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- Author or Editor: Olivier P. Prat x
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Abstract
The focus of this paper is on the numerical solution of the stochastic collection equation–stochastic breakup equation (SCE–SBE) describing the evolution of raindrop spectra in warm rain. The drop size distribution (DSD) is discretized using the fixed-pivot scheme proposed by Kumar and Ramkrishna, and new discrete equations for solving collision breakup are presented. The model is evaluated using established coalescence and breakup parameterizations (kernels) available in the literature, and in that regard this paper provides a substantial review of the relevant science. The challenges posed by the need to achieve stable and accurate numerical solutions of the SCE–SBE are examined in detail. In particular, this paper focuses on the impact of varying the shape of the initial DSD on the equilibrium solution of the SCE–SBE for a wide range of rain rates and breakup kernels. The results show that, although there is no dependence of the equilibrium DSD on initial conditions for the same rain rate and breakup kernel, there is large variation in the time that it takes to reach steady state. This result suggests that, in coupled simulations of in-cloud motions and microphysics and for short time scales (<30 min) for which transient conditions prevail, the equilibrium DSD may not be attainable except for very heavy rainfall. Furthermore, simulations for the same initial conditions show a strong dependence of the dynamic evolution of the DSD on the breakup parameterization. The implication of this result is that, before the debate on the uniqueness of the shape of the equilibrium DSD can be settled, there is critical need for fundamental research including laboratory experiments to improve understanding of collisional mechanisms in DSD evolution.
Abstract
The focus of this paper is on the numerical solution of the stochastic collection equation–stochastic breakup equation (SCE–SBE) describing the evolution of raindrop spectra in warm rain. The drop size distribution (DSD) is discretized using the fixed-pivot scheme proposed by Kumar and Ramkrishna, and new discrete equations for solving collision breakup are presented. The model is evaluated using established coalescence and breakup parameterizations (kernels) available in the literature, and in that regard this paper provides a substantial review of the relevant science. The challenges posed by the need to achieve stable and accurate numerical solutions of the SCE–SBE are examined in detail. In particular, this paper focuses on the impact of varying the shape of the initial DSD on the equilibrium solution of the SCE–SBE for a wide range of rain rates and breakup kernels. The results show that, although there is no dependence of the equilibrium DSD on initial conditions for the same rain rate and breakup kernel, there is large variation in the time that it takes to reach steady state. This result suggests that, in coupled simulations of in-cloud motions and microphysics and for short time scales (<30 min) for which transient conditions prevail, the equilibrium DSD may not be attainable except for very heavy rainfall. Furthermore, simulations for the same initial conditions show a strong dependence of the dynamic evolution of the DSD on the breakup parameterization. The implication of this result is that, before the debate on the uniqueness of the shape of the equilibrium DSD can be settled, there is critical need for fundamental research including laboratory experiments to improve understanding of collisional mechanisms in DSD evolution.
Abstract
The objective of this study is to characterize the signature of dynamical microphysical processes on reflectivity–rainfall (Z–R) relationships used for radar rainfall estimation. For this purpose, a bin model with explicit microphysics was used to perform a sensitivity analysis of the shape parameters of the drop size distribution (DSD) as a function of time and rainfall regime. Simulations show that coalescence is the dominant microphysical process for low to moderate rain intensity regimes (R < 20 mm h−1) and that the rain rate in this regime is strongly dependent on the spectral properties of the DSD (i.e., the shape). The time to equilibrium for light rainfall is at least twice as long as in the case of heavy rainfall (1 h for stratiform vis-à-vis 30 min for thunderstorms). For high-intensity rainfall (R > 20 mm h−1), collision–breakup dynamics dominate the evolution of the raindrop spectra. The time-dependent Z–R relationships produced by the model converge to a universal Z–R relationship for heavy intensity rainfall (A = 1257; b ∼ 1) centered on the region of Z–R space defined by the ensemble of over 100 empirical Z–R relationships. Given the intrinsically transient nature of the DSD for light rainfall, it is proposed that the vertical raindrop spectra and corresponding rain rates should be modeled explicitly by a microphysical model. A demonstration using a multicolumn simulation of a Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) overpass over Darwin for a stratiform event during the Tropical Warm Pool–International Cloud Experiment (TWP-ICE) is presented.
