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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Cloud types and the tropical Earth radiation budget, revised

Nimbus-7 cloud and Earth radiation budget data are compared in a study of the effects of clouds on the tropical radiation budget. The data consist of daily averages over fixed 500 sq km target areas, and the months of July 1979 and January 1980 were chosen to show the effect of seasonal changes. Six climate regions, consisting of 14 to 24 target areas each, were picked for intensive analysis because they exemplified the range in the tropical cloud/net radiation interactions. The normal analysis was to consider net radiation as the independent variable and examine how cloud cover, cloud type, albedo and emitted radiation varied with the net radiation. Two recurring themes keep repeating on a local, regional, and zonal basis: the net radiation is strongly influenced by the average cloud type and amount present, but most net radiation values could be produced by several combinations of cloud types and amount. The regions of highest net radiation (greater than 125 W/sq m) tend to have medium to heavy cloud cover. In these cases, thin medium altitude clouds predominate. Their cloud tops are normally too warm to be classified as cirrus by the Nimbus cloud algorithm. A common feature in the tropical oceans are large regions where the total regional cloud cover varies from 20 to 90 percent, but with little regional difference in the net radiation. The monsoon and rain areas are high net radiation regions.

Dhuria, Harbans L.↗
NASA NTRS1992

Tropical Pacific Ocean response to observed winds in a layered general circulation model

The effect of forcing by monthly wind-stress variability is assessed with respect to the behavior of an isopycnic coordinate general circulation model. The isopycnic model incorporates an embedded mixed layer, and the equations are given for the interior layers, the surface mixed layer, and the atmospheric forcing. The anomalous variability of several variables is examined in a simulation using data from 1970-1985 with specific attention given to the anomalous response related to the 1982-1983 ENSO. The model fields describing sea-surface temperature (SST), sea level, and currents are found to be comparable to those reported from observational campaigns. Anomalous values of SST compare best with observed data when averaged over large spatial regions, and the amplitudes of the mean horizontal currents and anomalous zonal currents are comparable except with respect to amplitude data. The present study permits the simulation of basin-scale tropical Pacific mixed-layer depth and the mean vertical velocity field.

Miller, Arthur J.↗
NASA NTRS2010

Global Variability of Mesoscale Convective System Anvil Structure from A-Train Satellite Data

Mesoscale convective systems (MCSs) in the tropics produce extensive anvil clouds, which significantly affect the transfer of radiation. This study develops an objective method to identify MCSs and their anvils by combining data from three A-train satellite instruments: Moderate Resolution Imaging Spectroradiometer (MODIS) for cloud-top size and coldness, Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) for rain area size and intensity, and CloudSat for horizontal and vertical dimensions of anvils. The authors distinguish three types of MCSs: small and large separated MCSs and connected MCSs. The latter are MCSs sharing a contiguous rain area. Mapping of the objectively identified MCSs shows patterns of MCSs that are consistent with previous studies of tropical convection, with separated MCSs dominant over Africa and the Amazon regions and connected MCSs favored over the warm pool of the Indian and west Pacific Oceans. By separating the anvil from the raining regions of MCSs, this study leads to quantitative global maps of anvil coverage. These maps are consistent with the MCS analysis, and they lay the foundation for estimating the global radiative effects of anvil clouds. CloudSat radar data show that the modal thickness of MCS anvils is about 4-5 km. Anvils are mostly confined to within 1.5-2 times the equivalent radii of the primary rain areas of the MCSs. Over the warm pool, they may extend out to about 5 times the rain area radii. The warm ocean MCSs tend to have thicker non-raining and lightly raining anvils near the edges

Yuan, Jian↗
NASA NTRS1999

The Lightning Imaging Sensor

The Lightning Imaging Sensor (LIS) is a NASA Earth Observing System (EOS) instrument on the Tropical Rainfall Measuring Mission (TRMM) platform designed to acquire and investigate the distribution and variability of total lightning (i.e., cloud-to-ground and intracloud) between q35' in latitude. Since lightning is one of the responses of the atmosphere to thermodynamic and dynamic forcing, the LIS data is being used to detect deep convection without land-ocean bias, estimate the precipitation mass in the mixed phased region of thunderclouds, and differentiate storms with strong updrafts from those with weak vertical motion.

