scholarly journals A Survey and Perspectives on Mathematical Models for Quantitative Precipitation Estimation Using Lightning

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Carlos Manuel Minjarez-Sosa ◽  
Julio Waissman
Keyword(s):  
Mathematical Models ◽  
Convective Precipitation ◽  
Future Research ◽  
The Novel ◽  
Mathematical Methods ◽  
Simple Observation ◽  
Quantitative Precipitation Estimation ◽  
Precipitation Estimation ◽  
Cloud To Ground Lightning ◽  
Electrically Charged

Lightning is one of the most spectacular phenomena in nature. It is produced when there is a breakdown in the resistance in the electric field between the ground and an electrically charged cloud. By simple observation, we observe that precipitation, especially the most intense, is often accompanied by lightning. Given this observation, lightning has been employed to estimate convective precipitation since 1969. In early studies, mathematical models were deduced to quantify this relationship and used to estimate precipitation. Currently, the use of several techniques to estimate precipitation is gaining momentum, and lightning is one of the novel techniques to complement the traditional techniques for Quantitative Precipitation Estimation. In this paper, the authors provide a survey of the mathematical methods employed to estimate precipitation through the use of cloud-to-ground lightning. We also offer a perspective on the future research to this end.

scholarly journals Analysis of Z–R Relations Based on LDR Signatures within the Melting Layer

2010 ◽  
Vol 27 (9) ◽  
pp. 1555-1561 ◽  
Author(s):  
Stefan Kowalewski ◽  
Gerhard Peters
Keyword(s):  
Empirical Relation ◽  
Future Research ◽  
Melting Layer ◽  
Weather Radars ◽  
Quantitative Precipitation Estimation ◽  
Precipitation Estimation ◽  
Linear Depolarization Ratio ◽  
Layer Region ◽  
The Impact ◽  
R Relation

Abstract The inclusion of polarimetric measurements for the quantitative precipitation estimation (QPE) by weather radars as well as space- and airborne radars is considered most promising now-a-days. Because the melting layer region is usually marked by a distinct peak of the linear depolarization ratio (LDR), a possible correlation between LDR peak values and underlying drop sizes in terms of the Z–R relation is investigated, that is, the empirical relation between radar reflectivity factor Z and rain rate R. For this purpose, data taken during the Convective and Orographically Induced Precipitation Study (COPS) campaign in 2007 from two vertically pointing radars—a 24.15-GHz Micro Rain Radar (MRR) and a 35.5-GHz polarimetric cloud radar—were analyzed. In this analysis a correlation between parameters of the Z–R relation and LDR peak values are revealed, implying that the LDR magnitude within the melting layer must be influenced by the size of melting particles. Furthermore, an LDR classification scheme shows an improvement of R retrieval with respect to the global Z–R relation optimized for the dataset herein. However, to asses the impact for improved QPE in the above-mentioned applications, future research is necessary.

A Case Study of Radar-Derived Quantitative Precipitation Estimation

2013 ◽  
Vol 726-731 ◽  
pp. 4541-4546 ◽  
Author(s):  
Li Li Yang ◽  
Yi Yang ◽  
You Cun Qi ◽  
Xue Xing Qiu ◽  
Zhong Qiang Gong
Keyword(s):  
Doppler Radar ◽  
Heavy Precipitation ◽  
Radar Data ◽  
Convective Precipitation ◽  
Precipitation Process ◽  
Fuzzy Logic Algorithm ◽  
Rain Gauges ◽  
Quantitative Precipitation Estimation ◽  
Precipitation Estimation

The convective and stratiform precipitations have different precipitation mechanisms. Different reflectivityrainfall rate (ZR) relations should be used for them. A heavy precipitation process on 22nd July, 2009(UTC) in Anhui Province is analyzed with Hefei Doppler radar and 269 rain gauges. First, the type of precipitation is obtained by a fuzzy logic algorithm with radar data. Then the reflectivity values are converted to rainfall rates using an adaptive Z-R relation according to different rain types. It is tested with the case and showed significant improvements over the current operational Z-R QPE when compared with gauges. Results also show that the precipitation process is caused by stratiform and convective precipitation; the rain estimated from radar corresponds well with cloud classification.

scholarly journals A Comparison of Convective and Stratiform Precipitation Microphysics of the Record-Breaking Typhoon In-Fa (2021)

