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- Author or Editor: Alexander V. Ryzhkov x
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Abstract
Differential sedimentation of precipitation occurs because heavier hydrometeors fall faster than lighter ones. Updrafts and vertical wind shear can maintain this otherwise transient size sorting, resulting in prolonged regions of ongoing particle sorting in storms. This study quantifies the impact of size sorting on the S-band polarimetric radar variables (radar reflectivity factor at horizontal polarization ZH , differential reflectivity Z DR, specific differential phase K DP, and the copolar cross-correlation coefficient ρ hv). These variables are calculated from output of two idealized bin models: a one-dimensional model of pure raindrop fallout and a two-dimensional rain shaft encountering vertical wind shear. Additionally, errors in the radar variables as simulated by single-, double-, and triple-moment bulk microphysics parameterizations are quantified for the same size sorting scenarios.
Size sorting produces regions of sparsely concentrated large drops with a lack of smaller drops, causing Z DR enhancements as large as 1 dB in areas of decreased ZH , often along a ZH gradient. Such areas of enhanced Z DR are offset from those of high ZH and K DP. Illustrative examples of polarimetric radar observations in a variety of precipitation regimes demonstrate the widespread occurrence of size sorting and are consistent with the bin model simulations. Single-moment schemes are incapable of size sorting, leading to large underestimations in Z DR (>2 dB) compared to the bin model solution. Double-moment schemes with a fixed spectral shape parameter produce excessive size sorting by incorrectly increasing the number of large raindrops, overestimating Z DR by 2–3 dB. Three-moment schemes with variable shape parameters better capture the narrowing drop size distribution resulting from size sorting but can underestimate Z DR and overestimate K DP by as much as 20%. Implications for polarimetric radar data assimilation into storm-scale numerical weather prediction models are discussed.
Abstract
Differential sedimentation of precipitation occurs because heavier hydrometeors fall faster than lighter ones. Updrafts and vertical wind shear can maintain this otherwise transient size sorting, resulting in prolonged regions of ongoing particle sorting in storms. This study quantifies the impact of size sorting on the S-band polarimetric radar variables (radar reflectivity factor at horizontal polarization ZH , differential reflectivity Z DR, specific differential phase K DP, and the copolar cross-correlation coefficient ρ hv). These variables are calculated from output of two idealized bin models: a one-dimensional model of pure raindrop fallout and a two-dimensional rain shaft encountering vertical wind shear. Additionally, errors in the radar variables as simulated by single-, double-, and triple-moment bulk microphysics parameterizations are quantified for the same size sorting scenarios.
Size sorting produces regions of sparsely concentrated large drops with a lack of smaller drops, causing Z DR enhancements as large as 1 dB in areas of decreased ZH , often along a ZH gradient. Such areas of enhanced Z DR are offset from those of high ZH and K DP. Illustrative examples of polarimetric radar observations in a variety of precipitation regimes demonstrate the widespread occurrence of size sorting and are consistent with the bin model simulations. Single-moment schemes are incapable of size sorting, leading to large underestimations in Z DR (>2 dB) compared to the bin model solution. Double-moment schemes with a fixed spectral shape parameter produce excessive size sorting by incorrectly increasing the number of large raindrops, overestimating Z DR by 2–3 dB. Three-moment schemes with variable shape parameters better capture the narrowing drop size distribution resulting from size sorting but can underestimate Z DR and overestimate K DP by as much as 20%. Implications for polarimetric radar data assimilation into storm-scale numerical weather prediction models are discussed.
Abstract
The dual-polarization radar variables are especially sensitive to the microphysical processes of melting and size sorting of precipitation particles. In deep convective storms, polarimetric measurements of such processes can provide information about the airflow in and around the storm that may be used to elucidate storm behavior and evolution. Size sorting mechanisms include differential sedimentation, vertical transport, strong rotation, and wind shear. In particular, winds that veer with increasing height typical of supercell environments cause size sorting that is manifested as an enhancement of differential reflectivity (Z DR) along the right or inflow edge of the forward-flank downdraft precipitation echo, which has been called the Z DR arc signature. In some cases, this shear profile can be augmented by the storm inflow. It is argued that the magnitude of this enhancement is related to the low-level storm-relative environmental helicity (SRH) in the storm inflow.
To test this hypothesis, a simple numerical model is constructed that calculates trajectories for raindrops based on their individual sizes, which allows size sorting to occur. The modeling results indicate a strong positive correlation between the maximum Z DR in the arc signature and the low-level SRH, regardless of the initial drop size distribution aloft. Additional observational evidence in support of the conceptual model is presented. Potential changes in the Z DR arc signature as the supercell evolves and the low-level mesocyclone occludes are described.
