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Abstract
A band of enhanced thermocline variability at 10°–15°N in the Pacific found in nature also occurs in an ocean general circulation model forced with observed fluxes of momentum, heat, and freshwater over the period 1958–97. The variability in the model is primarily associated with long baroclinic Rossby waves characterized by periods in the decadal range (7–10 yr). The waves are forced by westward propagating Ekman pumping anomalies east of the date line and propagate at a speed of ∼13 cm s−1, which is slower than the phase speed of the first mode unforced baroclinic waves (15–16 cm s−1). West of the date line, the correlations between thermocline displacements and local Ekman pumping are relatively small, and the ocean signals have a phase speed of ∼20 cm s−1, very similar to the phase speed of the first baroclinic mode in the western half of the basin (18–20 cm s−1). The phase speeds of the ocean model signals have been estimated using cospectral analysis, while the WKB approximation has been used to evaluate the phase speed of the baroclinic Rossby wave modes for the given model stratification. The thermocline displacements are coherent all the way across the basin in the 10°–15°N latitude band. After reaching the western boundary the signal appears to propagate along the boundary, both to the north and the south. Along the southern branch, the signal reaches the equator and propagates along the equator, contributing to low-frequency equatorial thermocline variability.
Abstract
A band of enhanced thermocline variability at 10°–15°N in the Pacific found in nature also occurs in an ocean general circulation model forced with observed fluxes of momentum, heat, and freshwater over the period 1958–97. The variability in the model is primarily associated with long baroclinic Rossby waves characterized by periods in the decadal range (7–10 yr). The waves are forced by westward propagating Ekman pumping anomalies east of the date line and propagate at a speed of ∼13 cm s−1, which is slower than the phase speed of the first mode unforced baroclinic waves (15–16 cm s−1). West of the date line, the correlations between thermocline displacements and local Ekman pumping are relatively small, and the ocean signals have a phase speed of ∼20 cm s−1, very similar to the phase speed of the first baroclinic mode in the western half of the basin (18–20 cm s−1). The phase speeds of the ocean model signals have been estimated using cospectral analysis, while the WKB approximation has been used to evaluate the phase speed of the baroclinic Rossby wave modes for the given model stratification. The thermocline displacements are coherent all the way across the basin in the 10°–15°N latitude band. After reaching the western boundary the signal appears to propagate along the boundary, both to the north and the south. Along the southern branch, the signal reaches the equator and propagates along the equator, contributing to low-frequency equatorial thermocline variability.
Abstract
Atmospheric gravity waves are known to influence global circulations. Understanding these waves and their sources help to develop parameterizations that include their effects in climate and weather forecasting models. Deep convection is believed to be a major source for these waves and hurricanes may be particularly intense sources. Simulations of Hurricane Humberto (2001) are studied using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). Humberto is simulated at both tropical storm and hurricane stages. Fourier transform and wavelet analysis are employed to investigate wave characteristics and their behavior in the lower stratosphere. The Fourier analysis gives a regional view of storm affects, whereas wavelet analysis gives a local picture of isolated events. Analysis of the movement of convective sources and local winds gives further insight into the mechanisms that can cause gravity waves. Convectively generated gravity waves are observed in the lower stratosphere of this model with horizontal scales of 15–300 km, vertical scales of 4–8 km, and intrinsic periods of approximately 20–100 min.
Abstract
Atmospheric gravity waves are known to influence global circulations. Understanding these waves and their sources help to develop parameterizations that include their effects in climate and weather forecasting models. Deep convection is believed to be a major source for these waves and hurricanes may be particularly intense sources. Simulations of Hurricane Humberto (2001) are studied using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). Humberto is simulated at both tropical storm and hurricane stages. Fourier transform and wavelet analysis are employed to investigate wave characteristics and their behavior in the lower stratosphere. The Fourier analysis gives a regional view of storm affects, whereas wavelet analysis gives a local picture of isolated events. Analysis of the movement of convective sources and local winds gives further insight into the mechanisms that can cause gravity waves. Convectively generated gravity waves are observed in the lower stratosphere of this model with horizontal scales of 15–300 km, vertical scales of 4–8 km, and intrinsic periods of approximately 20–100 min.