2022 ◽  
Vol 14 (2) ◽  
pp. 344
Author(s):  
Zuhang Wu ◽  
Yun Zhang ◽  
Lifeng Zhang ◽  
Hepeng Zheng ◽  
Xingtao Huang
Keyword(s):  
Eastern China ◽  
Convective Precipitation ◽  
Considerable Proportion ◽  
Stratiform Rain ◽  
Convective Rain ◽  
Microphysical Properties ◽  
Quantitative Precipitation Estimation ◽  
Precipitation Estimation ◽  
Typhoon Rainfall ◽  
Spaceborne Radar

In July 2021, Typhoon In-Fa attacked eastern China and broke many records for extreme precipitation over the last century. Such an unrivaled impact results from In-Fa’s slow moving speed and long residence time due to atmospheric circulations. With the supports of 66 networked surface disdrometers over eastern China and collaborative observations from the advanced GPM satellite, we are able to reveal the unique precipitation microphysical properties of the record-breaking Typhoon In-Fa (2021). After separating the typhoon precipitation into convective and stratiform types and comparing the drop size distribution (DSD) properties of Typhoon In-Fa with other typhoons from different climate regimes, it is found that typhoon precipitation shows significant internal differences as well as regional differences in terms of DSD-related parameters, such as mass-weighted mean diameter (Dm), normalized intercept parameter (Nw), radar reflectivity (Z), rain rate (R), and intercept, shape, and slope parameters (N0, µ, Λ). Comparing different rain types inside Typhoon In-Fa, convective rain (Nw ranging from 3.80 to 3.96 mm−1 m−3) shows higher raindrop concentration than stratiform rain (Nw ranging from 3.40 to 3.50 mm−1 m−3) due to more graupels melting into liquid water while falling. Large raindrops occupy most of the region below the melting layer in convective rain due to a dominant coalescence process of small raindrops (featured by larger ZKu, Dm, and smaller N0, µ, Λ), while small raindrops account for a considerable proportion in stratiform rain, reflecting a significant collisional breakup process of large raindrops (featured by smaller ZKu, Dm, and larger N0, µ, Λ). Compared with other typhoons in Hainan and Taiwan, the convective precipitation of Typhoon In-Fa shows a larger (smaller) raindrop concentration than that of Taiwan (Hainan), while smaller raindrop diameter than both Hainan and Taiwan. Moreover, the typhoon convective precipitation measured in In-Fa is more maritime-like than precipitation in Taiwan. Based on a great number of surface disdrometer observational data, the GPM precipitation products were further validated for both rain types, and a series of native quantitative precipitation estimation relations, such as Z–R and R–Dm relations were derived to improve the typhoon rainfall retrieval for both ground-based radar and spaceborne radar.

scholarly journals Two Different Integration Methods for Weather Radar-Based Quantitative Precipitation Estimation

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jing Ren ◽  
Yong Huang ◽  
Li Guan ◽  
Jie Zhou
Keyword(s):  
Radar Data ◽  
Convective Precipitation ◽  
Integration Scheme ◽  
Echo Intensity ◽  
Rain Intensity ◽  
Integration Methods ◽  
Quantitative Precipitation Estimation ◽  
Normalized Error ◽  
Precipitation Estimation ◽  
The Difference

We discuss two different integration methods for radar-based quantitative precipitation estimation (QPE): the echo intensity integral and the rain intensity integral. Theoretical analyses and simulations were used to test differences between these two methods. Cumulative rainfall calculated by the echo intensity integral is usually greater than that from rain intensity integral. The difference of calculated precipitation using these two methods is generally smaller for stable precipitation systems and larger for unstable precipitation systems. If the echo intensity signal is sinusoidal, the discrepancy between the two methods is most significant. For stratiform and convective precipitation, the normalized error ranges from −0.138 to −0.15 and from −0.11 to −0.122, respectively. If the echo intensity signal is linear, the normalized error ranges from 0 to −0.13 and from 0 to −0.11, respectively. If the echo intensity signal is exponential, the normalized error ranges from 0 to −0.35 and from 0 to −0.30, respectively. When both the integration scheme and real radar data were used to estimate cumulative precipitation for one day, their spatial distributions were similar.

scholarly journals Evaluation of the dual-polarization weather radar quantitative precipitation estimation using long-term datasets