Abstract
The objective of this study is to characterize the signature of dynamical microphysical processes on reflectivity–rainfall (Z–R) relationships used for radar rainfall estimation. For this purpose, a bin model with explicit microphysics was used to perform a sensitivity analysis of the shape parameters of the drop size distribution (DSD) as a function of time and rainfall regime. Simulations show that coalescence is the dominant microphysical process for low to moderate rain intensity regimes (R < 20 mm h−1) and that the rain rate in this regime is strongly dependent on the spectral properties of the DSD (i.e., the shape). The time to equilibrium for light rainfall is at least twice as long as in the case of heavy rainfall (1 h for stratiform vis-à-vis 30 min for thunderstorms). For high-intensity rainfall (R > 20 mm h−1), collision–breakup dynamics dominate the evolution of the raindrop spectra. The time-dependent Z–R relationships produced by the model converge to a universal Z–R relationship for heavy intensity rainfall (A = 1257; b ∼ 1) centered on the region of Z–R space defined by the ensemble of over 100 empirical Z–R relationships. Given the intrinsically transient nature of the DSD for light rainfall, it is proposed that the vertical raindrop spectra and corresponding rain rates should be modeled explicitly by a microphysical model. A demonstration using a multicolumn simulation of a Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) overpass over Darwin for a stratiform event during the Tropical Warm Pool–International Cloud Experiment (TWP-ICE) is presented.
Abstract
The impact of the collisional warm-rain microphysical processes on the polarimetric radar variables is quantified using a coupled microphysics–electromagnetic scattering model. A one-dimensional bin-microphysical rain shaft model that resolves explicitly the evolution of the drop size distribution (DSD) under the influence of collisional coalescence and breakup, drop settling, and aerodynamic breakup is coupled with electromagnetic scattering calculations that simulate vertical profiles of the polarimetric radar variables: reflectivity factor at horizontal polarization Z H , differential reflectivity Z DR, and specific differential phase K DP. The polarimetric radar fingerprint of each individual microphysical process is quantified as a function of the shape of the initial DSD and for different values of nominal rainfall rate. Results indicate that individual microphysical processes (collisional processes, evaporation) display a distinctive signature and evolve within specific areas of Z H –Z DR and Z DR–K DP space. Furthermore, a comparison of the resulting simulated vertical profiles of the polarimetric variables with radar and disdrometer observations suggests that bin-microphysical parameterizations of drop breakup most frequently used are overly aggressive for the largest rainfall rates, resulting in very “tropical” DSDs heavily skewed toward smaller drops.
Abstract
The impact of the collisional warm-rain microphysical processes on the polarimetric radar variables is quantified using a coupled microphysics–electromagnetic scattering model. A one-dimensional bin-microphysical rain shaft model that resolves explicitly the evolution of the drop size distribution (DSD) under the influence of collisional coalescence and breakup, drop settling, and aerodynamic breakup is coupled with electromagnetic scattering calculations that simulate vertical profiles of the polarimetric radar variables: reflectivity factor at horizontal polarization Z H , differential reflectivity Z DR, and specific differential phase K DP. The polarimetric radar fingerprint of each individual microphysical process is quantified as a function of the shape of the initial DSD and for different values of nominal rainfall rate. Results indicate that individual microphysical processes (collisional processes, evaporation) display a distinctive signature and evolve within specific areas of Z H –Z DR and Z DR–K DP space. Furthermore, a comparison of the resulting simulated vertical profiles of the polarimetric variables with radar and disdrometer observations suggests that bin-microphysical parameterizations of drop breakup most frequently used are overly aggressive for the largest rainfall rates, resulting in very “tropical” DSDs heavily skewed toward smaller drops.
Abstract
The objective of this paper is to characterize the precipitation amounts originating from tropical cyclones (TCs) in the southeastern United States during the tropical storm season from June to November. Using 12 years of precipitation data from the Tropical Rainfall Measurement Mission (TRMM), the authors estimate the TC contribution on the seasonal, interannual, and monthly precipitation budget using TC information derived from the International Best Track Archive for Climate Stewardship (IBTrACS). Results derived from the TRMM Multisatellite Precipitation Analysis (TMPA) 3B42 showed that TCs accounted for about 7% of the seasonal precipitation total from 1998 to 2009. Rainfall attributable to TCs was found to contribute as much as 8%–12% for inland areas located between 150 and 300 km from the coast and up to 15%–20% for coastal areas from Louisiana to the Florida Panhandle, southern Florida, and coastal Carolinas. The interannual contribution varied from 1.3% to 13.8% for the period 1998–2009 and depended on the TC seasonal activity, TC intensity, and TC paths as they traveled inland. For TCs making landfall, the rainfall contribution could be locally above 40% and, on a monthly basis, TCs contributed as much as 20% of September rainfall. The probability density functions of rainfall attributable to tropical cyclones showed that the percentage of rainfall associated with TC over land increased with increasing rain intensity and represent about 20% of heavy rainfall (>20 mm h−1), while TCs account for less than 5% of all seasonal precipitation events.