Abstract
Observation and modeling studies indicate that the wave flux from tropical heating sources that propagates into the lower stratosphere is sensitive to the buoyancy frequency profile N(z) in the troposphere. This sensitivity is explained by examining analytic solutions to the vertical structure equation for various simplified models of the tropical troposphere. An efficient method for obtaining expressions for these analytic solutions when N(z) is piecewise constant is presented. The solution is expressed in terms of reflection and transmission coefficients. It is found that the response to heating for Hough modes with small equivalent depth is quite sensitive to the shape of the heating profile, the magnitude of N(z) within the heating profile, and the internal wave reflections that result from the sharp change in N(z) at the tropopause. The location of the primary peak in the wave response, which occurs where the wavelength is twice the depth of the heating for a constant N(z) profile, is also sensitive to the occurrence of internal wave reflection.
Abstract
Observation and modeling studies indicate that the wave flux from tropical heating sources that propagates into the lower stratosphere is sensitive to the buoyancy frequency profile N(z) in the troposphere. This sensitivity is explained by examining analytic solutions to the vertical structure equation for various simplified models of the tropical troposphere. An efficient method for obtaining expressions for these analytic solutions when N(z) is piecewise constant is presented. The solution is expressed in terms of reflection and transmission coefficients. It is found that the response to heating for Hough modes with small equivalent depth is quite sensitive to the shape of the heating profile, the magnitude of N(z) within the heating profile, and the internal wave reflections that result from the sharp change in N(z) at the tropopause. The location of the primary peak in the wave response, which occurs where the wavelength is twice the depth of the heating for a constant N(z) profile, is also sensitive to the occurrence of internal wave reflection.
Abstract
Latent heating estimates derived from rainfall observations are used to construct model experiments that isolate equatorial waves forced by tropical convection from midlatitude synoptic-scale waves. These experiments are used to demonstrate that quasi-stationary equatorial Rossby waves forced by latent heating drive most of the observed residual-mean upwelling across the tropopause transition layer within 15° of the equator. The seasonal variation of the equatorial waves and the mean meridional upwelling that they cause is examined for two full years from 2006 to 2007. Changes in equatorial Rossby wave propagation through seasonally varying mean winds are the primary mechanism for producing an annual variation in the residual-mean upwelling. In the tropical tropopause layer, averaged within 15° of the equator and between 90 and 190 hPa, the annual cycle varies between a maximum upwelling of 0.4 mm s−1 during boreal winter and spring and a minimum of 0.2 mm s−1 during boreal summer. This variability seems to be due to small changes in the mean wind speed in the tropics. Seasonal variations in latent heating have only a relatively minor effect on seasonal variations in tropical tropopause upwelling. In addition, Kelvin waves drive a small downward component of the total circulation over the equator that may be modulated by the quasi-biennial oscillation.
Abstract
Latent heating estimates derived from rainfall observations are used to construct model experiments that isolate equatorial waves forced by tropical convection from midlatitude synoptic-scale waves. These experiments are used to demonstrate that quasi-stationary equatorial Rossby waves forced by latent heating drive most of the observed residual-mean upwelling across the tropopause transition layer within 15° of the equator. The seasonal variation of the equatorial waves and the mean meridional upwelling that they cause is examined for two full years from 2006 to 2007. Changes in equatorial Rossby wave propagation through seasonally varying mean winds are the primary mechanism for producing an annual variation in the residual-mean upwelling. In the tropical tropopause layer, averaged within 15° of the equator and between 90 and 190 hPa, the annual cycle varies between a maximum upwelling of 0.4 mm s−1 during boreal winter and spring and a minimum of 0.2 mm s−1 during boreal summer. This variability seems to be due to small changes in the mean wind speed in the tropics. Seasonal variations in latent heating have only a relatively minor effect on seasonal variations in tropical tropopause upwelling. In addition, Kelvin waves drive a small downward component of the total circulation over the equator that may be modulated by the quasi-biennial oscillation.
Abstract
Recent observational analyses have indicated that tropospheric quasi-biennial oscillations (QBs) may play a fundamental role in regulating the timing and strength of El Niño and the Southern Oscillation. The biennial variability is examined in the tropical troposphere of a 35-year general circulation model (GCM) simulation forced by observed sea surface temperatures (SSTs). The results of spectral analyses and temporal filtering applied to the SST boundary conditions and the simulated lower- and upper-tropospheric zonal winds, precipitation, and sea level pressure anomalies are compared with observations and used to investigate the relationship between variables.
