Engineering topics

Blakeslee, Richard J.

Publications and source records attributed to Blakeslee, Richard J..

At least 37 records · Page 2

NASA NTRS2015

Insight into the Physical and Dynamical Processes that Control Rapid Increases in Total Flash Rate

Rapid increases in total lightning (also termed "lightning jumps") have been observed for many decades. Lightning jumps have been well correlated to severe and hazardous weather occurrence. The main focus of lightning jump work has been on the development of lightning algorithms to be used in real‐time assessment of storm intensity. However, in these studies it is typically assumed that the updraft "increases" without direct measurements of the vertical motion, or specification of which updraft characteristic actually increases (e.g., average speed, maximum speed, or convective updraft volume). Therefore, an end‐to‐end physical and dynamical basis for coupling rapid increases in total flash rate to increases in updraft speed and volume must be understood in order to ultimately relate lightning occurrence to severe storm metrics. Herein, we use polarimetric, multi‐Doppler, and lightning mapping array measurements to provide physical context as to why rapid increases in total lightning are closely tied to severe and hazardous weather.

Schultz, Christopher J.↗

NASA NTRS2015

The Intra-Cloud Lightning Fraction in the Contiguous United States

Lightning is dangerous and destructive; cloud-to-ground (CG) lightning flashes can start fires, interrupt power delivery, destroy property and cause fatalities. Its rate-of-occurrence reflects storm kinematics and microphysics. For decades lightning research has been an important focus, and advances in lightning detection technology have been essential contributors to our increasing knowledge of lightning. A significant step in detection technology is the Geostationary Lightning Mapper (GLM) to be onboard the Geostationary Operational Environment Satellite R-Series (GOES-R) to be launched in early 2016. GLM will provide continuous "Total Lightning" observations [CG and intra-cloud lightning (IC)] with near-uniform spatial resolution over the Americas by measuring radiance at the cloud tops from the different types of lightning. These Total Lightning observations are expected to significantly improve our ability to nowcast severe weather. It may be important to understand the long-term regional differences in the relative occurrence of IC and CG lightning in order to understand and properly use the short-term changes in Total Lightning flash rate for evaluating individual storms.

lightning↗

NASA NTRS2014

Physical and Dynamical Linkages between Lightning Jumps and Storm Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; this conference) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014; this conference) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end-to-end physical and dynamical basis for coupling total lightning flash rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relationship to updraft strength, updraft volume, precipitation-sized ice mass, etc.; however, their relationship specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler and polarimetric radar techniques to resolve the physical and dynamical storm characteristics specifically around the time of the lightning jump. This information will help forecasters anticipate lightning jump occurrence, or even be of use to determine future characteristics of a given storm (e.g., development of a mesocyclone, downdraft, or hail signature on radar), providing additional lead time/confidence in the severe storm warning paradigm.

Schultz, Christopher J.↗

NASA NTRS2014

Physical and Dynamical Linkages Between Lightning Jumps and Storm Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; this conference) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end-to-end physical and dynamical basis for coupling total lightning flash rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relationship to updraft strength, updraft volume, precipitation-sized ice mass, etc.; however, their relationship specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler and polarimetric radar techniques to resolve the physical and dynamical storm characteristics specifically around the time of the lightning jump. This information will help forecasters anticipate lightning jump occurrence, or even be of use to determine future characteristics of a given storm (e.g., development of a mesocyclone, downdraft, or hail signature on radar), providing additional lead time/confidence in the severe storm warning paradigm.

Schultz, Christopher J.↗

NASA NTRS2014

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; AMS 10th Satellite Symposium) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014; this conference) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end to end physical and dynamical basis for relating lightning rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relation to updraft strength, updraft volume, precipitation‐sized ice mass, etc.; however, relation specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler techniques to resolve the physical and dynamical storm characteristics specifically around the time of the lightning jump. This information will help forecasters anticipate lightning jump occurrence, or even be of use to determine future characteristics of a given storm (e.g., development of a mesocyclone, downdraft, or hail signature on radar), providing additional lead time/confidence in the severe storm warning paradigm.

Shultz, Christopher J.↗

NASA NTRS2013

Total Lightning Observations within Electrified Snowfall using Polarimetric Radar LMA, and NWN Measurements

Tall structures play and important role in development of winter time lightning flashes.To what extent still needs to be assessed. Tower initiated flashes typically occur as banded structures pass near/overhead. Hi resolution RHI s from polarimetric radar show that the lightning has a tendency to propagate through layered structures within these snowstorms.

