Drop Size Distribution Research Articles

Role of viscosity in turbulent drop break-up

We investigate drop break-up morphology, occurrence, time and size distribution, through large ensembles of high-fidelity direct-numerical simulations of drops in homogeneous isotropic turbulence, spanning a wide range of parameters in terms of the Weber number $We$ , viscosity ratio between the drop and the carrier flow $\mu _r=\mu _d/\mu _l$ , where d is the drop diameter, and Reynolds ( $Re$ ) number. For $\mu _r \leq 20$ , we find a nearly constant critical $We$ , while it increases with $\mu _r$ (and $Re$ ) when $\mu _r > 20$ , and the transition can be described in terms of a drop Reynolds number. The break-up time is delayed when $\mu _r$ increases and is a function of distance to criticality. The first break-up child-size distributions for $\mu _r \leq 20$ transition from M to U shape when the distance to criticality is increased. At high $\mu _r$ , the shape of the distribution is modified. The first break-up child-size distribution gives only limited information on the fragmentation dynamics, as the subsequent break-up sequence is controlled by the drop geometry and viscosity. At high $We$ , a $d^{-3/2}$ size distribution is observed for $\mu _r \leq 20$ , which can be explained by capillary-driven processes, while for $\mu _r > 20$ , almost all drops formed by the fragmentation process are at the smallest scale, controlled by the diameter of the very extended filament, which exhibits a snake-like shape prior to break-up.

A Statistical Framework for Evaluating Rain Microphysics in Model Simulations and Disdrometer Observations

AbstractStatistical analyses of a large disdrometer data set and a diverse set of model simulations for convection using the Regional Atmospheric Modeling System were conducted, with the mutual goal of providing insights into precipitation formation and microphysical processes. We demonstrate that a two‐moment bulk microphysical model successfully captures the dominant observed modes of variability in rainfall related to rainfall intensity and raindrop size distributions. The model reproduced the general distribution of observed precipitation groups (PGs) derived from Principal Component Analysis. The multi‐variable analysis also uncovered some shortcomings in the model as well as limitations of the disdrometer data. The model solutions were constrained in their predicted drop size distributions (DSDs) due to the fixed DSD parameters assumed in a two‐moment microphysics scheme. A case study from the Mid‐latitude Continental Clouds and Convection Experiment field project demonstrated how model results can be used to contextualize the disdrometer observations which are limited in sample size, spatial coherence, and detection of small drops and low drop concentrations. The case study also showed that the spatial patterns of the statistically derived PGs revealed by the model are consistent with the hypothesized microphysical processes that determine surface rain DSDs. This work demonstrates how leveraging the strengths of observations and models together can improve our understanding and representation of rain microphysical processes.

Population balance modelling of an electrocoalescer

The mechanism of dehydration of a water-in-oil emulsion is complex and involves the growth of an emulsion of polydispersed water droplets in oil, under an electric field, and their gravitational settling and phase separation. In this work, a simple configuration is chosen to understand the mechanism of this complex process. A population balance-based model is developed to predict the performance of an electrocoalescer. The model explicitly accounts for the coalescence of water drops by the action of dipolar forces and gravity settling. A distributed parameter plug flow and a tank-in-series model are developed to account for the gravity settling. The dynamics of electrocoalescence are captured by analyzing the drop size distribution and mean diameter along with the height of the coalescer and time. A simplified model - considering that monodispersity prevails throughout the process is also developed, and the separation curves are compared with the polydispersed system. The effect of operational parameters, such as the strength of the electric field, water cut, viscosity of oil, the height of the coalescer, and polydispersity in the initial drop size distribution, is investigated. The main insight from this work is that there are essentially three stages of electrocoalescence, a slow initial incubation stage where droplets grow to around 1 mm in size without much settling, followed by a rapid settling of these droplets to set in the fast coalescence stage where most water is removed to result in a lean emulsion, followed by a slow simultaneous electrocoalescence and separation stage of this lean emulsion to result in a final separation. A scaled masterplot for the performance of an electrocoalescer, encompassing the effect of the process parameters is obtained. The model also suggests that electrocoalescence essentially leads to a polydisperse system and a population balance approach is critical to its analysis.