Christian, Hugh J.↗
NASA NTRS2003

Collaborative Research: Atlantic Ocean Tropical/Subtropical Processes from Seasonal to Decadal Time Scales: Model/Data, Model/Model Comparison and Model/Data Synthesis Through Assimilation

The effort of this first year of research has been focused on the assimilation of TOPEX/Poseidon altimetric data into a primitive equation model of the Atlantic tropical/subtropical circulation. A reduced-rank, stationary Kalman filter has been constructed to assimilate the altimetric sea surface height anomaly (SHA) into the model. The goal is to assess how the inter-hemispheric transports between the Atlantic subtropics and tropics are affected by the assimilation and how the subsurface thermocline structure , and its variability ,is dynamically constrained by the SHA. The model is a reduced-gravity primitive equation GCM of the upper Atlantic Ocean between 30 S and 30 N. The assimilation scheme is an approximation to the extended Kalman filter in which the error covariances of the state estimates are calculated only in a reduced- dimension subspace. The subspace is defined by the leading empirical orthogonal functions calculated from an unconstrained model calculation. Both an identical twin experiment using simulated SHA observations and assimilation of the real TOPEX data were performed. Results from the twin experiments demonstrate the ability of the method to constrain the ocean circulation and the subsurface temperature structure. The impact on the subsurface temperature structure of TOPEX assimilation was assessed using data from expandable bathythermographs. This showed a substantial improvement in the estimated temperature variability only within 13 degrees in latitude around the equator. The impact of TOPEX SHA assimilation on zonally integrated meridional transport across different latitudes was also estimated. Again within 13 degrees from the equator both the mean amplitude and interannual variability of the surface and subsurface transports were significantly enhanced, while the transports were insensitive to the assimilation in the subtropics.

Malannotte-Rizzoli, Paola↗
NASA NTRS2005

Research on the Natural Variability of Climate and the Impact of Anthropogenic Forcing on Climate

The paper, "Latitude-dependent vertical mixing and the tropical thermocline in a global OGCM", was revised and published in Geophysical Research Letters. It treats the new GISS mixing scheme which includes the latitudinal dependence of the interior ocean turbulence field reported by Gregg, Sanford & Winkel. When implemented in the 3x3 degree NCAR CSMl OGCM [NCOMl] the new mixing scheme produces an improved, sharper equatorial thermoclines in both the Atlantic and the Pacific while simultaneously maintaining the realistic meridional overturning and northward heat transports found already with the previous GISS scheme. Also the paper "Diagnostics of the oceanic thermohaline circulation in a coupled climate model" describing earlier work on the grany was published.

Stone, Peter H.↗
NASA NTRS2005

Estimating moisture transport over oceans using space-based observations

The moisture transport integrated over the depth of the atmosphere (0) is estimated over oceans using satellite data. The transport is the product of the precipitable water and an equivalent velocity (ue), which, by definition, is the depth-averaged wind velocity weighted by humidity. An artificial neural network is employed to construct a relation between the surface wind velocity measured by the spaceborne scatterometer and coincident ue derived using humidity and wind profiles measured by rawinsondes and produced by reanalysis of operational numerical weather prediction (NWP). On the basis of this relation, 0 fields are produced over global tropical and subtropical oceans (40_N- 40_S) at 0.25_ latitude-longitude and twice daily resolutions from August 1999 to December 2003 using surface wind vector from QuikSCAT and precipitable water from the Tropical Rain Measuring Mission. The derived ue were found to capture the major temporal variability when compared with radiosonde measurements. The average error over global oceans, when compared with NWP data, was comparable with the instrument accuracy specification of space-based scatterometers. The global distribution exhibits the known characteristics of, and reveals more detailed variability than in, previous data.

Artificial Neural Network↗
NASA NTRS2019

Exposure of the EU-28 Food Imports to Extreme Weather Disasters in Exporting Countries

EU-28 relies on a diversified foreign market, even for crops for which it has a high self-sufficiency.This study contributes to the discussion on the vulnerability of agri-food supply to the impacts of extreme weather disasters (EWD). We focus on the largest import commodities of the EU-28 and we aim to (1) map external dependencies of EU-28 agri-food sector, (2) estimate the impact of EWD on crop production in countries from which the EU-28 receives their imports, and (3) assess the exposure of EU-28 agri-food imports to such impacts. Crop and trade data areacquired through EUROSTAT and FAOSTAT, EWD records from EM-DAT, all between 1961 and 2016. A superposed epoch analysis is used to estimate the impact of EWD on the average national production, yield and harvested area of selected crops in exporting countries. The EU-28 imports between 35-100% of its consumption of soybeans, banana, tropical fruits, coffee and cocoa. Our study reveals a substantial impact of EWD, especially due to droughts andheat waves, on the production of soybeans, tropical fruits, and cocoa, with import weighted impacts of 3, 8, and 7%, respectively. Floods cause weighted impacts of 7% (soybeans) and 8% (tropical fruits). Coffee production shows gains during cold waves, but the inter-annual variability offsets these effects.