Schultz, Christopher J.↗

NASA NTRS2012

Using an A-10 Aircraft for Airborne measurements of TGFs

Plans are underway to convert an A-10 combat attack aircraft into a research aircraft for thunderstorm research. This aircraft would be configured and instrumented for flights into large, convective thunderstorms. It would have the capabilities of higher altitude performance and protection for thunderstorm conditions that exceed those of aircraft now in use for this research. One area of investigation for this aircraft would be terrestrial gamma ]ray flashes (TGFs), building on the pioneering observations made by the Airborne Detector for Energetic Lightning Emissions (ADELE) project several years ago. A new and important component of the planned investigations are the continuous, detailed correlations of TGFs with the electric fields near the aircraft, as well as detailed measurements of nearby lightning discharges. Together, the x-and gamma-radiation environments, the electric field measurements, and the lightning observations (all measured on microsecond timescales) should provide new insights into this TGF production mechanism. The A -10 aircraft is currently being modified for thunderstorm research. It is anticipated that the initial test flights for this role will begin next year.

Fishman, Gerald J.↗

NASA NTRS2012

Flash Detection Efficiencies of Long Range Lightning Detection Networks During GRIP

We flew our Lightning Instrument Package (LIP) on the NASA Global Hawk as a part of the Genesis and Rapid Intensification Processes (GRIP) field program. The GRIP program was a NASA Earth science field experiment during the months of August and September, 2010. During the program, the LIP detected lighting from 48 of the 213 of the storms overflown by the Global Hawk. The time and location of tagged LIP flashes can be used as a "ground truth" dataset for checking the detection efficiency of the various long or extended range ground-based lightning detection systems available during the GRIP program. The systems analyzed included Vaisala Long Range (LR), Vaisala GLD360, the World Wide Lightning Location Network (WWLLN), and the Earth Networks Total Lightning Network (ENTLN). The long term goal of our research is to help understand the advantages and limitations of these systems so that we can utilize them for both proxy data applications and cross sensor validation of the GOES-R Geostationary Lightning Mapper (GLM) sensor when it is launched in the 2015 timeframe.

Mach, Douglas M.↗

NASA NTRS2012

Relationships Between Long-Range Lightning Networks and TRMM/LIS Observations

Recent advances in long-range lightning detection technologies have improved our understanding of thunderstorm evolution in the data sparse oceanic regions. Although the expansion and improvement of long-range lightning datasets have increased their applicability, these applications (e.g., data assimilation, atmospheric chemistry, and aviation weather hazards) require knowledge of the network detection capabilities. The present study intercompares long-range lightning data with observations from the Lightning Imaging Sensor (LIS) aboard the Tropical Rainfall Measurement Mission (TRMM) satellite. The study examines network detection efficiency and location accuracy relative to LIS observations, describes spatial variability in these performance metrics, and documents the characteristics of LIS flashes that are detected by the long-range networks. Improved knowledge of relationships between these datasets will allow researchers, algorithm developers, and operational users to better prepare for the spatial and temporal coverage of the upcoming GOES-R Geostationary Lightning Mapper (GLM).

Rudlosky, Scott D.↗

NASA NTRS2011

Inter-Comparison of Lightning Trends from Ground-Based Networks During Severe Weather: Applications Toward GLM

The planned GOES-R Geostationary Lightning Mapper (GLM) will provide total lightning data on the location and intensity of thunderstorms over a hemispheric spatial domain. Ongoing GOES-R research activities are demonstrating the utility of total flash rate trends for enhancing forecasting skill of severe storms. To date, GLM total lightning proxy trends have been well served by ground-based VHF systems such as the Northern Alabama Lightning Mapping Array (NALMA). The NALMA (and other similar networks in Washington DC and Oklahoma) provide high detection efficiency (> 90%) and location accuracy (< 1 km) observations of total lightning within about 150 km from network center. To expand GLM proxy applications for high impact convective weather (e.g., severe, aviation hazards), it is desirable to investigate the utility of additional sources of continuous lightning that can serve as suitable GLM proxy over large spatial scales (order 100 s to 1000 km or more), including typically data denied regions such as the oceans. Potential sources of GLM proxy include ground-based long-range (regional or global) VLF/LF lightning networks such as the relatively new Vaisala Global Lightning Dataset (GLD360) and Weatherbug Total Lightning Network (WTLN). Before using these data in GLM research applications, it is necessary to compare them with LMAs and well-quantified cloud-to-ground (CG) lightning networks, such as Vaisala s National Lightning Detection Network (NLDN), for assessment of total and CG lightning location accuracy, detection efficiency and flash rate trends. Preliminary inter-comparisons from these lightning networks during selected severe weather events will be presented and their implications discussed.