Adjustment of 1 min rain gauge time series using co-located drop size distribution and wind speed measurements

Abstract. A procedure to adjust rainfall intensity (RI) measurements to account for the wind-induced measurement bias of traditional catching-type gauges is proposed and demonstrated with an application to a suitable case study. The objective is to demonstrate that adjustment curves derived from numerical simulations and disdrometer measurements allow for a posteriori correction of rainfall time series based on the wind velocity measurements alone. To quantify the impact of wind on long-term records, 1 min RI measurements from a cylindrical tipping-bucket rain gauge installed at the Hong Kong Observatory are adjusted. Catch ratios derived from the instrument's aerodynamic behaviour under varying wind speed and drop size combinations are obtained by fitting computational fluid-dynamic simulation results already available in the literature. Co-located high-resolution wind speed measurements from a cup and vane sensor and drop size distribution measurements from an optical video disdrometer (the 2DVD or two-dimensional video disdrometer) are used to infer the collection efficiency of the gauge as a function of wind speed and RI alone and to adjust raw data from a 4-year dataset (2018–2021) of 1 min RI measurements. Due to the specific local climatology, where strong wind is often associated with intense precipitation, 80 % of the dataset adjustments are limited to 4 % of the observed RI values. This, however, results in a significant amount of available freshwater resources that would be missing from the calculated hydrological and water management budget of the region should the adjustments be neglected. This work raises the need to quantify the impact of the wind-induced bias at other sites where disdrometer data support a characterisation of the relationship between the drop size distribution and the measured RI. Depending on the local rain and wind climatology, the correction may account for a significant portion of the annual rainfall amount.

Comprehensive properties of non-penetrating and penetrating deep convection precipitation in summer over the Tibetan Plateau derived from GPM observations

The spatial-temporal distribution, drop size distribution and their associated thermal structure as well as the tropopause anomalies of non-penetrating and penetrating deep convection precipitation in summer of 2014–2021 over the Tibetan Plateau are explored using GPM observations, ERA5 reanalysis data and topographic data in this study. The result shows that frequencies and intensities of non-penetrating deep convection precipitation are generally larger than those of penetrating deep convection precipitation. The storm tops of non-penetrating and penetrating deep convection are approximately 15–16 km and 18–19 km respectively, whereas the corresponding lapse rate tropopause heights for both types of deep convection are similar (about 17.4 km). The radar reflectivity decreases with height and the maximum appears near the surface. Latent heat release of non-penetrating deep convection is largely confined in the lower troposphere, while latent heating of penetrating deep convection is higher. Moreover, rain drop concentration of non-penetrating deep convection distributes uniformly (5–15 km) and particle size is large (2.0–2.5 mm) near the surface. In contrast, penetrating deep convection particles concentrate below 10 km and near the storm top (19–20 km), with small size (1.0–1.5 mm). Furthermore, there are evident differences in thermal structure during non-penetrating and penetrating deep convection process over the Tibetan Plateau. Notably, slight net warming anomaly occurs above tropopause during penetrating deep convection due to subsidence from divergent flow. Moistening anomaly is more significant below 11 km following non-penetrating deep convection. However, slight dehydration appears near the tropopause after penetrating deep convection. Descending tropopause and increasing CAPE before penetrating deep convection are more significant and conducive to penetrating. These results suggest macro-micro features of non-penetrating and penetrating deep convection and interaction between two types of deep convection and thermal structure over the Tibetan Plateau.

Long-term changes in rainfall epochs and intensity patterns of Indian summer monsoon in changing climate

The rainfall spell patterns of the Indian Summer Monsoon (ISM) and their respective intensities have been analyzed in light of changing climate by using climatology of gridded rainfall data during the period 1901–2022. The active and break days over the monsoon core zone are identified for peak monsoon months for each year based on the standard criteria. In general, maximum of four active spells are observed within the monsoon season (99% of the time) with occasional occurrences of additional spells. A significant change is observed from 1901 to 2022 in the contribution of each active spell to the respective cumulative ISM rainfall; but the sum of all the active spells rainfall contributions remained the same. The spell-1 rainfall contribution to the total ISM rainfall is decreasing (−0.4 ± 0.15 mm/decade); while it is increasing (0.22 ± 0.11 mm/decade) in spell-2. Also, it is found that the number of break days between the first and second active spells is declined by 11 days over 122 years along with the enhancement in the number of second active spell days. It is proposed that these may be partly due to the observed decline in the northward propagation speed of the monsoon and partly due to significant shift from positive to negative cloud radiative forcing over the Indian ocean region during the first-half (June–July) of the monsoon to the second-half (August–September) of the monsoon. In addition, the probability density distribution of active spell-4 is observed to be distinctly different from the rest of the active spells. In association, the monsoon trough axis is observed to be shifting southward along with the weakening of low level winds (at 850mb level) from beginning to the end of the active monsoon season. Concurrently, in-situ observations of drop size distributions of low, moderate and extreme rainfall events suggests that the controlling microphysical processes shift from size controlled to number controlled drop size distributions with extreme rainfall events being primarily number controlled. Thus, the significance of the present study may provide the better understanding of the role of duration active spells to the monsoon in changing climate.