2021 ◽  
Vol 25 (3) ◽  
pp. 1245-1258
Author(s):  
Tanel Voormansik ◽  
Roberto Cremonini ◽  
Piia Post ◽  
Dmitri Moisseev
Keyword(s):  
Weather Radar ◽  
Early Warning Systems ◽  
Rain Gauge ◽  
Convective Precipitation ◽  
Dual Polarization ◽  
Climate Conditions ◽  
Differential Phase ◽  
Quantitative Precipitation Estimation ◽  
Precipitation Estimation

Abstract. Accurate, timely, and reliable precipitation observations are mandatory for hydrological forecast and early warning systems. In the case of convective precipitation, traditional rain gauge networks often miss precipitation maxima, due to density limitations and the high spatial variability of the rainfall field. Despite several limitations like attenuation or partial beam blocking, the use of C-band weather radar has become operational in most European weather services. Traditionally, weather-radar-based quantitative precipitation estimation (QPE) is derived from horizontal reflectivity data. Nevertheless, dual-polarization weather radar can overcome several shortcomings of the conventional horizontal-reflectivity-based estimation. As weather radar archives are growing, they are becoming increasingly important for climatological purposes in addition to operational use. For the first time, the present study analyses one of the longest datasets from fully operational polarimetric C-band weather radars; these are located in Estonia and Italy, in very different climate conditions and environments. The length of the datasets used in the study is 5 years for both Estonia and Italy. The study focuses on long-term observations of summertime precipitation and their quantitative estimations by polarimetric observations. From such derived QPEs, accumulations for 1 h, 24 h, and 1-month durations are calculated and compared with reference rain gauges to quantify uncertainties and evaluate performances. Overall, the radar products showed similar results in Estonia and Italy when compared to each other. The product where radar reflectivity and specific differential phase were combined based on a threshold exhibited the best agreement with gauge values in all accumulation periods. In both countries reflectivity-based rainfall QPE underestimated and specific differential-phase-based product overestimated gauge measurements.

scholarly journals A Prototype Quantitative Precipitation Estimation Algorithm for Operational S-Band Polarimetric Radar Utilizing Specific Attenuation and Specific Differential Phase. Part II: Performance Verification and Case Study Analysis

2019 ◽  
Vol 20 (5) ◽  
pp. 999-1014 ◽  
Author(s):  
Stephen B. Cocks ◽  
Lin Tang ◽  
Pengfei Zhang ◽  
Alexander Ryzhkov ◽  
Brian Kaney ◽  
...  
Keyword(s):  
Real Time ◽  
Heavy Precipitation ◽  
Estimation Algorithm ◽  
Differential Phase ◽  
Specific Attenuation ◽  
Quantitative Precipitation Estimation ◽  
Precipitation Estimation ◽  
Bias Ratio ◽  
Using Data ◽  
Precipitation Events

Abstract The quantitative precipitation estimate (QPE) algorithm developed and described in Part I was validated using data collected from 33 Weather Surveillance Radar 1988-Doppler (WSR-88D) radars on 37 calendar days east of the Rocky Mountains. A key physical parameter to the algorithm is the parameter alpha α, defined as the ratio of specific attenuation A to specific differential phase KDP. Examination of a significant sample of tropical and continental precipitation events indicated that α was sensitive to changes in drop size distribution and exhibited lower (higher) values when there were lower (higher) concentrations of larger (smaller) rain drops. As part of the performance assessment, the prototype algorithm generated QPEs utilizing a real-time estimated and a fixed α were created and evaluated. The results clearly indicated ~26% lower errors and a 26% better bias ratio with the QPE utilizing a real-time estimated α as opposed to using a fixed value as was done in previous studies. Comparisons between the QPE utilizing a real-time estimated α and the operational dual-polarization (dual-pol) QPE used on the WSR-88D radar network showed the former exhibited ~22% lower errors, 7% less bias, and 5% higher correlation coefficient when compared to quality controlled gauge totals. The new QPE also provided much better estimates for moderate to heavy precipitation events and performed better in regions of partial beam blockage than the operational dual-pol QPE.