Carey, Lawrence D.↗

NASA NTRS2011

Multicolor Photometric Observation of Lightning from Space: Comparison with Radio Measurements

This study evaluates the effectiveness of spectrophotometric measurements from space in revealing properties of lightning flash. The multicolor optical waveform data obtained by FORMOSAT-2/Imager of Sprites and Upper Atmospheric Lightning (ISUAL) were analyzed in relation to National Lightning Detection Network (NLDN), North Alabama Lightning Mapping Array (LMA). As of July 2011, we found six lightning events which were observed by ISUAL and North Alabama LMA. In two of these events, NLDN showed clear positive cloud-to-ground (CG) discharges with peak current of +139.9 kA and +41.6 kA and, around that time, LMA showed continuous intra-cloud (IC) leader activities at 4-6 km altitudes. ISUAL also observed consistent optical waveforms of the IC and CG components and, interestingly, it was found that the blue/red spectral ratio clearly decreased by a factor of 1.5-2.5 at the time of CG discharges. Other four lightning events in which NLDN did not detect any CG discharges were also investigated, but such a feature was not found in any of these cases. These results suggest that the optical color of CG component is more reddish than that of IC component and we explain this as a result of more effective Rayleigh scattering in blue light emissions coming from lower-altitude light source. This finding suggests that spectral measurements could be a new useful technique to characterize ICs and CGs from space. In this talk, we will also present a result from lightning statistical analysis of ISUAL spectrophotometric data and ULF magnetic data.

Adachi, Toru↗

NASA NTRS2011

Evaluation of Long-Range Lightning Detection Networks Using TRMM/LIS Observations

Recent advances in long-range lightning detection technologies have improved our understanding of thunderstorm evolution in the data sparse oceanic regions. Although the expansion and improvement of long-range lightning datasets have increased their applicability, these applications (e.g., data assimilation, atmospheric chemistry, and aviation weather hazards) require knowledge of the network detection capabilities. Toward this end, the present study evaluates data from the World Wide Lightning Location Network (WWLLN) using observations from the Lightning Imaging Sensor (LIS) aboard the Tropical Rainfall Measurement Mission (TRMM) satellite. The study documents the WWLLN detection efficiency and location accuracy relative to LIS observations, describes the spatial variability in these performance metrics, and documents the characteristics of LIS flashes that are detected by WWLLN. Improved knowledge of the WWLLN detection capabilities will allow researchers, algorithm developers, and operational users to better prepare for the spatial and temporal coverage of the upcoming GOES-R Geostationary Lightning Mapper (GLM).

Rudlosky, Scott D.↗

NASA NTRS2011

The CHUVA Lightning Mapping Campaign

The primary science objective for the CHUVA lightning mapping campaign is to combine measurements of total lightning activity, lightning channel mapping, and detailed information on the locations of cloud charge regions of thunderstorms with the planned observations of the CHUVA (Cloud processes of tHe main precipitation systems in Brazil: A contribUtion to cloud resolVing modeling and to the GPM (GlobAl Precipitation Measurement) field campaign. The lightning campaign takes place during the CHUVA intensive observation period October-December 2011 in the vicinity of S o Luiz do Paraitinga with Brazilian, US, and European government, university and industry participants. Total lightning measurements that can be provided by ground-based regional 2-D and 3-D total lightning mapping networks coincident with overpasses of the Tropical Rainfall Measuring Mission Lightning Imaging Sensor (LIS) and the SEVIRI (Spinning Enhanced Visible and Infrared Imager) on the Meteosat Second Generation satellite in geostationary earth orbit will be used to generate proxy data sets for the next generation US and European geostationary satellites. Proxy data, which play an important role in the pre-launch mission development and in user readiness preparation, are used to develop and validate algorithms so that they will be ready for operational use quickly following the planned launch of the GOES-R Geostationary Lightning Mapper (GLM) in 2015 and the Meteosat Third Generation Lightning Imager (LI) in 2017. To date there is no well-characterized total lightning data set coincident with the imagers. Therefore, to take the greatest advantage of this opportunity to collect detailed and comprehensive total lightning data sets, test and validate multi-sensor nowcasting applications for the monitoring, tracking, warning, and prediction of severe and high impact weather, and to advance our knowledge of thunderstorm physics, extensive measurements from lightning mapping networks will be collected in conjunction with electric field mills, field change sensors, high speed cameras and other lightning sensors, dual-polarimetric radars, and aircraft in-situ microphysics which will allow for excellent cross-network inter-comparisons, assessments, and physical understanding.