On the Mechanism of Sulfur Dioxide Oxidation in Cloud Droplets

Data from field experiments on the dynamics of SO2 oxidation in cloud droplets are presented. The rapid oxidation of SO2 by molecular oxygen observed in experiments is attributed here to the catalytic action of a pair of manganese and iron ions in droplets. Their inhomogeneous effect by the drop-size distribution, attributed in experiments only to the leaching of ions of these metals from coarse particles of mineral dust is also due to the transition of the oxidation reaction into a branched mode. The results obtained indicate that the branched regime of catalytic oxidation of SO2 detected in cloud droplets should be considered as a new and significant source of sulfates in the atmosphere. This process must be taken into account when considering both the budget of sulfates in the global atmosphere and their impact on the climate.

Does “right” simulated extreme rainfall result from the “right” representation of rain microphysics?

AbstractUsing the observations from the two‐dimensional video disdrometer and polarimetric radar, a detailed process‐based evaluation of five bulk microphysics schemes in the simulation of an extreme rainfall event over the mountainous coast of South China is performed. Most schemes reproduce one of the heavy rainfall areas, and the National Severe Storms Laboratory (NSSL) scheme successfully simulates both heavy rainfall areas in this event. However, our analysis reveals that even the NSSL simulation still cannot accurately represent the rain microphysics for this event. Observational analysis shows that abundant small‐ and medium‐sized (1–4 mm) raindrops are the main contributors to the extreme rainfall. All the simulations tend to underpredict raindrops for diameter around 3 mm. The Lin, WSM6, and Morrison simulations agree better with the observed drop size distribution (DSD) for diameters between 1 and 2 mm for higher rain rates. The Thompson simulation shows a relatively narrow distribution with overpredicted small‐sized (1–2 mm) raindrops. The NSSL simulation has a broad distribution with more large (>4 mm) raindrops probably related to its efficient rain self‐collection process at the low levels, which is conducive to producing extreme rainfall. Proper rain evaporation rate is important in generating cold pools with favorable strength for the maintenance of a convective system in this event. Similar results are obtained in the simulations of two additional extreme rainfall cases, in which the NSSL simulation also overpredicts large raindrops while the Thompson simulation produces more small raindrops. This study indicates that more efforts are needed to improve the representation of rain self‐collection/breakup, rain evaporation processes, and DSD for extreme rainfall over South China. It also highlights the importance in careful consideration of rain DSD in addition to radar reflectivity and surface precipitation when analyzing simulations of extreme rainfall in order to avoid “wrong” interpretation of “right” results.

Sediment modeling using laboratory-scale rainfall simulator and laser precipitation monitor

The characterization of a rainfall simulator provides an excellent opportunity to study the potential of soil erosivity without waiting for natural rain. But, precise instrumentation is required to estimate the parameters, which is seldom available. To overcome this problem, the empirical and conceptual relationships obtained through physically-based modeling help to correlate the rain parameters contributing to soil erosion. The present laboratory study used five pressurized nozzles of different capacities and a Laser Precipitation Monitor (LPM) to generate different rain intensities (21.0–79.0 mm h−1) and to register drop size distribution, respectively. The sediment transportation induced by rain and runoff was measured with an erosion flume of 2.50 × 1.25 × 0.56 m with an adjustable longitudinal slope. The spatial uniformity, drop size distribution, drop velocity, and kinetic energy were used to evaluate the simulator's performance. The different rain erosivity parameters were correlated and tested statistically using linear and non-linear regression analysis. The rain simulation experiments of different intensities at different pressure ranges were performed on flat, 5, 10, and 15% slopes of the erosion flume to evaluate rain characteristics and record the surface runoff and sediment yield. The median drop sizes produced during the simulator ranged from 0.38 to 2.11 mm, coinciding with natural rain. The empirical relationships were developed to correlate surface discharge and sediment yield with rain intensity by optimizing the parameters for further study of experimental field plots of different slopes. The observed and estimated rain erosivity parameters showed a significant relationship (R2 = 0.75 to 0.93; P < 0.001) in multiple regression analysis, and the metrics used to test the developed regression equations showed lower MAE, MSE, and RMSE errors indicating the adequacy of the relationships. The results indicated that the simulator helps to understand the complex task of soil erosion with hydrologic and geomorphic processes in laboratory experimentation with sufficient accuracy in measuring sediment transport events.

