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Abstract
Simulation of sampling from gamma-distributed raindrop populations demonstrates that significant biases and substantial errors can occur in estimates of polarimetric radar variables based on samples of raindrop populations obtained with disdrometers. Biases and RMS errors of 0.5 dB or more in estimates of differential reflectivity Z dr can occur with samples of even a few hundred drops; significant biases and errors also occur in estimates of reflectivity Z H or specific differential phase K dp. The results indicate that very large samples would be required to obtain adequate representation of the population characteristics for many radar applications. They also suggest that greater attention is needed to the sample sizes in the disdrometer data used in developing polarimetric rainfall-rate estimators or hydrometeor classification algorithms.
Abstract
Simulation of sampling from gamma-distributed raindrop populations demonstrates that significant biases and substantial errors can occur in estimates of polarimetric radar variables based on samples of raindrop populations obtained with disdrometers. Biases and RMS errors of 0.5 dB or more in estimates of differential reflectivity Z dr can occur with samples of even a few hundred drops; significant biases and errors also occur in estimates of reflectivity Z H or specific differential phase K dp. The results indicate that very large samples would be required to obtain adequate representation of the population characteristics for many radar applications. They also suggest that greater attention is needed to the sample sizes in the disdrometer data used in developing polarimetric rainfall-rate estimators or hydrometeor classification algorithms.
Abstract
This paper discusses the subject of weather radar system sensitivity from a general point of view, with emphasis an the influence of wavelength. Expressions for the echo signal-to-noise ratio are examined using a detection theory approach to develop factors describing the effects of different signal processing techniques. Then the variation of the equivalent signal-to-noise ratio with wavelength under certain typical system design constraints is examined. The effects of both theoretical and technology system design considerations are assessed. The results vary with the design scenario and the signal processing method, but the main conclusion is that short-wavelength weather radars are not necessarily more sensitive than long-wavelength ones.
Abstract
This paper discusses the subject of weather radar system sensitivity from a general point of view, with emphasis an the influence of wavelength. Expressions for the echo signal-to-noise ratio are examined using a detection theory approach to develop factors describing the effects of different signal processing techniques. Then the variation of the equivalent signal-to-noise ratio with wavelength under certain typical system design constraints is examined. The effects of both theoretical and technology system design considerations are assessed. The results vary with the design scenario and the signal processing method, but the main conclusion is that short-wavelength weather radars are not necessarily more sensitive than long-wavelength ones.
This paper presents an analysis of the effects of shortcomings in the reporting of severe storm events on some common measures of warning performance. Such deficiencies lead to an apparent false alarm ratio (FAR) higher than the true value, and ordinarily to an apparent probability of detection (POD) also higher than the true value. An improved warning system may generate additional storm reports through closer collaboration between forecasters and storm spotters; an enhanced warning verification program will also tend to collect additional storm reports. Independently of any changes in the warning system, such additional reports tend to drive the apparent FAR down (and thus closer to the true value). If the verification efforts emphasize situations when warnings are in effect, the additional reports will further inflate the apparent POD. When changes occur in both the warning system and the verification program, the contributions of each to changes in the performance measures become intermingled. Understanding of these effects of the reporting system can aid in interpreting trends in the performance measures.
This paper presents an analysis of the effects of shortcomings in the reporting of severe storm events on some common measures of warning performance. Such deficiencies lead to an apparent false alarm ratio (FAR) higher than the true value, and ordinarily to an apparent probability of detection (POD) also higher than the true value. An improved warning system may generate additional storm reports through closer collaboration between forecasters and storm spotters; an enhanced warning verification program will also tend to collect additional storm reports. Independently of any changes in the warning system, such additional reports tend to drive the apparent FAR down (and thus closer to the true value). If the verification efforts emphasize situations when warnings are in effect, the additional reports will further inflate the apparent POD. When changes occur in both the warning system and the verification program, the contributions of each to changes in the performance measures become intermingled. Understanding of these effects of the reporting system can aid in interpreting trends in the performance measures.
Abstract
An objective technique has been developed for modifying precipitation probability guidance forecasts received from the National Meteorological Center by means of radar information which becomes available subsequent to receipt of the guidance forecasts. Tests show improvement with respect to both the centralized guidance and the official subjective forecasts. The findings also carry implications as to the resolution necessary in radar data used in such a procedure.