Goodman, Steven J.↗

NASA NTRS2011

GLM Proxy Data Generation: Methods for Stroke/Pulse Level Inter-Comparison of Ground-Based Lightning Reference Networks

In order to produce useful proxy data for the GOES-R Geostationary Lightning Mapper (GLM) in regions not covered by VLF lightning mapping systems, we intend to employ data produced by ground-based (regional or global) VLF/LF lightning detection networks. Before using these data in GLM Risk Reduction tasks, it is necessary to have a quantitative understanding of the performance of these networks, in terms of CG flash/stroke DE, cloud flash/pulse DE, location accuracy, and CLD/CG classification error. This information is being obtained through inter-comparison with LMAs and well-quantified VLF/LF lightning networks. One of our approaches is to compare "bulk" counting statistics on the spatial scale of convective cells, in order to both quantify relative performance and observe variations in cell-based temporal trends provided by each network. In addition, we are using microsecond-level stroke/pulse time correlation to facilitate detailed inter-comparisons at a more-fundamental level. The current development status of our ground-based inter-comparison and evaluation tools will be presented, and performance metrics will be discussed through a comparison of Vaisala s Global Lightning Dataset (GLD360) with the NLDN at locations within and outside the U.S.

Cummins, Kenneth L.↗

NASA NTRS2011

The Goes-R Geostationary Lightning Mapper (GLM)

The Geostationary Operational Environmental Satellite (GOES-R) is the next series to follow the existing GOES system currently operating over the Western Hemisphere. Superior spacecraft and instrument technology will support expanded detection of environmental phenomena, resulting in more timely and accurate forecasts and warnings. Advancements over current GOES capabilities include a new capability for total lightning detection (cloud and cloud-to-ground flashes) from the Geostationary Lightning Mapper (GLM), and improved storm diagnostic capability with the Advanced Baseline Imager. The GLM will map total lightning activity (in-cloud and cloud-to-ground lighting flashes) continuously day and night with near-uniform spatial resolution of 8 km with a product refresh rate of less than 20 sec over the Americas and adjacent oceanic regions. This will aid in forecasting severe storms and tornado activity, and convective weather impacts on aviation safety and efficiency. In parallel with the instrument development, a GOES-R Risk Reduction Team and Algorithm Working Group Lightning Applications Team have begun to develop the Level 2 algorithms, cal/val performance monitoring tools, and new applications. Proxy total lightning data from the NASA Lightning Imaging Sensor on the Tropical Rainfall Measuring Mission (TRMM) satellite and regional test beds are being used to develop the pre-launch algorithms and applications, and also improve our knowledge of thunderstorm initiation and evolution. In this paper we will report on new Nowcasting and storm warning applications being developed and evaluated at various NOAA Testbeds.

Goodman, Steven J.↗

NASA NTRS2011

The Development of the Puerto Rico Lightning Detection Network for Meteorological Research

A land-based Puerto Rico Lightning Detection Network (PR-LDN) dedicated to the academic research of meteorological phenomena has being developed. Five Boltek StormTracker PCI-Receivers with LTS-2 Timestamp Cards with GPS and lightning detectors were integrated to Pentium III PC-workstations running the CentOS linux operating system. The Boltek detector linux driver was compiled under CentOS, modified, and thoroughly tested. These PC-workstations with integrated lightning detectors were installed at five of the University of Puerto Rico (UPR) campuses distributed around the island of PR. The PC-workstations are left on permanently in order to monitor lightning activity at all times. Each is networked to their campus network-backbone permitting quasi-instantaneous data transfer to a central server at the UPR-Bayam n campus. Information generated by each lightning detector is managed by a C-program developed by us called the LDN-client. The LDN-client maintains an open connection to the central server operating the LDN-server program where data is sent real-time for analysis and archival. The LDN-client also manages the storing of data on the PC-workstation hard disk. The LDN-server software (also an in-house effort) analyses the data from each client and performs event triangulations. Time-of-arrival (TOA) and related hybrid algorithms, lightning-type and event discriminating routines are also implemented in the LDN-server software. We also have developed software to visually monitor lightning events in real-time from all clients and the triangulated events. We are currently monitoring and studying the spatial, temporal, and type distribution of lightning strikes associated with electrical storms and tropical cyclones in the vicinity of Puerto Rico.