A comparative study on emulsification in the presence of a nanoclay (Pickering emulsion) or a surfactant using high intensity mixing

The study explored the potential of using a nanoclay, Laponite RD, as a stabilizing agent in comparison to a surfactant, Tergitol TMN6, at dispersed phase volume fractions of 10–50% vol. An ultrasonicator was employed as an energy intensive device; covering a specific power input range of ∼ 36–52 W kg− 1. In both cases, final dispersions obtained could be considered stable over the period of ageing tests for 3 months as comparable drop size distributions were obtained although there were some differences in the rheology at the highest dispersed phase concentration. Whilst surfactant stabilized emulsions were of Newtonian behavior, Pickering emulsions stabilized with the nanoclay exhibited non-Newtonian behavior, which may be a desirable feature of the final product- certainly one that requires attention in design and scale up. Kinetics of breakup studied through the evolution of the Sauter mean diameter prior to reaching an equilibrium value on the basis of energy density have shown the breakup process being faster with the Pickering emulsions although the equilibrium drop diameters were larger. Overall, with emulsions stabilized using a surfactant, Sauter mean drop diameters could be as low as 240 nm, regardless of the dispersed phase volume fraction, drop sizes were larger with Pickering emulsions which depended on the dispersed phase concentration.

Development of Drop Size Distribution Model for Dropwise Condensation on a Superhydrophobic Surface

This study presents a mathematical model of drop size distribution during dropwise condensation on a superhydrophobic surface. The model is developed by combining a power law growth model, an exponentially decaying population model, and a Gaussian probability model for growth variations. The model is validated against experiment data, with correlations ranging from 88% to 94%. The growth model is shown to sufficiently describe the growth of drops from 0.02 mm to 0.1 mm but may be extrapolated to describe the growth of even smaller drops. The experiment data show that drop size distribution or frequency distribution of drops of different sizes varies significantly with time and may be considered pseudo-cyclic. The developed model, together with the sweep rate of drops, sufficiently describes this behavior and, consequently, may also be used to better estimate the heat transfer rate due to dropwise condensation.

Impacts of Drop Clustering and Entrainment‐Mixing on Mixed Phase Shallow Cloud Properties Over the Southern Ocean: Results From SOCRATES

AbstractEntrainment and associated mixing (i.e., entrainment‐mixing) have been shown to impact drop size distributions. However, most past studies have focused on warm clouds and have not considered the impacts on mixed phase clouds (i.e., those containing liquid and ice particles). This study characterizes the impacts of entrainment‐mixing on mixed phase cloud properties over the Southern Ocean using in situ observations. By taking advantage of strong correlations between droplet clustering and entrainment‐mixing, a clustering metric is used as a proxy to assess the degree of mixing. This maximizes the available sample size for a statistical analysis of entrainment‐mixing impacts on mixed phase properties. A positive relationship is found between the magnitude of droplet clustering and large ice concentrations (those with maximum dimensions greater than ∼300 μm), suggesting entrainment‐mixing enhances the Wegener‐Bergeron‐Findeisen (WBF) process. Particle size distributions are averaged over different ranges of liquid (liquid water content (LWC)) to total water content (TWC) ratio. Since the ratio is expected to transition from 1 to 0 during glaciation, differences in the distributions provide insight into the relation of entrainment‐mixing to mixed phase cloud evolution. Mixed phase samples with the greatest large ice concentrations occur at LWC/TWC &lt; 0.4 in low clustering regions. However, these samples are relatively few, whereas high clustering regions have a greater frequency of samples with LWC/TWC &lt; 0.4. This suggests sublimation/vapor sinks associated with entrainment can counteract the enhanced WBF. In high clustering regions, distributions of small droplets are relatively constant and large droplets (&gt;30 μm) are preferentially removed as LWC/TWC transitions from 1 to 0.