Abstract
An objective technique has been developed for modifying precipitation probability guidance forecasts received from the National Meteorological Center by means of radar information which becomes available subsequent to receipt of the guidance forecasts. Tests show improvement with respect to both the centralized guidance and the official subjective forecasts. The findings also carry implications as to the resolution necessary in radar data used in such a procedure.
Abstract
The moment estimators frequently used to estimate parameters for drop size distribution (DSD) functions being “fitted” to observed raindrop size distributions are biased. Consequently, the fitted functions often do not represent well either the raindrop samples or the underlying populations from which the samples were taken. Monte Carlo simulations of the process of sampling from a known exponential DSD, followed by the application of a variety of moment estimators, demonstrate this bias. Skewness in the sampling distributions of the DSD moments is the root cause of this bias, and this skewness increases with the order of the moment. As a result, the bias is stronger when higher-order moments are used in the procedures. Correlations of the sample moments with the size of the largest drop in a sample (D max) lead to correlations of the estimated parameters with D max, and, in turn, to spurious correlations between the parameters. These things can lead to erroneous inferences about characteristics of the raindrop populations that are being sampled. The bias, and the correlations, diminish as the sample size increases, so that with large samples the moment estimators may become sufficiently accurate for many purposes.
Abstract
The moment estimators frequently used to estimate parameters for drop size distribution (DSD) functions being “fitted” to observed raindrop size distributions are biased. Consequently, the fitted functions often do not represent well either the raindrop samples or the underlying populations from which the samples were taken. Monte Carlo simulations of the process of sampling from a known exponential DSD, followed by the application of a variety of moment estimators, demonstrate this bias. Skewness in the sampling distributions of the DSD moments is the root cause of this bias, and this skewness increases with the order of the moment. As a result, the bias is stronger when higher-order moments are used in the procedures. Correlations of the sample moments with the size of the largest drop in a sample (D max) lead to correlations of the estimated parameters with D max, and, in turn, to spurious correlations between the parameters. These things can lead to erroneous inferences about characteristics of the raindrop populations that are being sampled. The bias, and the correlations, diminish as the sample size increases, so that with large samples the moment estimators may become sufficiently accurate for many purposes.
Abstract
Because of the randomness associated with sampling from a population of raindrops, variations in the data reflect some undetermined mixture of sampling variability and inhomogeneity in the precipitation. Better understanding of the effects of sampling variability can aid in interpreting drop size observations. This study begins with a Monte Carlo simulation of the sampling process and then evaluates the resulting estimates of the characteristics of the underlying drop population. The characteristics considered include the liquid water concentration and the reflectivity factor; the maximum particle size in each sample is also determined. The results show that skewness in the sampling distributions when the samples are small (which is the usual case in practice) produces a propensity to underestimate all of the characteristic quantities. In particular, the distribution of the sample maximum drop sizes suggests that it may be futile to try to infer an upper truncation point for the size distribution on the basis of the maximum observed particle size.
Resulting paired values, for example, of Z and W for repeated sampling, were plotted on the usual type of loglog scatterplots. This yielded quite plausible-looking ZR and ZW relationships even though the parent drop population (and, hence, the actual values of the quantities) was unchanging; the “relationships” arose entirely from the sampling variability. Moreover, if the sample size is small, the sample points are shown to be necessarily displaced from the point corresponding to the actual population values of the variables. Consequently, any assessment of the “accuracy” of a ZR relationship based on drop size data should include some consideration of the numbers of drops involved in the samples making up the scatterplot.
Abstract
Because of the randomness associated with sampling from a population of raindrops, variations in the data reflect some undetermined mixture of sampling variability and inhomogeneity in the precipitation. Better understanding of the effects of sampling variability can aid in interpreting drop size observations. This study begins with a Monte Carlo simulation of the sampling process and then evaluates the resulting estimates of the characteristics of the underlying drop population. The characteristics considered include the liquid water concentration and the reflectivity factor; the maximum particle size in each sample is also determined. The results show that skewness in the sampling distributions when the samples are small (which is the usual case in practice) produces a propensity to underestimate all of the characteristic quantities. In particular, the distribution of the sample maximum drop sizes suggests that it may be futile to try to infer an upper truncation point for the size distribution on the basis of the maximum observed particle size.