Abstract
The dual-polarization radar variables are especially sensitive to the microphysical processes of melting and size sorting of precipitation particles. In deep convective storms, polarimetric measurements of such processes can provide information about the airflow in and around the storm that may be used to elucidate storm behavior and evolution. Size sorting mechanisms include differential sedimentation, vertical transport, strong rotation, and wind shear. In particular, winds that veer with increasing height typical of supercell environments cause size sorting that is manifested as an enhancement of differential reflectivity (Z DR) along the right or inflow edge of the forward-flank downdraft precipitation echo, which has been called the Z DR arc signature. In some cases, this shear profile can be augmented by the storm inflow. It is argued that the magnitude of this enhancement is related to the low-level storm-relative environmental helicity (SRH) in the storm inflow.
To test this hypothesis, a simple numerical model is constructed that calculates trajectories for raindrops based on their individual sizes, which allows size sorting to occur. The modeling results indicate a strong positive correlation between the maximum Z DR in the arc signature and the low-level SRH, regardless of the initial drop size distribution aloft. Additional observational evidence in support of the conceptual model is presented. Potential changes in the Z DR arc signature as the supercell evolves and the low-level mesocyclone occludes are described.
Abstract
The authors contrast rainfall in two Oklahoma squall lines: one with deep convection occurred in the spring and the other with shallower convection in the winter. Both passed over a micronetwork of densely spaced rain gauges and were observed with the National Severe Storm Laboratory's polarimetric weather radar. Polarimetric measurements reveal differences in storm structure that in turn imply that microphysical processes caused the drop size distributions to be quite distinct for the two events. In the winter squall line the conventional R(Z) algorithm for estimating rainfall fails badly, whereas in the summer squall line it performs well. The method based on specific differential phase measurements, however, yields a very good match between radar-derived areal precipitation amount and rain depth obtained from the micronetwork of densely located rain gauges for both events.
Abstract
The authors contrast rainfall in two Oklahoma squall lines: one with deep convection occurred in the spring and the other with shallower convection in the winter. Both passed over a micronetwork of densely spaced rain gauges and were observed with the National Severe Storm Laboratory's polarimetric weather radar. Polarimetric measurements reveal differences in storm structure that in turn imply that microphysical processes caused the drop size distributions to be quite distinct for the two events. In the winter squall line the conventional R(Z) algorithm for estimating rainfall fails badly, whereas in the summer squall line it performs well. The method based on specific differential phase measurements, however, yields a very good match between radar-derived areal precipitation amount and rain depth obtained from the micronetwork of densely located rain gauges for both events.
Abstract
This study derives simple analytical expressions for the theoretical height profiles of particle number concentrations (Nt ) and mean volume diameters (Dm ) during the steady-state balance of vapor growth and collision–coalescence with sedimentation. These equations are general for both rain and snow gamma size distributions with size-dependent power-law functions that dictate particle fall speeds and masses. For collision–coalescence only, Nt (Dm ) decreases (increases) as an exponential function of the radar reflectivity difference between two height layers. For vapor deposition only, Dm increases as a generalized power law of this reflectivity difference. Simultaneous vapor deposition and collision–coalescence under steady-state conditions with conservation of number, mass, and reflectivity fluxes lead to a coupled set of first-order, nonlinear ordinary differential equations for Nt and Dm . The solutions to these coupled equations are generalized power-law functions of height z for Dm (z) and Nt (z) whereby each variable is related to one another with an exponent that is independent of collision–coalescence efficiency. Compared to observed profiles derived from descending in situ aircraft Lagrangian spiral profiles from the CRYSTAL-FACE field campaign, these analytical solutions can on average capture the height profiles of Nt and Dm within 8% and 4% of observations, respectively. Steady-state model projections of radar retrievals aloft are shown to produce the correct rapid enhancement of surface snowfall compared to the lowest-available radar retrievals from 500 m MSL. Future studies can utilize these equations alongside radar measurements to estimate Nt and Dm below radar tilt elevations and to estimate uncertain microphysical parameters such as collision–coalescence efficiencies.
Significance Statement
While complex numerical models are often used to describe weather phenomenon, sometimes simple equations can instead provide equally good or comparable results. Thus, these simple equations can be used in place of more complicated models in certain situations and this replacement can allow for computationally efficient and elegant solutions. This study derives such simple equations in terms of exponential and power-law mathematical functions that describe how the average size and total number of snow or rain particles change at different atmospheric height levels due to growth from the vapor phase and aggregation (the sticking together) of these particles balanced with their fallout from clouds. We catalog these mathematical equations for different assumptions of particle characteristics and we then test these equations using spirally descending aircraft observations and ground-based measurements. Overall, we show that these mathematical equations, despite their simplicity, are capable of accurately describing the magnitude and shape of observed height and time series profiles of particle sizes and numbers. These equations can be used by researchers and forecasters along with radar measurements to improve the understanding of precipitation and the estimation of its properties.