Teresa Armada Bras↗
NASA NTRS2023

A SmallSat Concept to Resolve Diurnal and Vertical Variations of Aerosols, Clouds, and Boundary Layer Height

A SmallSat mission concept is formulated here to carry out Time-varying Optical Measurements of Clouds and Aerosol Transport (TOMCAT) from space while embracing low-cost opportunities enabled by the revolution in Earth science observation technologies. TOMCAT’s “around-the-clock” measurements will provide needed insights and strong synergy with existing Earth observation satellites to 1) statistically resolve diurnal and vertical variation of cirrus cloud properties (key to Earth’s radiation budget), 2) determine the impacts of regional and seasonal planetary boundary layer (PBL) diurnal variation on surface air quality and low-level cloud distributions, and 3) characterize smoke and dust emission processes impacting their long-range transport on the subseasonal to seasonal time scales. Clouds, aerosol particles, and the PBL play critical roles in Earth’s climate system at multiple spatiotemporal scales. Yet their vertical variations as a function of local time are poorly measured from space. Active sensors for profiling the atmosphere typically utilize sun-synchronous low-Earth orbits (LEO) with rather limited temporal and spatial coverage, inhibiting the characterization of spatiotemporal variability. Pairing compact active lidar and passive multiangle remote sensing technologies from an inclined LEO platform enables measurements of the diurnal and vertical variability of aerosols, clouds, and aerosol-mixing-layer (or PBL) height in tropical-to-midlatitude regions where most of the world’s population resides. TOMCAT is conceived to bring potential societal benefits by delivering its data products in near–real time and offering on-demand hazard-monitoring capabilities to profile fire injection of smoke particles, the frontal lofting of dust particles, and the eruptive rise of volcanic plumes.

John E. Yorks↗
NASA NTRS2004

Means, Variability and Trends of Precipitation in the Global Climate as Determined by the 25-year GEWEWGPCP Data Set

The Global Precipitation Climatology Project (GPCP) 25-year precipitation data set is used as a basis to evaluate the mean state, variability and trends (or inter-decadal changes) of global and regional scales of precipitation. The uncertainties of these characteristics of the data set are evaluated by examination of other, parallel data sets and examination of shorter periods with higher quality data (e.g., TRMM). The global and regional means are assessed for uncertainty by comparing with other satellite and gauge data sets, both globally and regionally. The GPCP global mean of 2.6 mdday is divided into values of ocean and land and major latitude bands (Tropics, mid-latitudes, etc.). Seasonal variations globally and by region are shown and uncertainties estimated. The variability of precipitation year-to-year is shown to be related to ENS0 variations and volcanoes and is evaluated in relation to the overall lack of a significant global trend. The GPCP data set necessarily has a heterogeneous time series of input data sources, so part of the assessment described above is to test the initial results for potential influence by major data boundaries in the record.

Adler, R. F.↗
NASA NTRS2018

A Comparative Study of Available Water in the Major River Basins of the World

Numerous large river basins of the world have few and irregular observations of the components of the terrestrial hydrological cycle with the exception of stream gauges at a few locations and at the outlet along with sparsely distributed rain gauges. Using observations from satellite sensors and output from global land surface models, it is possible to study these under-observed river basins. With populations greater than a billion people, some of these rivers (e.g., the Ganga-Brahmaputra, the Yangtze, the Nile and the Mekong) are the economic engines of the countries they transect, yet thorough assessment of their flow dynamics and variability in regard to water resource management is still lacking. In this paper, we use soil moisture (0-2m) and surface runoff from the NASA Global Land Data Assimilation System (GLDAS), evapotranspiration, and Normalized Difference Vegetation Index (NDVI) from the Moderate Resolution Imaging Spectroradiometer (MODIS) and rainfall from the Tropical Rainfall Measuring Mission (TRMM) and total water storage anomaly from the Gravity Recovery and Climate Experiment (GRACE) to examine variability of individual water balance components. To this end, understanding the inter-annual and intra-seasonal variability and the spatial variability of the water balance components in the major river basins of the world will help to plan for improved management of water resources for the future.