The GCM obtains regions of coherent biennial variability over the tropical Indian and Pacific Oceans in close correspondence with observations. In addition, the evolution of the stronger QBs and the physical relationship between variables are fairly well simulated. Zonal wind anomalies, with a simple baroclinic structure, tend to propagate eastward from the Indonesian region to the central Pacific where they increase in strength. The amplitude of the zonal wind and SST anomalies in the central Pacific vary together, with the largest anomalies occurring during the mid-1960s, mid-1970s, and early 1980s. During the time of the warmest SSTs, low pressure is found in the east Pacific with high pressure over Indonesia, and precipitation is enhanced between the date line and 120°W. However, the model underestimates the low-frequency variability in general and has approximately one-half to two-thirds of the observed variability in the biennial range. In addition, the observed phasing of the biennial and annual cycles in the zonal winds over the eastern Indian Ocean is not reproduced by the model.
The authors have also compared the amount of biennial variability of the near-surface zonal winds in the 35-year run with observed SSTs to two 35-year periods in a 100-year control run with climatological SSTs that repeat the seasonal cycle. Only the simulation with observed SSTs has an organized region of enhanced biennial variability near the equator, suggesting a strong oceanic component to the forcing of the QB.
Abstract
Recent observational analyses have indicated that tropospheric quasi-biennial oscillations (QBs) may play a fundamental role in regulating the timing and strength of El Niño and the Southern Oscillation. The biennial variability is examined in the tropical troposphere of a 35-year general circulation model (GCM) simulation forced by observed sea surface temperatures (SSTs). The results of spectral analyses and temporal filtering applied to the SST boundary conditions and the simulated lower- and upper-tropospheric zonal winds, precipitation, and sea level pressure anomalies are compared with observations and used to investigate the relationship between variables.
The GCM obtains regions of coherent biennial variability over the tropical Indian and Pacific Oceans in close correspondence with observations. In addition, the evolution of the stronger QBs and the physical relationship between variables are fairly well simulated. Zonal wind anomalies, with a simple baroclinic structure, tend to propagate eastward from the Indonesian region to the central Pacific where they increase in strength. The amplitude of the zonal wind and SST anomalies in the central Pacific vary together, with the largest anomalies occurring during the mid-1960s, mid-1970s, and early 1980s. During the time of the warmest SSTs, low pressure is found in the east Pacific with high pressure over Indonesia, and precipitation is enhanced between the date line and 120°W. However, the model underestimates the low-frequency variability in general and has approximately one-half to two-thirds of the observed variability in the biennial range. In addition, the observed phasing of the biennial and annual cycles in the zonal winds over the eastern Indian Ocean is not reproduced by the model.
The authors have also compared the amount of biennial variability of the near-surface zonal winds in the 35-year run with observed SSTs to two 35-year periods in a 100-year control run with climatological SSTs that repeat the seasonal cycle. Only the simulation with observed SSTs has an organized region of enhanced biennial variability near the equator, suggesting a strong oceanic component to the forcing of the QB.
Abstract
The process of glaciation in mixed-phase stratiform clouds was investigated by a novel Lagrangian–Eulerian model (LEM) in which thousands of adjoining Lagrangian parcels moved within a turbulent-like velocity field with statistical parameters typical of the Arctic boundary layer. We used detailed bin microphysics to describe the condensation/evaporation processes in each parcel, in which droplets, aerosols, and ice particles were described using size distributions of 500 mass bins. The model also calculated aerosol mass inside droplets and ice particles. Gravitational sedimentation of droplets and ice particles was also accounted for. Assuming that droplet freezing is the primary source of ice particles, the Arctic clouds observed in Indirect and Semi-Direct Aerosol Campaign (ISDAC) were successfully simulated. The model showed that at a low ice particle concentration typical of ISDAC, large vortices (eddies) led to a quasi-stationary regime, in which mixed-phase St existed for a long time. The large eddies controlled the water partitioning in the mixed-phase clouds. Droplets formed and grew in updrafts, typically reaching the cloud top, and evaporated in downdrafts. Ice particles grew in updrafts and downdrafts. The Wegener–Bergeron–Findeisen (WBF) mechanism was efficient in downdrafts and some parts of updrafts, depending on ice concentration and vertical velocity. At low ice concentrations, the effect of ice on the phase partitioning was negligible. In this regime, liquid droplets were found near the cloud top, whereas ice particles precipitated through the cloud base. When ice concentration exceeded about 10 L−1, the WBF mechanism led to glaciation of almost the entire cloud, with the exception of narrow cloud regions associated with strong updrafts. At ice particle concentrations of a few tens per liter, the oscillatory regime took place due to the ice–liquid interaction. The microphysical structure of mixed-phase St forms as a combined effect of cloud dynamics (large eddies) and the WBF mechanism.