Probabilistic derivation of droplet velocity using quadrature method of moments

Abstract Accurately prediction of dispersion and polydispersity of droplet flow is not a trivial task due to the complex behavior of the droplet size distribution (DSD) and the strong state of the instantaneous velocity of a droplet on the shape and size of the droplet. Describing the distribution of sizes and velocities of droplets initially formed in sprays is an essential piece of information needed in spray modeling, which is used to define the initial state of the spray droplets in the downstream two-phase flow fields’ predictive computations. The predictive model for the droplet size and velocity distributions in sprays is formulated as the droplet’s velocity magnitude has a power–law relationship with the droplet in this study. The present model incorporates the deterministic and stochastic aspects of the spray formation process. The quadrature method of moments (QMOM) is applied to solve numerically the transport equations of the probability density function coupled with conserved source terms incompressible Navier-Stokes equations for the liquid phase. The sub-models are connected by different source terms signifying the liquid-gas interaction. Equations of transport for spray moments are derived from DSD, and closure is attained using a gamma distribution. The integer spray moments concerning the volume are used to construct the continuous distribution of QMOM. In contrast, the velocity moments are used to determine the droplet velocity as a constant function of the droplet diameter. The model is first applied to simulate a diesel spray tip penetration under nonreactive conditions with different droplet velocity profiles to validate the approach with experimental data. An additional case of a liquid nitrogen spray is applied to show the gamma distribution’s ability to describe spray drop size distribution. The model generally predicts reasonable agreement with the experimental for both cases.

Lagrangian Simulation Methodology for Large-Eddy Simulations of Prefilming Air-Blast Injectors

A Lagrangian framework is proposed to address liquid film and atomization modeling in large-eddy simulations (LESs) of aeronautical air-blast injectors. The Lagrangian liquid film model of O’Rourke and Amsden (“A Spray/Wall Interaction Submodel for the KIVA-3 Wall Film Model,” SAE International TP 2000-01-0271, Warrendale, PA, 2000) is improved by introducing a subgrid contact angle to better predict the film height and the resulting film dynamics. Next, the phenomenological the primary atomization model for prefilming air-blast injectors (PAMELA) proposed by Chaussonnet et al. (“A New Phenomenological Model to Predict Drop Size Distribution in Large-Eddy Simulations of Airblast Atomizers,” International Journal of Multiphase Flow, Vol. 80, April 2016, pp. 29–42) for primary atomization at the prefilmer edge is enhanced to deal with complex geometries. This model is able to predict the droplet-size probability density function from the prefilmer height and flow conditions. The original formulation relied on correlations valid for flat plates to determine the gas boundary-layer thickness, and it required a gas velocity at film height to be set by the user. These two points make its use difficult for complex configurations where there is no simple correlation for the gas boundary-layer thickness and the gas velocity at film height cannot be a priori estimated. An embedded methodology, named the automatic PAMELA, is therefore proposed in this work to automatically determine these two quantities in the simulation. For each cell of the prefilmer edge where atomization occurs, the gas boundary-layer thickness is estimated by analyzing the local velocity profile thanks to Lagrangian probes; and the gas velocity is computed from the local film height by assuming a logarithmic velocity profile. Finally, the film and primary atomization models are coupled to a secondary atomization model, and they are assessed on an industrial air-blast aeronautical injector. The average droplet velocity profiles and Sauter mean diameters are compared against experimental phase Doppler particle analyzer measurements, and they demonstrate the ability of the proposed framework to perform Lagrangian LESs of liquid injection in complex geometries.

Characterization of Raindrop Size Distribution over Santa Clara Valley

This study presents a year-long (January 2019–April 2020) analysis of the Z–R relationship and drop size distribution (DSD) scaling parameters for size, concentration, and shape of rain events over Santa Clara Valley, CA. External influences were analyzed based on synoptic variability and seasons. For the former, 850 hPa winds were separated into groups based on direction and magnitude. Results show that greater drop size, lower concentration, and larger shape parameters for spring, while winter and fall showed smaller drop sizes, higher concentrations, and smaller shape parameters. For synoptic variability, southeasterly-to-southwesterly flow was associated with larger drop sizes, larger concentrations, and smaller shape parameters relative to northwesterly flow. Differences in the DSD scaling parameter values and Z–R relationship were also observed between strong and weak low-level flow. The results of this study suggest that it is beneficial to derive specific microphysical relationships based on seasons and different synoptic events to improve radar rain rate retrieval algorithms using the Z–R relationship.