GLDAS↗
NASA NTRS2013

Relationships between the Raindrop Size Distribution and Properties of the Environment and Clouds Inferred from TRMM

Variability in the raindrop sized distribution (DSD) has long been recognized as a source of uncertainty in relationships between radar reflectivity Z and rain rate R. In this study, we analyze DSD retrievals from two years of data gathered by the Tropical Rainfall Measuring Mission (TRMM) satellite and processed with a combined radar-radiometer retrieval algorithm over the global oceans equatorward of 35◦. Numerous variables describing properties of each reflectivity profile, large-scale organization, and the background environment are examined for relationships to the reflectivity-normalized median drop diameter, epsilonDSD. In general, we find that higher freezing levels and relative humidities are associated with smaller epsilonDSD. Within a given environment, the mesoscale organization of precipitation and the vertical profile of reflectivity are associated with DSD characteristics. In the tropics, the smallest epsilonDSD values are found in large but shallow convective systems, where warm rain formation processes are thought to be predominant, whereas larger sizes are found in the stratiform regions of organized deep convection. In the extratropics, the largest epsilonDSD values are found in the scattered convection that occurs when cold, dry continental air moves over the much warmer ocean after the passage of a cold front. The geographical distribution of the retrieved DSDs is consistent with many of the observed regional Z−R relationships found in the literature as well as discrepancies between the TRMM radar-only and radiometer-only precipitation products. In particular, mid-latitude and tropical regions near land tend to have larger drops for a given reflectivity, whereas the smallest drops are found in the eastern Pacific Intertropical Convergence Zone.

raindrop size distribution↗
NASA NTRS2011

Drop Size Distribution Measurements Supporting the NASA Global Precipitation Measurement Mission: Infrastructure and Preliminary Results

Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.

Petersen, Walter A.↗
NASA NTRS2000

Sensitivity of Latent Heating Profiles to Environmental Conditions: Implications for TRMM and Climate Research

The Tropical Rainfall Measuring Mission (TRMM) as a part of NASA's Earth System Enterprise is the first mission dedicated to measuring tropical rainfall through microwave and visible sensors, and includes the first spaceborne rain radar. Tropical rainfall comprises two-thirds of global rainfall. It is also the primary distributor of heat through the atmosphere's circulation. It is this circulation that defines Earth's weather and climate. Understanding rainfall and its variability is crucial to understanding and predicting global climate change. Weather and climate models need an accurate assessment of the latent heating released as tropical rainfall occurs. Currently, cloud model-based algorithms are used to derive latent heating based on rainfall structure. Ultimately, these algorithms can be applied to actual data from TRMM. This study investigates key underlying assumptions used in developing the latent heating algorithms. For example, the standard algorithm is highly dependent on a system's rainfall amount and structure. It also depends on an a priori database of model-derived latent heating profiles based on the aforementioned rainfall characteristics. Unanswered questions remain concerning the sensitivity of latent heating profiles to environmental conditions (both thermodynamic and kinematic), regionality, and seasonality. This study investigates and quantifies such sensitivities and seeks to determine the optimal latent heating profile database based on the results. Ultimately, the study seeks to produce an optimized latent heating algorithm based not only on rainfall structure but also hydrometeor profiles.

Shepherd, J. Marshall↗
NASA NTRS2000

Dry Air Entrainment into Hurricane Earl

Hurricane Earl formed in the Gulf of Mexico in September 1998. It quickly was upgraded from a tropical disturbance to tropical storm status and then to a hurricane. Earl possessed hybrid (tropical and extratropical) characteristics throughout its lifetime. The system maintained and erratic track, which led to wide variability in the operational track forecasts. It eventually made landfall on the Florida panhandle on 2 September and raced northeastward. During August and September 1998, NASA conducted the third Convection and Moisture Experiment (CAMEX-3). The experiment was focused on studying hurricanes with an emphasis toward developing a better understanding of their intensification and motion. Earl provides a unique opportunity to utilize high spatial and temporal resolution data collected from the DC-8 and high altitude ER-2 NASA platforms, which flew over Earl as it made landfall. These data can also be put into broader view provided by other instruments from the Geosychronous Operational Environmental Satellites (GOES) and the Tropical Rainfall Measuring Mission (TRMM) satellites. Hurricane Earl was affected by entrainment of dry air from the northwest. Hurricane Isis was intensifying and approaching the Mexican Pacific coast with its associated outflow potentially affecting the inflow into Earl as the storm neared Florida. In addition, a longwave synoptic trough circulation was present over the eastern U.S. Either or both of these could be responsible for the dry air into the system. This paper will focus on identifying the source of the dry by using upper-level wind and moisture fields derived from the GOES 6.7 um water vapor imagery. We will attempt to relate the large-scale observations to those from the NASA aircraft. An infrared instrument onboard the ER-2 also has a similar wavelength and may be able to confirm some of the GOES findings. In addition, a microwave radiometer with 4 channels focused on measuring precipitation and its associated ice scattering was also aboard the ER-2. The microwave observations will allow the authors to relate the entrainment to precipitation changes near the flight path of the aircraft.