Abstract
The process of glaciation in mixed-phase stratiform clouds was investigated by a novel Lagrangian–Eulerian model (LEM) in which thousands of adjoining Lagrangian parcels moved within a turbulent-like velocity field with statistical parameters typical of the Arctic boundary layer. We used detailed bin microphysics to describe the condensation/evaporation processes in each parcel, in which droplets, aerosols, and ice particles were described using size distributions of 500 mass bins. The model also calculated aerosol mass inside droplets and ice particles. Gravitational sedimentation of droplets and ice particles was also accounted for. Assuming that droplet freezing is the primary source of ice particles, the Arctic clouds observed in Indirect and Semi-Direct Aerosol Campaign (ISDAC) were successfully simulated. The model showed that at a low ice particle concentration typical of ISDAC, large vortices (eddies) led to a quasi-stationary regime, in which mixed-phase St existed for a long time. The large eddies controlled the water partitioning in the mixed-phase clouds. Droplets formed and grew in updrafts, typically reaching the cloud top, and evaporated in downdrafts. Ice particles grew in updrafts and downdrafts. The Wegener–Bergeron–Findeisen (WBF) mechanism was efficient in downdrafts and some parts of updrafts, depending on ice concentration and vertical velocity. At low ice concentrations, the effect of ice on the phase partitioning was negligible. In this regime, liquid droplets were found near the cloud top, whereas ice particles precipitated through the cloud base. When ice concentration exceeded about 10 L−1, the WBF mechanism led to glaciation of almost the entire cloud, with the exception of narrow cloud regions associated with strong updrafts. At ice particle concentrations of a few tens per liter, the oscillatory regime took place due to the ice–liquid interaction. The microphysical structure of mixed-phase St forms as a combined effect of cloud dynamics (large eddies) and the WBF mechanism.
Abstract
A linear equivalent barotropic (EB) model is applied to study the effects of the bottom topography H and baroclinicity on the total transport and the position of the Antarctic Circumpolar Current (ACC). The model is based on the observation of Killworth that the time mean velocity field of the FRAM Model is self-similar in the vertical.
A realistic large-scale topography H̄ is constructed by filtering 5-minute resolution data with an appropriate smoothing kernel. It is shown that the asymptotic behavior of the solution of the barotropic model (a particular case of the EB model) in the limit of very small bottom friction depends on subtle details of topography and basin geometry. Given the uncertainties of the smoothing procedure the authors conclude that the barotropic model is not robust with respect to possible variations of model topography.
The authors found that the EB model with a vertical profile function similar to that of Killworth reproduces the major features of the time- and depth-averaged FRAM solution, including the position and the transport of the ACC, reasonably well. The solution is robust with respect to uncertainties in H̄. The EB model is much improved by a parameterization of the bottom friction via near-bottom velocity, which tends to shut off the flow in the shallow regions.
Abstract
A linear equivalent barotropic (EB) model is applied to study the effects of the bottom topography H and baroclinicity on the total transport and the position of the Antarctic Circumpolar Current (ACC). The model is based on the observation of Killworth that the time mean velocity field of the FRAM Model is self-similar in the vertical.
A realistic large-scale topography H̄ is constructed by filtering 5-minute resolution data with an appropriate smoothing kernel. It is shown that the asymptotic behavior of the solution of the barotropic model (a particular case of the EB model) in the limit of very small bottom friction depends on subtle details of topography and basin geometry. Given the uncertainties of the smoothing procedure the authors conclude that the barotropic model is not robust with respect to possible variations of model topography.