Experimental study of the injection angle impact on the column Waves: Wavelength, frequency and drop size

An experimental study was performed to investigate the influence of injection angle on further details of breakup of a circular liquid jet injected into an airstream. Wavelength and frequency of axial oscillations caused by column waves, drops size distribution, orientation and aspect ratio of these drops were measured and reported. Injection angles between 30 and 90 degrees were considered. High-speed photography and shadowgraphy techniques were utilized to visualize and record the flow. Experimental data were obtained by processing images with the help of an in-house developed code. We found that gas Weber number and the injection angle are influential on wavelength and frequency of the column waves. The wavelength decreased and the frequency increased with increasing gas Weber number or decreasing the injection angle. Also, momentum ratio, gas Weber number and injection angle were affecting drop's average diameter. By reducing the injection angle, the atomization process was prolonged and the produced drops were larger. Although the injection angle affected the average drop size and number, as long as the regime was not changed, the probability distribution of drop size was independent of the injection angle.We extended theory of Ng et al. [1] to estimate wavelength, frequency of column waves formed on the liquid jet that was injected into an airstream to account for injection angle. A relative gas Weber number was defined by using the relative velocity of the gas to that of the liquid along the flow direction. The introduced relative gas Weber number was found useful in classifying the breakup regimes of the flow. A relation was proposed to estimate these wavelengths with good agreement with our data at different injection angles and other previously published data at normal injection of liquid jets. Two separate correlations for SMD estimation were proposed for before and after bag formation in the flow.

Cloud and precipitation microphysical retrievals from the EarthCARE Cloud Profiling Radar: the C-CLD product

Abstract. The Earth Clouds, Aerosols and Radiation Explorer (EarthCARE) satellite mission is a joint endeavour developed by the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA) and features a 94 GHz Doppler Cloud Profiling Radar. This paper presents the theoretical basis of the cloud and precipitation microphysics (C-CLD) EarthCARE Level 2 (L2) algorithm. The C-CLD algorithm provides the best estimates of the vertical profiles of water mass content and hydrometeor characteristic size, obtained from radar reflectivity, path-integrated signal attenuation and hydrometeor sedimentation Doppler velocity estimates using optimal estimation (OE) theory. To obtain the forward model relations and the associated uncertainty, an ensemble-based method is used. This ensemble consists of a collection of in situ measured drop size distributions that cover natural microphysical variability. The ensemble mean and standard deviation represent the forward model relations and their microphysics-based uncertainty. The output variables are provided on the joint standard grid horizontal and EarthCARE Level 1b (L1b) vertical grid (1 km along track and 100 m vertically). The OE framework is not applied to liquid-only clouds in drizzle-free and lightly drizzling conditions, where a more statistical approach is preferred.

Effect of surfactants and interfacial rheology on equilibrium drop size in turbulent liquid-liquid dispersions

Surfactants are often required to stabilize liquid-liquid dispersions produced by high shear mixers. Due to the high power input, drops are deformed rapidly in the dispersion zone so the dynamic interfacial properties governed by the surfactant adsorption rate can have a significant impact on the resulting drop size. The objective of this work is to develop a fundamental link between surfactant adsorption dynamics, interfacial properties, and turbulent emulsification processes. To ensure constant bulk surfactant concentration during dispersion, equilibrium drop size for dilute dispersions produced by a batch rotor-stator mixer were studied. Silicone oils of various viscosity were dispersed in aqueous nonionic surfactant solutions. Drop size distributions (DSD) were measured via a video microscopy/automated image analysis technique. Equilibrium interfacial tension was measured via a pendant drop technique, as a function of surfactant concentration. The dynamic surface tension was similarly measured. The data were fit to the Langmuir adsorption isotherm and the long-times approximation to the Ward – Tordai equation and the adsorption parameters and surfactant diffusivities so obtained were employed, with an estimate of the drop deformation timescale, to estimate the surface dilational modulus (Esd) or Marangoni stress acting on the drop’ surface due to interfacial tension gradients. Trends observed in the measured equilibrium mean drop size and DSD are explained in terms of the interfacial and rheological properties. Below the CMC, Esd peaks and the drop size increases with bulk surfactant concentration, despite a decrease in equilibrium interfacial tension. Above the CMC, Marangoni stresses are small but the presence of the surfactant still modifies the rheology of the interface, increasing the effective viscosity of the drops. A comprehensive set of mechanistic models for drop size in turbulent flows, based on Kolmogorov-Hinze theory, was developed and modified to partially account for the effect of surfactants via an appropriately defined effective viscosity. The approach allows integration of surfactant phenomena into widely accepted correlations for drop size in surfactant free systems.