Resulting paired values, for example, of Z and W for repeated sampling, were plotted on the usual type of loglog scatterplots. This yielded quite plausible-looking ZR and ZW relationships even though the parent drop population (and, hence, the actual values of the quantities) was unchanging; the “relationships” arose entirely from the sampling variability. Moreover, if the sample size is small, the sample points are shown to be necessarily displaced from the point corresponding to the actual population values of the variables. Consequently, any assessment of the “accuracy” of a ZR relationship based on drop size data should include some consideration of the numbers of drops involved in the samples making up the scatterplot.
Abstract
Digital radar data are used to investigate further a simple technique for estimating rainfall amounts on the basis of area coverage information. The basis of the technique is the existence of a strong correlation between a measure of the rain area coverage and duration called the Area-Time Integral (ATI) and the rain volume. This strong correlation is again demonstrated using echo cluster data from the North Dakota Cloud Modification Project 5 cm radars.
Integration on a scan-by-scan basis proved to be superior for determining ATI values to the hour-by-hour integration used previously. A 25 dB(z) reflectivity threshold was found suitable for the ATI calculation. The correlation coefficient on log-log plots of cluster rain volume versus ATI is approximately 0.98, indicating a power-law relationship between the variables. The exponent of that relationship is just a little higher than one, which indicates that the cluster average rainfall rate is almost independent of the storm size and duration.
A test of the relationship derived from one set of data (1980) against an independent set (1981) showed it to be consistent. Using the 1980 relationship to estimate the 1981 cluster rain volume for a given ATI, the uncertainty of the rain volume estimates was found to be −31%, +46%.
Abstract
Digital radar data are used to investigate further a simple technique for estimating rainfall amounts on the basis of area coverage information. The basis of the technique is the existence of a strong correlation between a measure of the rain area coverage and duration called the Area-Time Integral (ATI) and the rain volume. This strong correlation is again demonstrated using echo cluster data from the North Dakota Cloud Modification Project 5 cm radars.
Integration on a scan-by-scan basis proved to be superior for determining ATI values to the hour-by-hour integration used previously. A 25 dB(z) reflectivity threshold was found suitable for the ATI calculation. The correlation coefficient on log-log plots of cluster rain volume versus ATI is approximately 0.98, indicating a power-law relationship between the variables. The exponent of that relationship is just a little higher than one, which indicates that the cluster average rainfall rate is almost independent of the storm size and duration.
A test of the relationship derived from one set of data (1980) against an independent set (1981) showed it to be consistent. Using the 1980 relationship to estimate the 1981 cluster rain volume for a given ATI, the uncertainty of the rain volume estimates was found to be −31%, +46%.
Abstract
On 28 October 1986 the NCAR Sabreliner observed a cirrus cloud layer in the vicinity of Green Bay, Wisconsin. A portion of each flight leg was conducted over western Lake Michigan and over the adjacent western shore. The cirrus layer would be qualitatively described as optically thin and tenuous, yet broadband infrared effective emittances were found between about 0.4 and 0.6 while broadband shortwave extinction values ranged from as low as 5% to 32%. This investigation examines the bulk radiative properties of the cirrus layer and the horizontal variability of these radiative properties. In addition, the microphysical characteristics and the dynamic properties of the layer are presented and analyzed. The broadband infrared volume absorption coefficients were deduced for the cirrus layer and found to be very similar in terms of a dependence on temperature to results recently presented by other authors. Infrared radiative heating rates were calculated and found to be typical of the optically thin cirrus layer examined here. The horizontal structures of the radiative properties of the cirrus cloud layer and the vertical velocity observations were very similar. Both showed a smaller scale variation at the top of the cirrus layer which merged into larger scale common elements near the bases of the layer. Power spectra analyses of along-wind and cross-wind components near the base of the clouds sampled exhibited a steep spectral slope of k −3 at the smaller wave numbers (scalelengths greater than 1 km). This k −3 slope is characteristic of two-dimensional eddies. The same k −3 slope is present in the power spectra of the radiative properties. It is probable that these radiative properties, which are modulated by the cloud elements, have their scales determined by the eddies detected in the analysis of wind components.