The authors found that the EB model with a vertical profile function similar to that of Killworth reproduces the major features of the time- and depth-averaged FRAM solution, including the position and the transport of the ACC, reasonably well. The solution is robust with respect to uncertainties in H̄. The EB model is much improved by a parameterization of the bottom friction via near-bottom velocity, which tends to shut off the flow in the shallow regions.
Abstract
Characteristic properties of gravity waves from convection over the continental United States are derived from idealized high-resolution numerical simulations. In a unique modeling approach, waves are forced by a realistic thermodynamic source based on observed precipitation data. The square of the precipitation rate and the gravity wave momentum fluxes both show lognormal occurrence distributions, with long tails of extreme events. Convectively generated waves can give forces in the lower stratosphere that at times rival orographic wave forcing. Throughout the stratosphere, zonal forces due to convective wave drag are much stronger than accounted for by current gravity wave drag parameterizations, so their contribution to the summer branch of the stratospheric Brewer–Dobson circulation is in fact much larger than models predict. A comparison of these forces to previous estimates of the total drag implies that convectively generated gravity waves are a primary source of summer-hemisphere stratospheric wave drag. Furthermore, intermittency and strength of the zonal forces due to convective gravity wave drag in the lower stratosphere resemble analysis increments, suggesting that a more realistic representation of these waves may help alleviate model biases on synoptic scales. The properties of radar precipitation and gravity waves seen in this study lead to a proposed change for future parameterization methods that would give more realistic drag forces in the stratosphere without compromising mesospheric gravity wave drag.
Abstract
Characteristic properties of gravity waves from convection over the continental United States are derived from idealized high-resolution numerical simulations. In a unique modeling approach, waves are forced by a realistic thermodynamic source based on observed precipitation data. The square of the precipitation rate and the gravity wave momentum fluxes both show lognormal occurrence distributions, with long tails of extreme events. Convectively generated waves can give forces in the lower stratosphere that at times rival orographic wave forcing. Throughout the stratosphere, zonal forces due to convective wave drag are much stronger than accounted for by current gravity wave drag parameterizations, so their contribution to the summer branch of the stratospheric Brewer–Dobson circulation is in fact much larger than models predict. A comparison of these forces to previous estimates of the total drag implies that convectively generated gravity waves are a primary source of summer-hemisphere stratospheric wave drag. Furthermore, intermittency and strength of the zonal forces due to convective gravity wave drag in the lower stratosphere resemble analysis increments, suggesting that a more realistic representation of these waves may help alleviate model biases on synoptic scales. The properties of radar precipitation and gravity waves seen in this study lead to a proposed change for future parameterization methods that would give more realistic drag forces in the stratosphere without compromising mesospheric gravity wave drag.
Abstract
This feasibility study explores the potential benefits of polarization adjustment for spaceborne radar sensing of precipitation. More specifically, the role of the wave polarization in separating or “distinguishing” ocean surface return from the hydrometeor echoes of a “chirped” signal is examined.
To that end, experimental as well as computational data for the polarization scattering matrices of hydrometeors and ocean surfaces are obtained and used to calculate ocean and precipitation “response” to the transmitted pulse for various rain rates and incidence angles. The analysis is restricted to X and C bands, but simulations are performed for several signal-to-noise ratios, rain rates, and ocean surfaces. The problem is further restricted to the monostatic case (same polarizations for transmitter and receiver).
Even when the ocean and hydrometeor echoes are mixed throughout the entire radar resolution volume, the results appear promising. It is found that polarization, which provides the best contrast between rain and ocean returns, varies from almost circular near nadir to elliptical at large off-nadir look angles of incidence (ellipticity of 23° at a 40° incidence angle). Calculations show an order of magnitude improvement in the ratio of the returns when compared with the traditional choice of HH (horizontal transmit and receive polarization). The improvement is largest for the range of angles between 15° and 20° but depends on the assumed rain rate and, in particular, on the ocean surface roughness.
The general method described in this paper can be applied to many problems of radar and lidar meteorology, while the specific results reported here may have relevance for future precipitation measurement missions such as Tropical Rainfall Measuring Mission 2.
Abstract
This feasibility study explores the potential benefits of polarization adjustment for spaceborne radar sensing of precipitation. More specifically, the role of the wave polarization in separating or “distinguishing” ocean surface return from the hydrometeor echoes of a “chirped” signal is examined.