Guillory, Anthony R.↗
NASA NTRS1999

Entrainment of Upper Level Dry Air Into Hurricane Earl

Hurricane Earl formed in the Gulf of Mexico in September 1998. It quickly was upgraded from a tropical disturbance to tropical storm status and then to a hurricane. Earl possessed hybrid (tropical and extratropical) characteristics throughout its lifetime. The system maintained and erratic track, which led to wide variability in the operational track forecasts. It eventually made landfall on the Florida panhandle on 2 September and raced northeastward. During August and September 1998, NASA conducted the third Convection and Moisture Experiment (CAMEX-3). The experiment was focused on studying hurricanes with an emphasis toward developing a better understanding of their intensification and motion. Earl provides a unique opportunity to utilize high spatial and temporal resolution data collected from the DC-8 and high altitude ER-2 NASA platforms, which flew over Earl as it made landfall. These data can also be put into broader view provided by other instruments from the Geosynchronous Operational Environmental Satellites (GOES) and the Tropical Rainfall Measuring Mission (TRMM) satellites. Hurricane Earl was affected by entrainment of dry air from the northwest. Hurricane Isis was intensifying and approaching the Mexican Pacific coast with its associated outflow potentially affecting the inflow into Earl as the storm neared Florida. In addition, a longwave synoptic trough circulation was present over the eastern U.S. Either or both of these could be responsible for the dry air into the system. This paper will focus on identifying the source of the dry by using upper-level wind and moisture fields derived from the GOES 6.7 um water vapor imagery. We will attempt to relate the large-scale observations to those from the NASA aircraft. An infrared instrument onboard the ER-2 also has a similar wavelength and may be able to confirm some of the GOES findings. In addition, a microwave radiometer with 4 channels focused on measuring precipitation and its associated ice scattering was also aboard the ER-2. The microwave observations will allow the authors to relate the entrainment to precipitation changes near the flight path of the aircraft.

Guillory, Anthony R.↗
NASA NTRS1990

On the interannual variation of the earth radiation balance

The interannual variability of the top of the atmosphere net radiation budget as measured from the Nimbus-7 earth radiation budget instruments was calculated for an eight-year period 1979-1986. The largest fluctuations are shown to occur in three tropical areas: the Atlantic off the west coast of Africa, the eastern Pacific near South America, and the western Pacific northeast of Indonesia. The variability in the Atlantic was 20 percent greater than in the eastern Pacific and 35 percent greater than in the Indonesian area. The maximum anomalies in these two Pacific regions occurred during the El Nino year 1982-1983, while the maximum Atlantic anomalies, south of the Gulf of Guinea, were during 1984. An independent data set of derived cloud type and amount from the Temperature Humidity Infrared Radiometer and the Total Ozone Mapping Spectrometer instruments shows interannual changes in multilevel convective cloud systems have a minimal effect of the net balance. However, changes in middle and low clouds drastically affect the balance, and are the most likely cause of the maximum radiation balance variability in the Gulf of Guinea region. This observed interannual variation of the top of the atmosphere net balance denotes the most variable 'cloud radiative forcing' situation observed to date.

Randel, David L.↗
NASA NTRS1992

Lightning Imaging Sensor (LIS) for the Earth Observing System

Not only are scientific objectives and instrument characteristics given of a calibrated optical LIS for the EOS but also for the Tropical Rainfall Measuring Mission (TRMM) which was designed to acquire and study the distribution and variability of total lightning on a global basis. The LIS can be traced to a lightning mapper sensor planned for flight on the GOES meteorological satellites. The LIS consists of a staring imager optimized to detect and locate lightning. The LIS will detect and locate lightning with storm scale resolution (i.e., 5 to 10 km) over a large region of the Earth's surface along the orbital track of the satellite, mark the time of occurrence of the lightning, and measure the radiant energy. The LIS will have a nearly uniform 90 pct. detection efficiency within the area viewed by the sensor, and will detect intracloud and cloud-to-ground discharges during day and night conditions. Also, the LIS will monitor individual storms and storm systems long enough to obtain a measure of the lightning flashing rate when they are within the field of view of the LIS. The LIS attributes include low cost, low weight and power, low data rate, and important science. The LIS will study the hydrological cycle, general circulation and sea surface temperature variations, along with examinations of the electrical coupling of thunderstorms with the ionosphere and magnetosphere, and observations and modeling of the global electric circuit.

Christian, Hugh J.↗