Abstract
The objective of this paper is to characterize the precipitation amounts originating from tropical cyclones (TCs) in the southeastern United States during the tropical storm season from June to November. Using 12 years of precipitation data from the Tropical Rainfall Measurement Mission (TRMM), the authors estimate the TC contribution on the seasonal, interannual, and monthly precipitation budget using TC information derived from the International Best Track Archive for Climate Stewardship (IBTrACS). Results derived from the TRMM Multisatellite Precipitation Analysis (TMPA) 3B42 showed that TCs accounted for about 7% of the seasonal precipitation total from 1998 to 2009. Rainfall attributable to TCs was found to contribute as much as 8%–12% for inland areas located between 150 and 300 km from the coast and up to 15%–20% for coastal areas from Louisiana to the Florida Panhandle, southern Florida, and coastal Carolinas. The interannual contribution varied from 1.3% to 13.8% for the period 1998–2009 and depended on the TC seasonal activity, TC intensity, and TC paths as they traveled inland. For TCs making landfall, the rainfall contribution could be locally above 40% and, on a monthly basis, TCs contributed as much as 20% of September rainfall. The probability density functions of rainfall attributable to tropical cyclones showed that the percentage of rainfall associated with TC over land increased with increasing rain intensity and represent about 20% of heavy rainfall (>20 mm h−1), while TCs account for less than 5% of all seasonal precipitation events.
Abstract
The authors evaluate the contribution of tropical cyclones (TCs) to daily precipitation extremes over land for TC-active regions around the world. From 1998 to 2012, data from the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA 3B42) showed that TCs account for an average of 3.5% ± 1% of the total number of rainy days over land areas experiencing cyclonic activity regardless of the basin considered. TC days represent between 13% and 31% of daily extremes above 4 in. day−1, but can account locally for the large majority (>70%) or almost all (≈100%) of extreme rainfall even over higher-latitude areas marginally affected by cyclonic activity. Moreover, regardless of the TC basin, TC-related extremes occur preferably later in the TC season after the peak of cyclonic activity.
Abstract
The authors evaluate the contribution of tropical cyclones (TCs) to daily precipitation extremes over land for TC-active regions around the world. From 1998 to 2012, data from the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA 3B42) showed that TCs account for an average of 3.5% ± 1% of the total number of rainy days over land areas experiencing cyclonic activity regardless of the basin considered. TC days represent between 13% and 31% of daily extremes above 4 in. day−1, but can account locally for the large majority (>70%) or almost all (≈100%) of extreme rainfall even over higher-latitude areas marginally affected by cyclonic activity. Moreover, regardless of the TC basin, TC-related extremes occur preferably later in the TC season after the peak of cyclonic activity.
Abstract
Three satellite precipitation datasets—CMORPH, PERSIANN-CDR, and GPCP—from the NOAA/Climate Data Record program were evaluated in their ability to capture seasonal differences in precipitation for the period 2007–18 over the conterminous United States. Data from the in situ U.S. Climate Reference Network (USCRN) provided reference precipitation measurements and collocated atmospheric conditions (temperature) at the daily scale. Satellite precipitation products’ (SPP) performance with respect to cold season precipitation was compared to warm season and full-year analysis for benchmarking purposes. Considering an ensemble of typical performance metrics including accuracy, false alarm ratio, probability of detection, probability of false detection, and the Kling–Gupta efficiency (KGE) that combines correlation, bias, and variability, we found that the three SPPs displayed better performances during the warm season than during the cold season. Among the three datasets, CMORPH displayed better performance—smaller bias, higher correlation, and a better KGE score—than the two other SPPs on an annual basis and during the warm season. During the cold season, CMORPH showed the worst performance at higher latitudes over areas experiencing recurring snow or frozen and mixed precipitation. CMORPH’s performances were further degraded compared to PERSIANN-CDR and GPCP when considering freezing temperatures (T < 0°C) due to the inability to microwave sensors to retrieve precipitation over snow-covered surface. However, for cold rainfall events detected simultaneously by the satellite and the USCRN stations (i.e., conditional case), CMORPH performance noticeably improved but remained inferior to the two other datasets. The quantification of seasonal precipitation errors and biases for three satellite precipitation datasets presented in this work provides an objective basis for the improvement of rainfall retrieval algorithms of the next generation of satellite precipitation products.