To that end, experimental as well as computational data for the polarization scattering matrices of hydrometeors and ocean surfaces are obtained and used to calculate ocean and precipitation “response” to the transmitted pulse for various rain rates and incidence angles. The analysis is restricted to X and C bands, but simulations are performed for several signal-to-noise ratios, rain rates, and ocean surfaces. The problem is further restricted to the monostatic case (same polarizations for transmitter and receiver).
Even when the ocean and hydrometeor echoes are mixed throughout the entire radar resolution volume, the results appear promising. It is found that polarization, which provides the best contrast between rain and ocean returns, varies from almost circular near nadir to elliptical at large off-nadir look angles of incidence (ellipticity of 23° at a 40° incidence angle). Calculations show an order of magnitude improvement in the ratio of the returns when compared with the traditional choice of HH (horizontal transmit and receive polarization). The improvement is largest for the range of angles between 15° and 20° but depends on the assumed rain rate and, in particular, on the ocean surface roughness.
The general method described in this paper can be applied to many problems of radar and lidar meteorology, while the specific results reported here may have relevance for future precipitation measurement missions such as Tropical Rainfall Measuring Mission 2.
Abstract
The objective of this work is to explore relationships between the microphysical properties of precipitation and optimal polarizations. The dependence of three optimal polarization parameters (asymmetry ratio 𝒜, optimal tilt τop, and optimal ellipticity εop,) on the reflectivity-weighted mean drop shape, mean canting angle, and standard deviation of a Gaussian canting angle distribution is studied. This is accomplished by using computer simulations that provide the rms scattering matrix for an ensemble of canted drops with a prescribed two-parameter canting angle distribution. Also examined are the effects of propagation on the polarization parameters for nonattenuating wavelengths.
The asymmetry ratio 𝒜 is simply the ratio of the maximal to minimal total backwattered energy (ratio of the largest and smallest eigenvalue of the Graves power matrix G=S† ). Similar to Z DR, this ratio decreases with increasing mean axial ratio, but unlike Z DR, it is not affected by canting (for a single drop). The dependence of 𝒜 on the reflectivity-weighted mean drop shape is examined, and a power-law relationship similar to that which exists for Z DR is established. The asymmetry ratio 𝒜 can be regarded as a generalization of Z DR because it requires only a measurement of linear depolarization ratio (in addition to Z DR), is independent of the propagation phase, and is less sensitive to canting. In a similar manner, the dependence of optimal ellipticity and till on the microphysical parameters is studied. In particular, it appears that the rms tilt of die optimal polarization ellipse is proportional to the variance of the canting angle distribution. Several other promising relationships between optimal polarizations and the microphysical variables of an ensemble of hydrometeors am also discussed.
Abstract
The objective of this work is to explore relationships between the microphysical properties of precipitation and optimal polarizations. The dependence of three optimal polarization parameters (asymmetry ratio 𝒜, optimal tilt τop, and optimal ellipticity εop,) on the reflectivity-weighted mean drop shape, mean canting angle, and standard deviation of a Gaussian canting angle distribution is studied. This is accomplished by using computer simulations that provide the rms scattering matrix for an ensemble of canted drops with a prescribed two-parameter canting angle distribution. Also examined are the effects of propagation on the polarization parameters for nonattenuating wavelengths.
The asymmetry ratio 𝒜 is simply the ratio of the maximal to minimal total backwattered energy (ratio of the largest and smallest eigenvalue of the Graves power matrix G=S† ). Similar to Z DR, this ratio decreases with increasing mean axial ratio, but unlike Z DR, it is not affected by canting (for a single drop). The dependence of 𝒜 on the reflectivity-weighted mean drop shape is examined, and a power-law relationship similar to that which exists for Z DR is established. The asymmetry ratio 𝒜 can be regarded as a generalization of Z DR because it requires only a measurement of linear depolarization ratio (in addition to Z DR), is independent of the propagation phase, and is less sensitive to canting. In a similar manner, the dependence of optimal ellipticity and till on the microphysical parameters is studied. In particular, it appears that the rms tilt of die optimal polarization ellipse is proportional to the variance of the canting angle distribution. Several other promising relationships between optimal polarizations and the microphysical variables of an ensemble of hydrometeors am also discussed.