Abstract
This study derives simple analytical expressions for the theoretical height profiles of particle number concentrations (Nt ) and mean volume diameters (Dm ) during the steady-state balance of vapor growth and collision–coalescence with sedimentation. These equations are general for both rain and snow gamma size distributions with size-dependent power-law functions that dictate particle fall speeds and masses. For collision–coalescence only, Nt (Dm ) decreases (increases) as an exponential function of the radar reflectivity difference between two height layers. For vapor deposition only, Dm increases as a generalized power law of this reflectivity difference. Simultaneous vapor deposition and collision–coalescence under steady-state conditions with conservation of number, mass, and reflectivity fluxes lead to a coupled set of first-order, nonlinear ordinary differential equations for Nt and Dm . The solutions to these coupled equations are generalized power-law functions of height z for Dm (z) and Nt (z) whereby each variable is related to one another with an exponent that is independent of collision–coalescence efficiency. Compared to observed profiles derived from descending in situ aircraft Lagrangian spiral profiles from the CRYSTAL-FACE field campaign, these analytical solutions can on average capture the height profiles of Nt and Dm within 8% and 4% of observations, respectively. Steady-state model projections of radar retrievals aloft are shown to produce the correct rapid enhancement of surface snowfall compared to the lowest-available radar retrievals from 500 m MSL. Future studies can utilize these equations alongside radar measurements to estimate Nt and Dm below radar tilt elevations and to estimate uncertain microphysical parameters such as collision–coalescence efficiencies.
Significance Statement
While complex numerical models are often used to describe weather phenomenon, sometimes simple equations can instead provide equally good or comparable results. Thus, these simple equations can be used in place of more complicated models in certain situations and this replacement can allow for computationally efficient and elegant solutions. This study derives such simple equations in terms of exponential and power-law mathematical functions that describe how the average size and total number of snow or rain particles change at different atmospheric height levels due to growth from the vapor phase and aggregation (the sticking together) of these particles balanced with their fallout from clouds. We catalog these mathematical equations for different assumptions of particle characteristics and we then test these equations using spirally descending aircraft observations and ground-based measurements. Overall, we show that these mathematical equations, despite their simplicity, are capable of accurately describing the magnitude and shape of observed height and time series profiles of particle sizes and numbers. These equations can be used by researchers and forecasters along with radar measurements to improve the understanding of precipitation and the estimation of its properties.
Abstract
Polarimetric radar observations of convective storms routinely reveal positive differential reflectivity Z DR extending above the 0°C level, indicative of the presence of supercooled liquid particles lofted by the storm’s updraft. The summit of such “Z DR columns” is marked by a zone of enhanced linear depolarization ratio L DR or decreased copolar cross-correlation coefficient ρ hv and a sharp decrease in Z DR that together mark a particle freezing zone. To better understand the relation between changes in the storm updraft and the observed polarimetric variables, it is necessary to first understand the physics governing this freezing process and the impact of freezing on the polarimetric variables.
A simplified, one-dimensional explicit bin microphysics model of stochastic drop nucleation by an immersed foreign particle and subsequent deterministic freezing is developed and coupled with an electromagnetic scattering model to explore the impact of the freezing process on the polarimetric radar variables. As expected, the height of the Z DR column is closely related to the updraft strength and initial drop size distribution. Additionally, the treatment of the stochastic nucleation process can also affect the depth of the freezing zone, underscoring the need to accurately depict this process in parameterizations. Representation of stochastic nucleation and deterministic freezing for each drop size bin yields better agreement between observations and the modeled vertical profiles of the surface reflectivity factor ZH and Z DR than bulk microphysics schemes. Further improvements in the representation of the L DR cap, the observed ZDR gradient in the freezing zone, and the magnitude of the ρ hv minimum may require inclusion of accretion, which was not included in this model.
Abstract
Polarimetric radar observations of convective storms routinely reveal positive differential reflectivity Z DR extending above the 0°C level, indicative of the presence of supercooled liquid particles lofted by the storm’s updraft. The summit of such “Z DR columns” is marked by a zone of enhanced linear depolarization ratio L DR or decreased copolar cross-correlation coefficient ρ hv and a sharp decrease in Z DR that together mark a particle freezing zone. To better understand the relation between changes in the storm updraft and the observed polarimetric variables, it is necessary to first understand the physics governing this freezing process and the impact of freezing on the polarimetric variables.