Abstract
Three satellite precipitation datasets—CMORPH, PERSIANN-CDR, and GPCP—from the NOAA/Climate Data Record program were evaluated in their ability to capture seasonal differences in precipitation for the period 2007–18 over the conterminous United States. Data from the in situ U.S. Climate Reference Network (USCRN) provided reference precipitation measurements and collocated atmospheric conditions (temperature) at the daily scale. Satellite precipitation products’ (SPP) performance with respect to cold season precipitation was compared to warm season and full-year analysis for benchmarking purposes. Considering an ensemble of typical performance metrics including accuracy, false alarm ratio, probability of detection, probability of false detection, and the Kling–Gupta efficiency (KGE) that combines correlation, bias, and variability, we found that the three SPPs displayed better performances during the warm season than during the cold season. Among the three datasets, CMORPH displayed better performance—smaller bias, higher correlation, and a better KGE score—than the two other SPPs on an annual basis and during the warm season. During the cold season, CMORPH showed the worst performance at higher latitudes over areas experiencing recurring snow or frozen and mixed precipitation. CMORPH’s performances were further degraded compared to PERSIANN-CDR and GPCP when considering freezing temperatures (T < 0°C) due to the inability to microwave sensors to retrieve precipitation over snow-covered surface. However, for cold rainfall events detected simultaneously by the satellite and the USCRN stations (i.e., conditional case), CMORPH performance noticeably improved but remained inferior to the two other datasets. The quantification of seasonal precipitation errors and biases for three satellite precipitation datasets presented in this work provides an objective basis for the improvement of rainfall retrieval algorithms of the next generation of satellite precipitation products.
Abstract
The objective of this study is to evaluate the impact of a new parameterization of drop–drop collision outcomes based on the relationship between Weber number and drop diameter ratios on the dynamical simulation of raindrop size distributions. Results of the simulations with the new parameterization are compared with those of the classical parameterizations. Comparison with previous results indicates on average an increase of 70% in the drop number concentration and a 15% decrease in rain intensity for the equilibrium drop size distribution (DSD). Furthermore, the drop bounce process is parameterized as a function of drop size based on laboratory experiments for the first time in a microphysical model. Numerical results indicate that drop bounce has a strong influence on the equilibrium DSD, in particular for very small drops (<0.5 mm), leading to an increase of up to 150% in the small drop number concentration (left-hand side of the DSD) when compared to previous modeling results without accounting for bounce effects.
Abstract
The objective of this study is to evaluate the impact of a new parameterization of drop–drop collision outcomes based on the relationship between Weber number and drop diameter ratios on the dynamical simulation of raindrop size distributions. Results of the simulations with the new parameterization are compared with those of the classical parameterizations. Comparison with previous results indicates on average an increase of 70% in the drop number concentration and a 15% decrease in rain intensity for the equilibrium drop size distribution (DSD). Furthermore, the drop bounce process is parameterized as a function of drop size based on laboratory experiments for the first time in a microphysical model. Numerical results indicate that drop bounce has a strong influence on the equilibrium DSD, in particular for very small drops (<0.5 mm), leading to an increase of up to 150% in the small drop number concentration (left-hand side of the DSD) when compared to previous modeling results without accounting for bounce effects.