Legault, Marc D.↗

NASA NTRS2011

The GOES-R GeoStationary Lightning Mapper (GLM)

The Geostationary Operational Environmental Satellite (GOES-R) is the next series to follow the existing GOES system currently operating over the Western Hemisphere. Superior spacecraft and instrument technology will support expanded detection of environmental phenomena, resulting in more timely and accurate forecasts and warnings. Advancements over current GOES capabilities include a new capability for total lightning detection (cloud and cloud-to-ground flashes) from the Geostationary Lightning Mapper (GLM), and improved capability for the Advanced Baseline Imager (ABI). The Geostationary Lighting Mapper (GLM) will map total lightning activity (in-cloud and cloud-to-ground lighting flashes) continuously day and night with near-uniform spatial resolution of 8 km with a product refresh rate of less than 20 sec over the Americas and adjacent oceanic regions. This will aid in forecasting severe storms and tornado activity, and convective weather impacts on aviation safety and efficiency among a number of potential applications. In parallel with the instrument development (a prototype and 4 flight models), a GOES-R Risk Reduction Team and Algorithm Working Group Lightning Applications Team have begun to develop the Level 2 algorithms (environmental data records), cal/val performance monitoring tools, and new applications using GLM alone, in combination with the ABI, merged with ground-based sensors, and decision aids augmented by numerical weather prediction model forecasts. Proxy total lightning data from the NASA Lightning Imaging Sensor on the Tropical Rainfall Measuring Mission (TRMM) satellite and regional test beds are being used to develop the pre-launch algorithms and applications, and also improve our knowledge of thunderstorm initiation and evolution. An international field campaign planned for 2011-2012 will produce concurrent observations from a VHF lightning mapping array, Meteosat multi-band imagery, Tropical Rainfall Measuring Mission (TRMM) Lightning Imaging Sensor (LIS) overpasses, and related ground and in-situ lightning and meteorological measurements in the vicinity of Sao Paulo. These data will provide a new comprehensive proxy data set for algorithm and application development.

Goodman, Steven J.↗

NASA NTRS2011

Summary of Almost 20 Years of Storm Overflight Electric Field, Conductivity, Flash Rates, and Electric Current Statistics

We determined total conduction currents and flash rates for around 900 high-altitude aircraft overflights of electrified clouds over 17 years. The overflights include a wide geographical sample of storms over land and ocean, with and without lightning, and with positive (i.e., upward-directed) and negative current. Peak electric field, with lightning transients removed, ranged from -1.0 kV m(sup -1) to 16. kV m(sup -1), with mean (median) of 0.9 kV m(sup -1) (0.29 kV m(sup -1)). Total conductivity at flight altitude ranged from 0.6 pS m(sup -1) to 3.6 pS m(sup -1), with mean and median of 2.2 pS m(sup -1). Peak current densities ranged from -2.0 nA m(sup -2) to 33.0 nA m(sup -2) with mean (median) of 1.9 nA m(sup -2) (0.6 nA m(sup -2)). Total upward current flow from storms in our dataset ranged from -1.3 to 9.4 A. The mean current for storms with lightning is 1.6 A over ocean and 1.0 A over land. The mean current for electrified shower clouds (i.e. electrified storms without lightning) is 0.39 A for ocean and 0.13 A for land. About 78% (43%) of the land (ocean) storms have detectable lightning. Land storms have 2.8 times the mean flash rate as ocean storms (2.2 versus 0.8 flashes min(sup -1), respectively). Approximately 7% of the overflights had negative current. The mean and median currents for positive (negative) polarity storms are 1.0 and 0.35 A (-0.30 and -0.26 A). We found no regional or latitudinal-based patterns in our storm currents, nor support for simple scaling laws between cloud top height and lightning flash rate.

Blakeslee, Richard J.↗