A simplified, one-dimensional explicit bin microphysics model of stochastic drop nucleation by an immersed foreign particle and subsequent deterministic freezing is developed and coupled with an electromagnetic scattering model to explore the impact of the freezing process on the polarimetric radar variables. As expected, the height of the Z DR column is closely related to the updraft strength and initial drop size distribution. Additionally, the treatment of the stochastic nucleation process can also affect the depth of the freezing zone, underscoring the need to accurately depict this process in parameterizations. Representation of stochastic nucleation and deterministic freezing for each drop size bin yields better agreement between observations and the modeled vertical profiles of the surface reflectivity factor ZH and Z DR than bulk microphysics schemes. Further improvements in the representation of the L DR cap, the observed ZDR gradient in the freezing zone, and the magnitude of the ρ hv minimum may require inclusion of accretion, which was not included in this model.
Relationship between Aerosols, Hail Microphysics, and Z
DR ColumnsAbstract
Mechanisms of formation of differential reflectivity columns are investigated in simulations of a midlatitude summertime hailstorm with hailstones up to several centimeters in diameter. Simulations are performed using a new version of the Hebrew University Cloud Model (HUCM) with spectral bin microphysics. A polarimetric radar forward operator is used to calculate radar reflectivity and differential reflectivity Z DR. It is shown that Z DR columns are associated with raindrops and with hail particles growing in a wet growth regime within convective updrafts. The height and volume of Z DR columns increases with an increase in aerosol concentration. Small hail forming under clean conditions grows in updrafts largely in a dry growth regime corresponding to low Z DR. Characteristics of Z DR columns are highly correlated with vertical velocity, hail size, and aerosol concentration.
Abstract
Mechanisms of formation of differential reflectivity columns are investigated in simulations of a midlatitude summertime hailstorm with hailstones up to several centimeters in diameter. Simulations are performed using a new version of the Hebrew University Cloud Model (HUCM) with spectral bin microphysics. A polarimetric radar forward operator is used to calculate radar reflectivity and differential reflectivity Z DR. It is shown that Z DR columns are associated with raindrops and with hail particles growing in a wet growth regime within convective updrafts. The height and volume of Z DR columns increases with an increase in aerosol concentration. Small hail forming under clean conditions grows in updrafts largely in a dry growth regime corresponding to low Z DR. Characteristics of Z DR columns are highly correlated with vertical velocity, hail size, and aerosol concentration.
Effect of Aerosols on Freezing Drops, Hail, and Precipitation in a Midlatitude StormAbstract
A midlatitude hail storm was simulated using a new version of the spectral bin microphysics Hebrew University Cloud Model (HUCM) with a detailed description of time-dependent melting and freezing. In addition to size distributions of drops, plate-, columnar-, and branch-type ice crystals, snow, graupel, and hail, new distributions for freezing drops as well as for liquid water mass within precipitating ice particles were implemented to describe time-dependent freezing and wet growth of hail, graupel, and freezing drops.
Simulations carried out using different aerosol loadings show that an increase in aerosol loading leads to a decrease in the total mass of hail but also to a substantial increase in the maximum size of hailstones. Cumulative rain strongly increases with an increase in aerosol concentration from 100 to about 1000 cm−3. At higher cloud condensation nuclei (CCN) concentrations, the sensitivity of hailstones’ size and surface precipitation to aerosols decreases. The physical mechanism of these effects was analyzed. It was shown that the change in aerosol concentration leads to a change in the major mechanisms of hail formation and growth. The main effect of the increase in the aerosol concentration is the increase in the supercooled cloud water content. Accordingly, at high aerosol concentration, the hail grows largely by accretion of cloud droplets in the course of recycling in the cloud updraft zone. The main mechanism of hail formation in the case of low aerosol concentration is freezing of raindrops.
Abstract
A midlatitude hail storm was simulated using a new version of the spectral bin microphysics Hebrew University Cloud Model (HUCM) with a detailed description of time-dependent melting and freezing. In addition to size distributions of drops, plate-, columnar-, and branch-type ice crystals, snow, graupel, and hail, new distributions for freezing drops as well as for liquid water mass within precipitating ice particles were implemented to describe time-dependent freezing and wet growth of hail, graupel, and freezing drops.
Simulations carried out using different aerosol loadings show that an increase in aerosol loading leads to a decrease in the total mass of hail but also to a substantial increase in the maximum size of hailstones. Cumulative rain strongly increases with an increase in aerosol concentration from 100 to about 1000 cm−3. At higher cloud condensation nuclei (CCN) concentrations, the sensitivity of hailstones’ size and surface precipitation to aerosols decreases. The physical mechanism of these effects was analyzed. It was shown that the change in aerosol concentration leads to a change in the major mechanisms of hail formation and growth. The main effect of the increase in the aerosol concentration is the increase in the supercooled cloud water content. Accordingly, at high aerosol concentration, the hail grows largely by accretion of cloud droplets in the course of recycling in the cloud updraft zone. The main mechanism of hail formation in the case of low aerosol concentration is freezing of raindrops.