Abstract
A model of rain shaft microphysics that solves the stochastic advection–coalescence–breakup equation in an atmospheric column was used to simulate the evolution of a stratiform rainfall event during the Tropical Warm Pool-International Cloud Experiment (TWP-ICE) in Darwin, Australia. For the first time, a dynamic simulation of the evolution of the drop spectra within a one-dimensional rain shaft is performed using realistic boundary conditions retrieved from real rain events. Droplet size distribution (DSD) retrieved from vertically pointing radar (VPR) measurements are sequentially imposed at the top of the rain shaft as boundary conditions to emulate a realistic rain event. Time series of model profiles of integral parameters such as reflectivity, rain rate, and liquid water content were subsequently compared with estimates retrieved from vertically pointing radars and Joss–Waldvogel disdrometer (JWD) observations. Results obtained are within the VPR retrieval uncertainty estimates. Besides evaluating the model’s ability to capture the dynamical evolution of the DSD within the rain shaft, a case study was conducted to assess the potential use of the model as a physically based interpolator to improve radar retrieval at low levels in the atmosphere. Numerical results showed that relative improvements on the order of 90% in the estimation of rain rate and liquid water content can be achieved close to the ground where the VPR estimates are less reliable. These findings raise important questions with regard to the importance of bin resolution and the lack of sensitivity for small raindrop size (<0.03 cm) in the interpretation of JWD data, and the implications of using disdrometer data to calibrate radar algorithms.
Abstract
A model of rain shaft microphysics that solves the stochastic advection–coalescence–breakup equation in an atmospheric column was used to simulate the evolution of a stratiform rainfall event during the Tropical Warm Pool-International Cloud Experiment (TWP-ICE) in Darwin, Australia. For the first time, a dynamic simulation of the evolution of the drop spectra within a one-dimensional rain shaft is performed using realistic boundary conditions retrieved from real rain events. Droplet size distribution (DSD) retrieved from vertically pointing radar (VPR) measurements are sequentially imposed at the top of the rain shaft as boundary conditions to emulate a realistic rain event. Time series of model profiles of integral parameters such as reflectivity, rain rate, and liquid water content were subsequently compared with estimates retrieved from vertically pointing radars and Joss–Waldvogel disdrometer (JWD) observations. Results obtained are within the VPR retrieval uncertainty estimates. Besides evaluating the model’s ability to capture the dynamical evolution of the DSD within the rain shaft, a case study was conducted to assess the potential use of the model as a physically based interpolator to improve radar retrieval at low levels in the atmosphere. Numerical results showed that relative improvements on the order of 90% in the estimation of rain rate and liquid water content can be achieved close to the ground where the VPR estimates are less reliable. These findings raise important questions with regard to the importance of bin resolution and the lack of sensitivity for small raindrop size (<0.03 cm) in the interpretation of JWD data, and the implications of using disdrometer data to calibrate radar algorithms.
Abstract
Ancillary information that exists within rain gauge and radar-based datasets provides opportunities to better identify error and bias between the two observing platforms as compared to error and bias statistics without ancillary information. These variables include precipitation type identification, air temperature, and radar quality. There are two NEXRAD-based datasets used for reference: the National Centers for Environmental Prediction (NCEP) Stage IV and the NOAA NEXRAD Reanalysis (NNR) gridded datasets. The NCEP Stage IV dataset is available at 4 km hourly and includes radar–gauge bias adjusted precipitation estimates. The NNR dataset is available at 1 km at 5-min and hourly time intervals and includes several different variables such as reflectivity, radar-only estimates, precipitation flag, radar quality indicator, and radar–gauge bias adjusted precipitation estimates. The NNR data product provides additional information to apply quality control such as identification of precipitation type, identification of storm type and Z–R relation. Other measures of quality control are a part of the NNR data product development. In addition, some of the variables are available at 5-min scale. We compare the radar-based estimates with the rain gauge observations from the U.S. Climate Reference Network (USCRN). The USCRN network is available at the 5-min scale and includes observations of air temperature, wind, and soil moisture, among others. We present statistical comparisons of rain gauge observations with radar-based estimates by segmenting information based on precipitation type, air temperature, and radar quality indicator.