An Improved S-Band Polarimetric Radar-Based QPE Algorithm for Typhoons over South China Using 2DVD Observations

Polarimetric radar data are an important tool for quantitative precipitation estimation (QPE), which is essential for monitoring and forecasting precipitation. Previous studies have shown that the drop size distribution (DSD) and polarimetric radar parameters of typhoon-induced precipitation differ significantly from those of other types of rainfall. South China is a region that frequently experiences typhoons and heavy rainfall, which can cause serious disasters. Therefore, it is critical to develop a QPE algorithm that is suitable for typhoon precipitation over South China. In this study, we constructed four simple QPE estimators, R(ZH), R(ZH, ZDR), R(KDP) and R(KDP, ZDR) based on two-dimensional video disdrometer (2DVD) DSD observations of typhoon-induced precipitation over South China in 2017–2018. We analyzed the DSD characteristics and the estimation accuracy of these four QPE estimators in the reflectivity–differential reflectivity (ZH–ZDR) space, as well as the S-band polarimetric radar (S-POL) data of seven typhoon-induced precipitation events that affected South China in 2017–2019. We used these data to quantitatively determine the optimal ranges of the estimators and establish a typhoon precipitation QPE algorithm for typhoon-induced precipitation over South China (2DVD-Typhoon). The evaluation results showed that: (1) compared to R(ZH) and R(KDP), R(ZH, ZDR) and R(KDP, ZDR) had lower performance in estimating typhoon-induced rainfall after incorporating the polarimetric parameter ZDR, as strong crosswind of the typhoon caused some bias in the raindrop-induced ZDR; (2) the 2DVD-Typhoon algorithm utilizes the respective advantages of the individual estimators to generate the best QPE results; (3) the QPE performance of 2DVD-Typhoon and the Colorado State University–Hydrometeor Identification Rainfall Optimization (CSU-HIDRO) is used as a comparison for hourly rainfall, cumulative rainfall and different rainfall intensity. The comparison shows that 2DVD-Typhoon gives a better normalized error (NE), root mean square error (RMSE) and correlation coefficient (CC), indicating its strength in rainfall estimation for typhoons over South China. The above results provide theoretical support for improving typhoon-induced rainfall monitoring and numerical weather forecasting models in South China.

The size distribution metrics and kinetic energy of raindrops above and below an isolated tree canopy in urban environment

Raindrop impact on bare soils is the initial phase of rainfall-induced soil erosion which is altered under any type of vegetation due to the interactions of rainfall with the canopies. This study examines the drop size distribution (DSD) and kinetic energy (KE) of raindrops above and below the birch tree (Betula pendula Roth.) canopy in a research plot in the city of Ljubljana, Slovenia using a one-year observation of 63 rainfall events and the effect of meteorological variables under moderate continental climate. Simultaneous measurement of the microstructures of open rainfall and throughfall was carried out using an optical disdrometer. The result of our analysis revealed that throughfall DSD showed two distinct major peaks (bimodal) occurring primarily on smaller drop sizes while open rainfall has only one. The cumulative drop number, median drop-volume diameter (D50), and drop fall velocity of throughfall were 16.4%, 26.6%, and 5.0% lower than those of open rainfall, respectively. Also, the relative volume percentage of raindrops > 1.5 mm is 1.5 times higher than those observed in throughfall drops which indicates that the presence of the canopy caused the fractionation of larger drops into smaller droplets. These reductions significantly differ depending on the phenoseasons of the canopy with the leafed state being higher than the leafless state. Similarly, the Kruskal-Wallis H test result revealed that birch tree elicits a statistically significant change in the kinetic energy of open rainfall, thus weakening the mean rainfall KE by 33.7%. On the other hand, KE is positively affected by the phenological condition of the canopy with higher attenuation being observed during its leafed state. Also, the correlation analysis demonstrated that vapor pressure deficit, air temperature, and relative humidity have stronger associations with throughfall kinetic energy among meteorological variables considered. These findings underscore the necessity of an optimized selection of tree species for afforestation programs.