Explore the vast range of titles available.

Micro rain radar (MRR-2) provides the measurement of the drop size distribution DSD with altitude and rain rates. In this paper, we show a new form of gamma drop size distribution (DSD) model. MRR-2 is based on the principle of Radar spectrum measurement of continuous-wave of frequency modulation. DSD measurements for the rain rates ~ 0–25 mm/h and the height from 150 to 2000 m during the south-west monsoon season for the period 2009 and 2010 are used in this study. From the variance of DSD (σ2) and mass-weighted mean drop diameter as well as after the mathematical calculation, two parameters (Λ and µ) are obtained for the use of lower-order moments. Both the moments are utilized for the best suitable of gamma DSD. Measured DSD for the different rain rates and different altitudes below the melting layer height (~ 2–3 km) compared among the exponential, lognormal and gamma DSD model over Darjeeling in the Eastern Himalaya. The correlation between best fit measured DSD and gamma distribution indicate that they correlate well for both lower and higher order moments for the heights 150 m and 1050 m. Whereas they correlated only for higher order moments for the 450 m, 1500 m and 1950 m. Thus, it is found that the observed pattern of DSD agrees well to the gamma DSD model.

The raindrop size distribution (DSD) is fundamental for quantitative precipitation estimation (QPE) and in numerical modeling of microphysical processes. Conventional disdrometers cannot capture the small drop end, in particular the drizzle mode which controls collisional processes as well as evaporation. To overcome this limitation, the DSD measurements were made using (i) a high-resolution (50 microns) meteorological particle spectrometer to capture the small drop end, and (ii) a 2D video disdrometer for larger drops. Measurements were made in two climatically different regions, namely Greeley, Colorado, and Huntsville, Alabama. To model the DSDs, a formulation based on (a) double-moment normalization and (b) the generalized gamma (GG) model to describe the generic shape with two shape parameters was used. A total of 4550 three-minute DSDs were used to assess the size-resolved fidelity of this model by direct comparison with the measurements demonstrating the suitability of the GG distribution. The shape stability of the normalized DSD was demonstrated across different rain types and intensities. Finally, for a tropical storm case, the co-variabilities of the two main DSD parameters (normalized intercept and mass-weighted mean diameter) were compared with those derived from the dual-frequency precipitation radar onboard the global precipitation mission satellite.

The rain drop size distribution (DSD) at Cherrapunji, Northeast India was observed by a laser optical disdrometer Parsivel 2 from May to October 2017; this town is known for the world’s heaviest orographic rainfall recorded. The disdrometer showed a 30% underestimation of the rainfall amount, compared with a collocated rain gauge. The observed DSD had a number of drops with a mean normalized intercept log 10 N w > 4.0 for all rain rate categories, ranging from <5 to >80 mm h − 1 , comparable to tropical oceanic DSDs. These results differ from those of tropical oceanic DSDs, in that data with a larger N w were confined to the stratiform side of a stratiform/convective separation line proposed by Bringi et al. (2009). A large number of small drops is important for quantitative precipitation estimates by in-situ radar and satellites, because it tends to miss or underestimate precipitation amounts. The large number of small drops, as defined by the second principal component (>+1.5) while using the principal component analysis approach of Dolan et al. (2018), was rare for the pre-monsoon season, but was prevalent during the monsoon season, accounting for 16% (19%) of the accumulated rainfall (precipitation period); it tended to appear over weak active spells or the beginning of active spells of intraseasonal variation during the monsoon season.

