centers were previously shown to correlate well (∼0.80) with the latitude-normalized deepening rate (NDR) of the study sample. This large correlation is replicated by the numerical model, although the area-averaged precipitation region yielding the maximum correlation coefficient differs significantly from that determined using microwave imagery. A similar correlation emerges between model-derived area- and vertically averaged vertical motion fields and NDR. The similarity of these correlations for nearly coincident averaging regions relative to the storm center implicates unrealistic rainfall patterns as the reason for the failure of the model to accurately capture the observed optimal area-averaging region. This region is located near the storm triple point and occluded (bent-back) front, both potentially strongly convective environments.
Abstract
Coincident satellite passive microwave (SSM/I) observations and 48-h numerical simulations of 23 intensifying extratropical cyclones located over the North Atlantic or North Pacific Oceans during a single cold season are examined in order to identify systematic differences in the moist processes of storms exhibiting rapid and ordinary intensification rates. Analysis of the observations and simulations focus on the 24-h period of most rapid intensification for each case as determined from European Centre for Medium-Range Weather Forecasts 12-h mean sea level pressure analyses.
SSM/I observations of area-averaged precipitation and an index that responds to cold-cloud (convective) precipitation to the northeast of surface cyclone centers were previously shown to correlate well (∼0.80) with the latitude-normalized deepening rate (NDR) of the study sample. This large correlation is replicated by the numerical model, although the area-averaged precipitation region yielding the maximum correlation coefficient differs significantly from that determined using microwave imagery. A similar correlation emerges between model-derived area- and vertically averaged vertical motion fields and NDR. The similarity of these correlations for nearly coincident averaging regions relative to the storm center implicates unrealistic rainfall patterns as the reason for the failure of the model to accurately capture the observed optimal area-averaging region. This region is located near the storm triple point and occluded (bent-back) front, both potentially strongly convective environments.
Abstract
Precipitation parameters derived from 31 SSM/I microwave images of 23 deepening extratropical oceanic cyclones have been examined for statistical correlations with storm surface central pressure and 12-h central pressure change. Good correlations (r ∼ 0.8) were found between precipitation observed in the northeast sector of the storm and latitude-normalized deepening rate. The correlation was highest (r = 0.83) for an SSM/I 85.5-GHz scattering index that responds specifically to cold-cloud (especially convective) precipitation. Considerably weaker correlations (approximately −0.3) were found between SSM/I rainfall indices and the estimated surface central pressure at the time of the overpasses. These observational results support a strong dynamic link between latent heat release due to precipitation and synoptic-scale cyclogenesis.
Abstract
Precipitation parameters derived from 31 SSM/I microwave images of 23 deepening extratropical oceanic cyclones have been examined for statistical correlations with storm surface central pressure and 12-h central pressure change. Good correlations (r ∼ 0.8) were found between precipitation observed in the northeast sector of the storm and latitude-normalized deepening rate. The correlation was highest (r = 0.83) for an SSM/I 85.5-GHz scattering index that responds specifically to cold-cloud (especially convective) precipitation. Considerably weaker correlations (approximately −0.3) were found between SSM/I rainfall indices and the estimated surface central pressure at the time of the overpasses. These observational results support a strong dynamic link between latent heat release due to precipitation and synoptic-scale cyclogenesis.