Abstract
Ancillary information that exists within rain gauge and radar-based datasets provides opportunities to better identify error and bias between the two observing platforms as compared to error and bias statistics without ancillary information. These variables include precipitation type identification, air temperature, and radar quality. There are two NEXRAD-based datasets used for reference: the National Centers for Environmental Prediction (NCEP) Stage IV and the NOAA NEXRAD Reanalysis (NNR) gridded datasets. The NCEP Stage IV dataset is available at 4 km hourly and includes radar–gauge bias adjusted precipitation estimates. The NNR dataset is available at 1 km at 5-min and hourly time intervals and includes several different variables such as reflectivity, radar-only estimates, precipitation flag, radar quality indicator, and radar–gauge bias adjusted precipitation estimates. The NNR data product provides additional information to apply quality control such as identification of precipitation type, identification of storm type and Z–R relation. Other measures of quality control are a part of the NNR data product development. In addition, some of the variables are available at 5-min scale. We compare the radar-based estimates with the rain gauge observations from the U.S. Climate Reference Network (USCRN). The USCRN network is available at the 5-min scale and includes observations of air temperature, wind, and soil moisture, among others. We present statistical comparisons of rain gauge observations with radar-based estimates by segmenting information based on precipitation type, air temperature, and radar quality indicator.
Abstract
Raindrop collision and breakup is a stochastic process that affects the evolution of drop size distributions (DSDs) in precipitating clouds. Low and List have remained the obligatory reference on this matter for almost three decades. Based on a limited number of drop sizes (10), Low and List proposed generalized parameterizations of collisional breakup across the raindrop spectra that are standard building blocks for numerical models of rainfall microphysics. Here, recent laboratory experiments of drop collision at NASA’s Wallops Island Facility (NWIF) using updated high-speed imaging technology with the objective of assessing the generality of Low and List are reported. The experimental fragment size distributions (FSDs) for the collision of selected drop pairs were evaluated against explicit simulations using a dynamical microphysics model (Prat and Barros, with parameterizations based on Low and List updated by McFarquhar). One-to-one comparison of the FSDs shows similar distributions; however, the model was found to underestimate the fragment numbers observed in the smallest diameter range (e.g., D < 0.2 mm), and to overestimate the number of fragments produced when small drops (diameter DS ≥ 1mm) and large drops (diameter DL ≥ 3mm) collide. This effect is particularly large for fragments in the 0.5–1.0-mm range, and more so for filament breakup (the most frequent type of breakup observed in laboratory conditions), reflecting up to 30% uncertainty in the left-hand side of the FSD (i.e., the submillimeter range). For coalescence, the NWIF experiments confirmed the drop collision energy cutoff (ET ) estimated by Low and List (i.e., ET > 5.0 μJ). Finally, the digital imagery of the laboratory experiments was analyzed to determine the characteristic time necessary to reach stability in relevant statistical properties. The results indicate that the temporal separation between particle (i.e., single hydrometeor) and population behavior, that is, the characteristic time scale to reach homogeneity in the NWIF raindrop populations, is 160 ms, which provides a lower bound to the governing time scale in population-based microphysical models.
Abstract
Raindrop collision and breakup is a stochastic process that affects the evolution of drop size distributions (DSDs) in precipitating clouds. Low and List have remained the obligatory reference on this matter for almost three decades. Based on a limited number of drop sizes (10), Low and List proposed generalized parameterizations of collisional breakup across the raindrop spectra that are standard building blocks for numerical models of rainfall microphysics. Here, recent laboratory experiments of drop collision at NASA’s Wallops Island Facility (NWIF) using updated high-speed imaging technology with the objective of assessing the generality of Low and List are reported. The experimental fragment size distributions (FSDs) for the collision of selected drop pairs were evaluated against explicit simulations using a dynamical microphysics model (Prat and Barros, with parameterizations based on Low and List updated by McFarquhar). One-to-one comparison of the FSDs shows similar distributions; however, the model was found to underestimate the fragment numbers observed in the smallest diameter range (e.g., D < 0.2 mm), and to overestimate the number of fragments produced when small drops (diameter DS ≥ 1mm) and large drops (diameter DL ≥ 3mm) collide. This effect is particularly large for fragments in the 0.5–1.0-mm range, and more so for filament breakup (the most frequent type of breakup observed in laboratory conditions), reflecting up to 30% uncertainty in the left-hand side of the FSD (i.e., the submillimeter range). For coalescence, the NWIF experiments confirmed the drop collision energy cutoff (ET ) estimated by Low and List (i.e., ET > 5.0 μJ). Finally, the digital imagery of the laboratory experiments was analyzed to determine the characteristic time necessary to reach stability in relevant statistical properties. The results indicate that the temporal separation between particle (i.e., single hydrometeor) and population behavior, that is, the characteristic time scale to reach homogeneity in the NWIF raindrop populations, is 160 ms, which provides a lower bound to the governing time scale in population-based microphysical models.