Abstract
On 28 October 1986 the NCAR Sabreliner observed a cirrus cloud layer in the vicinity of Green Bay, Wisconsin. A portion of each flight leg was conducted over western Lake Michigan and over the adjacent western shore. The cirrus layer would be qualitatively described as optically thin and tenuous, yet broadband infrared effective emittances were found between about 0.4 and 0.6 while broadband shortwave extinction values ranged from as low as 5% to 32%. This investigation examines the bulk radiative properties of the cirrus layer and the horizontal variability of these radiative properties. In addition, the microphysical characteristics and the dynamic properties of the layer are presented and analyzed. The broadband infrared volume absorption coefficients were deduced for the cirrus layer and found to be very similar in terms of a dependence on temperature to results recently presented by other authors. Infrared radiative heating rates were calculated and found to be typical of the optically thin cirrus layer examined here. The horizontal structures of the radiative properties of the cirrus cloud layer and the vertical velocity observations were very similar. Both showed a smaller scale variation at the top of the cirrus layer which merged into larger scale common elements near the bases of the layer. Power spectra analyses of along-wind and cross-wind components near the base of the clouds sampled exhibited a steep spectral slope of k −3 at the smaller wave numbers (scalelengths greater than 1 km). This k −3 slope is characteristic of two-dimensional eddies. The same k −3 slope is present in the power spectra of the radiative properties. It is probable that these radiative properties, which are modulated by the cloud elements, have their scales determined by the eddies detected in the analysis of wind components.
Abstract
Microphysical measurements in and near the weak echo region of a supercell thunderstorm are discussed. The observations were made in southeastern Montana with an armored T-28 aircraft, which has the capability to measure hydrometeors over almost the entire spectrum between about 3 μm and 5 cm diameter. The storm exhibited many of the classic supercell characteristics, such as a well-developed weak echo region, overhang, persistent hook echo, and a large high-reflectivity core. Peak updrafts in the weak echo region exceeded 50 m s−1, and a continuous region of updraft extending over a horizontal distance of more than 14 km was observed. The updraft core appeared to be undiluted, but the edges of the updraft were clearly mixed with air from other regions of the storm. Virtually no ice particles were observed in the weak echo region, but the cloud liquid water concentrations exceeded 6 g m−3. Hail larger than 4 cm was encountered in several locations to the west of the weak echo region. The observations suggested that the hail achieved most of its growth at levels above the T-28, became large enough to descend in the edge of the updraft, and depleted the cloud liquid during the descent.
Abstract
Microphysical measurements in and near the weak echo region of a supercell thunderstorm are discussed. The observations were made in southeastern Montana with an armored T-28 aircraft, which has the capability to measure hydrometeors over almost the entire spectrum between about 3 μm and 5 cm diameter. The storm exhibited many of the classic supercell characteristics, such as a well-developed weak echo region, overhang, persistent hook echo, and a large high-reflectivity core. Peak updrafts in the weak echo region exceeded 50 m s−1, and a continuous region of updraft extending over a horizontal distance of more than 14 km was observed. The updraft core appeared to be undiluted, but the edges of the updraft were clearly mixed with air from other regions of the storm. Virtually no ice particles were observed in the weak echo region, but the cloud liquid water concentrations exceeded 6 g m−3. Hail larger than 4 cm was encountered in several locations to the west of the weak echo region. The observations suggested that the hail achieved most of its growth at levels above the T-28, became large enough to descend in the edge of the updraft, and depleted the cloud liquid during the descent.
Abstract
The characteristics of the so-called “radar-identified big drop zones” (rBDZ) have been investigated. The study employs radar observations of several thunderstorms and simultaneous microphysical and vertical wind measurements with a penetrating T-28 aircraft. The comparison of aircraft-measured vertical wind and radar data revealed good coincidence between rBDZs and updraft regions, indicating that this part of the seeding hypothesis upon which Grossversuch IV was based is reasonable. The microphysical observations of rBDZs, however, show large concentrations of ice particles and practically no supercooled raindrops indicating that the latter do not play a significant role in the development of hail in the Swiss storms. There is no reason to believe that directing seeding material into such regions where natural ice already exists in great abundance will have any significant effect an the hail process.
Abstract
The characteristics of the so-called “radar-identified big drop zones” (rBDZ) have been investigated. The study employs radar observations of several thunderstorms and simultaneous microphysical and vertical wind measurements with a penetrating T-28 aircraft. The comparison of aircraft-measured vertical wind and radar data revealed good coincidence between rBDZs and updraft regions, indicating that this part of the seeding hypothesis upon which Grossversuch IV was based is reasonable. The microphysical observations of rBDZs, however, show large concentrations of ice particles and practically no supercooled raindrops indicating that the latter do not play a significant role in the development of hail in the Swiss storms. There is no reason to believe that directing seeding material into such regions where natural ice already exists in great abundance will have any significant effect an the hail process.