What every mathematician should know about modelling crime

2010 ◽  
Vol 21 (4-5) ◽  
pp. 275-281 ◽  
Author(s):  
MARCUS FELSON
Keyword(s):  
Mathematical Models ◽  
Real Data ◽  
Future Research ◽  
Data Modelling

This paper by a criminologist explains why it makes more sense to model criminal acts than to model criminals, how many preconceptions about crime can mislead modellers and offers some simple crime modelling ideas. Many opportunities for simulation now exist, and new opportunities for real-data modelling are emerging. The author suggests mathematical models of crime, including offender foraging for crime targets, as a rich area for future research.

scholarly journals The movement ecology of seagrasses

2014 ◽  
Vol 281 (1795) ◽  
pp. 20140878 ◽  
Author(s):  
Kathryn McMahon ◽  
Kor-jent van Dijk ◽  
Leonardo Ruiz-Montoya ◽  
Gary A. Kendrick ◽  
Siegfried L. Krauss ◽  
...  
Keyword(s):  
Life History ◽  
Clonal Growth ◽  
Movement Ecology ◽  
Future Research ◽  
The Novel ◽  
Long Distance ◽  
Spatial And Temporal Scales ◽  
Life History Stages ◽  
Research Areas ◽  
Time Movement

A movement ecology framework is applied to enhance our understanding of the causes, mechanisms and consequences of movement in seagrasses: marine, clonal, flowering plants. Four life-history stages of seagrasses can move: pollen, sexual propagules, vegetative fragments and the spread of individuals through clonal growth. Movement occurs on the water surface, in the water column, on or in the sediment, via animal vectors and through spreading clones. A capacity for long-distance dispersal and demographic connectivity over multiple timeframes is the novel feature of the movement ecology of seagrasses with significant evolutionary and ecological consequences. The space–time movement footprint of different life-history stages varies. For example, the distance moved by reproductive propagules and vegetative expansion via clonal growth is similar, but the timescales range exponentially, from hours to months or centuries to millennia, respectively. Consequently, environmental factors and key traits that interact to influence movement also operate on vastly different spatial and temporal scales. Six key future research areas have been identified.

scholarly journals Simple mathematical models for controlling COVID-19 transmission through social distancing and community awareness

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmed S. Elgazzar
Keyword(s):  
Mathematical Models ◽  
Virus Transmission ◽  
Small World ◽  
Vaccination Rate ◽  
The Novel ◽  
Social Distancing ◽  
Community Awareness ◽  
Sufficient Degree ◽  
And Control

Abstract The novel COVID-19 pandemic is a current, major global health threat. Up till now, there is no fully approved pharmacological treatment or a vaccine. Also, its origin is still mysterious. In this study, simple mathematical models were employed to examine the dynamics of transmission and control of COVID-19 taking into consideration social distancing and community awareness. Both situations of homogeneous and nonhomogeneous population were considered. Based on the calculations, a sufficient degree of social distancing based on its reproductive ratio is found to be effective in controlling COVID-19, even in the absence of a vaccine. With a vaccine, social distancing minimizes the sufficient vaccination rate to control the disease. Community awareness also has a great impact in eradicating the virus transmission. The model is simulated on small-world networks and the role of social distancing in controlling the infection is explained.

Introduction and Preliminary Investigation of Buoyancy Assisted Robots That Are Cheap, Safe, and Will Never Fall Down

2021 ◽  
Author(s):  
Matthew David Williams ◽  
Dennis Hong
Keyword(s):  
Genetic Algorithm ◽  
Preliminary Analysis ◽  
Preliminary Investigation ◽  
Research Work ◽  
Legged Robots ◽  
Dynamical Analysis ◽  
Future Research ◽  
The Novel ◽  
Drag Forces ◽  
New Family

Abstract We introduce and define a new family of mobile robots called BAR (Buoyancy Assisted Robots) that are cheap, safe, and will never fall down. BARs utilize buoyancy from lighter-than-air gases as a way to support the weight of the robot for locomotion. A new BAR robot named BLAIR (Buoyant Legged Actuated Inverted Robot) whose buoyancy is greater than its weight is also presented in this paper. BLAIRs can walk “upside-down” on the ceiling, providing unique advantages that no other robot platforms can. Unlike other legged robots, the mechanics of how BARs walk is fundamentally different. We also perform a preliminary investigation for BARs. This includes comparing safety, cost, and energy consumption with other commercially available robots. Additionally, the preliminary investigation also includes analyzing previous works relating to BARs. A dynamical analysis is performed on the novel robot BLAIR. This is presented to show the impacts of buoyant and drag forces on BLAIRs. Preliminary analysis with the prevalence of drag is presented with simulations using a genetic algorithm and simulations. Results show that BARs with different mechanisms prefer different styles of walking gaits such as prancing or skipping. This work lays the foundation for future research work on the gaits for BARs.

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