Quantitative precipitation estimation using polarimetric radar in attenuation-prone frequency (X-band) in tropical regions characterized by convective rain systems with high intensities is a major challenge due to strong attenuations that can lead to total signal extinction over short distances. However, some authors have addressed this issue in Benin since 2006 in the framework of the African Monsoon Multidisciplinary Analysis program. Thus, with an experimental setup consisting of an X-band polarimetric weather radar (Xport) and a network of rain gauges, investigations have started on the subject with the aim of improving rainfall estimates. Based on simulated polarimetric variables and using a Multilayer Perceptron artificial neural network, several bi-variable and tri-variable algorithms were assessed in this study. The data used in this study are of two categories: (i) simulated polarimetric variables (Rayleigh reflectivity Z, horizontal attenuation Ah, horizontal reflectivity Zh, differential reflectivity Zdr, and specific differential phase Kdp) and rainfall intensity (R) obtained from Rain Drop Size Distribution (DSD) measurements used for algorithm evaluation (training and testing); (ii) polarimetric variables measured by the Xport radar and rainfall intensity measured by rain gauges used for algorithm validation. The simulations are performed using the T-matrix code, which leverages the scattering properties of spheroidal particles. The DSD measurements taken in northwest Benin were used as input for this code. For each spectrum, the T-matrix code simulates multiple variables. The simulated data (first category) were divided into two parts: one for training and one for testing. Subsequently, the best algorithms were validated with the second category of data. The performance of the algorithms during training, testing, and validation was evaluated using metrics. The best selected algorithms are A1:R(Z,Kdp) and A12:R(Zdr,Kdp) (among the bi-variable); B2:R(Zh,Zdr,Kdp) and B3:R(Ah,Zdr,Kdp) (among the tri-variable). Tri-variable algorithms outperform bi-variable algorithms. Validation with observation data (Xport measurements and rain gauge network) showed that the algorithm B3:R(Ah,Zdr,Kdp) performs better than B2:R(Zh,Zdr,Kdp).

Effect of orography on tropical rain drop size distribution (DSD), which was not well known, is evidenced through the present study. DSD is the number of raindrops/unit volume/diameter interval, which tells about the underlying physics of rainfall process. Rain DSD was studied, using a Joss–Waldvogel disdrometer, at three coastal and a hill station in the Tropics. The variation in the characteristics of three physically significant parameters derived from the DSD with rain rate clearly unraveled the effect of orography on rain physics. The orographic rain appears to have larger drops compared with nonorographic rains when rain rate is high.

Understanding drop size distribution (DSD) variability has important implications for remote sensing and numerical modeling applications. Twelve disdrometer datasets across three latitude bands are analyzed in this study, spanning a broad range of precipitation regimes: light rain, orographic, deep convective, organized midlatitude, and tropical oceanic. Principal component analysis (PCA) is used to reveal comprehensive modes of global DSD spatial and temporal variability. Although the locations contain different distributions of individual DSD parameters, all locations are found to have the same modes of variability. Based on PCA, six groups of points with unique DSD characteristics emerge. The physical processes that underpin these groups are revealed through supporting radar observations. Group 1 (group 2) is characterized by high (low) liquid water content (LWC), broad (narrow) distribution widths, and large (small) median drop diameters D 0 . Radar analysis identifies group 1 (group 2) as convective (stratiform) rainfall. Group 3 is characterized by weak, shallow radar echoes and large concentrations of small drops, indicative of warm rain showers. Group 4 identifies heavy stratiform precipitation. The low latitudes exhibit distinct bimodal distributions of the normalized intercept parameter N w , LWC, and D 0 and are found to have a clustering of points (group 5) with high rain rates, large N w , and moderate D 0 , a signature of robust warm rain processes. A distinct group associated with ice-based convection (group 6) emerges in the midlatitudes. Although all locations exhibit the same covariance of parameters associated with these groups, it is likely that the physical processes responsible for shaping the DSDs vary as a function of location.

We build a tractable growth model in which multiproduct incumbents invest in internal innovations to improve their existing products, while new entrants and incumbents invest in external innovations to acquire new product lines. External and internal innovations generate heterogeneous innovation qualities, and firm size affects innovation incentives. We analyze how different types of innovation contribute to economic growth and the role of the firm size distribution. Our model aligns with many observed empirical regularities, and we quantify our framework with Census Bureau and patent data for US firms. Internal innovation scales moderately faster with firm size than external innovation.

Remote sensing instruments are heavily used to provide observations for both the operational and research communities. These sensors do not provide direct observations of the desired atmospheric variables, but instead, retrieval algorithms are necessary to convert the indirect observations into the variable of interest. It is critical to be aware of the underlying assumptions made by many retrieval algorithms, including that the retrieval problem is often ill posed and that there are various sources of uncertainty that need to be treated properly. In short, the retrieval challenge is to invert a set of noisy observations to obtain estimates of atmospheric quantities. The problem is often complicated by imperfect forward models, by imperfect prior knowledge, and by the existence of nonunique solutions. Optimal estimation (OE) is a widely used physical retrieval method that combines measurements, prior information, and the corresponding uncertainties based on Bayes’s theorem to find an optimal solution for the atmospheric state. Furthermore, OE also allows the relative contributions of the different sources of error to the uncertainty in the final retrieved atmospheric state to be understood. Here, we provide a novel Python library to illustrate the use of OE for inverse problems in the atmospheric sciences. We introduce two example problems: how to retrieve drop size distribution parameters from radar observations and how to retrieve the temperature profile from ground-based microwave sensors. Using these examples, we discuss common pitfalls, how the various error sources impact the retrieval, and how the quality of the retrieval results can be quantified.

An impact-type Joss-Waldvogel disdrometer (JWD), a two-dimensional video disdrometer (2DVD), and a laser optical OTT Particle Size and Velocity (PARSIVEL) disdrometer (PD) were used to measure the raindrop size distribution (DSD) over a 6-month period in Huntsville, Alabama. Comparisons indicate event rain totals for all three disdrometers that were in reasonable agreement with a reference rain gauge. In a relative sense, hourly composite DSDs revealed that the JWD was more sensitive to small drops (,1 mm), while the PD appeared to severely underestimate small drops less than 0.76mm in diameter. The JWD and 2DVD measured comparable number concentrations of midsize drops (1-3mm) and large drops (3-5 mm), while the PD tended to measure relatively higher drop concentrations at sizes larger than 2.44mm in diameter. This concentration disparity tended to occur when hourly rain rates and drop counts exceeded 2.5mm/h and 400/min, respectively. Based on interactions with the PD manufacturer, the partially inhomogeneous laser beam is considered the cause of the PD drop count overestimation. PD drop fall speeds followed the expected terminal fall speed relationship quite well, while the 2DVD occasionally measured slower drops for diameters larger than 2.4mm, coinciding with events where wind speeds were greater than 4m/s. The underestimation of small drops by the PD had a pronounced effect on the intercept and shape of parameters of gamma-fitted DSDs, while the overestimation of midsize and larger drops resulted in higher mean values for PD integral rain parameters

Effects of eccentricity and horizontal electric field (EH) on the binary‐collision outcomes of water drops are examined using numerically calculated collision characteristics from previous studies and results of simulation experiment conducted by the authors. For a fixed collision kinetic energy (CKE), filament breakups can occur at all values of eccentricity but events of coalescence decrease, and that of sheet breakup increase with increasing eccentricity in absence of EH. However, as EH increases to ∼300 kVm−1 it opposes the variability of the coalescence and sheet breakup events with eccentricity. When EH exceeds ∼300 kVm−1 the collision outcomes might be determined only by the CKE and EH. The calculated value of coalescence efficiency and total number of fragments after a binary collision decreases with an increase in EH. It is argued that an electric field can significantly modify drop size distribution in thunderclouds and needs to be considered for development of precipitation. Plain Language Summary Growth of water drops in clouds is mostly governed by the drop size distribution in them. When two drops collide with each other, they can either coalesce to form a single larger drop, or disintegrate into many smaller drops, or bounce back. These different outcomes after their collisions are mostly determined by whether the collisions are centric where the eccentricity of the collision is zero or grazing where the eccentricity is one or somewhere in between the two extremes. The present study shows that if the collisions occur in presence of a horizontal electric field, it opposes the effect of eccentricity on the outcomes of the collisions. In this study, simultaneous effects of eccentricity and horizontal electric field are examined from numerically calculated collision characteristics from previous studies and utilizing the results of a simulation experiment recently conducted by the authors. Simultaneous effects of eccentricity and electric field on coalescence efficiency and total and spectral size distribution of fragments generated after the collision have also been evaluated. The results suggest that the electric field can significantly modify drop size distribution in thunderclouds and need to be considered for the development of precipitation. Key Points Horizontal electric field opposes the variability of coalescence/sheet breakup of water drops with eccentricity in binary collisions Number of fragments close to small (large) parent drop size decreases (increases) after collisions in the higher horizontal electric field Binary collisions in horizontal electric fields can substantially modify drop size distribution in thunderclouds