TEMPEST-D (Temporal Experiment for Storms and Tropical Systems Technology - Demonstration)
Launched to the International Space Station in May 2018, Temporal Experiment for Storms and Tropical Systems Technology - Demonstration (TEMPEST-D) aimed to demonstrate the ability to monitor the atmosphere with small satellites. Developed by Colorado State University (CSU), the nanosatellite measured the temporal evolution of clouds until it was deorbited in June 2021.
|Launch date||May 2018|
|End of life date||June 2021|
TEMPEST-D featured a Millimeter-wave Radiometer (MM Radiometer) developed by the National Aeronautics and Space Administration (NASA). The five-frequency radiometer performed continuous measurements between 89 and 165 GHz to directly observe the time evolution of clouds and study the conditions that control the transition from non-precipitating to precipitating clouds using high-temporal resolution observations.
By measuring the temporal evolution of clouds from the onset of precipitation, TEMPEST-D aimed to improve understanding of cloud processes and precipitation, which is essential to an understanding of climate change. Uncertainties in the representation of key processes that govern the formation and dissipation of clouds and, in turn, control the global water and energy budgets have led to substantially different predictions of future climate in current models.
The MM radiometer performed cross-track scanning, measuring the Earth scene between ±45° nadir angles, to provide a 825 km wide swath with each radiometer pixel sampled for 5 ms. The radiometer observed both cosmic background radiation at 2.7 K and ambient blackbody calibration target every 2 seconds, for a scan rate of 30 RPM (Revolutions Per Minute).
TEMPEST-D was launched from the International Space Station (ISS) and undertook a near circular orbit at an altitude of 400 km and inclination of 51.6°.
Space and Hardware Components
Built by Blue Canyon Technologies Inc. (BCT), TEMPEST-D occupied a volume of 3U Cubesat and was designed for deployment in a 6U CubeSat. The instrument was mounted on a temperature controlled bench that interfaces with the spacecraft structure using thermally isolating spacers.
The nanosatellite features a mass of 1.23 kg with a design life of five years.
TEMPEST-D (Temporal Experiment for Storms and Tropical Systems Technology - Demonstration)
TEMPEST-D was a CubeSat project of CSU (Colorado State University) Fort Collins, CO, with the objective to demonstrate the ability to monitor the atmosphere with small satellites. The team demonstrated a radiometer aboard a 6U CubeSat (30 cm x 20 cm x 10 cm) and subsequently plan to deploy a constellation of satellites to study cloud processes. The team, led by Steven Reising (PI), professor of electrical and computer engineering, developed instrumentation for CubeSats that can observe, in real-time, a storm as it grows and progresses. 1)
TEMPEST-D will reduce the risk, cost and development time of a future constellation of 6U-Class nanosatellites to directly observe the time evolution of clouds and study the conditions that control the transition from non-precipitating to precipitating clouds using high-temporal resolution observations. TEMPEST-D provided passive millimetre-wave observations using a compact radiometer (90-183 GHz) that fits well within the size, weight and power (SWaP) requirements of the 6U-Class satellite architecture. TEMPEST-D is suitable for launch through NASA’s CSLI (CubeSat Launch Initiative), for which it was selected in February 2015. 2) 3)
By measuring the temporal evolution of clouds from the moment of the onset of precipitation, a TEMPEST constellation mission would improve our understanding of cloud processes and help to constrain one of the largest sources of uncertainty in climate models. Knowledge of clouds, cloud processes and precipitation is essential to our understanding of climate change. Uncertainties in the representation of key processes that govern the formation and dissipation of clouds and, in turn, control the global water and energy budgets lead to substantially different predictions of future climate in current models.
The goal of the TEMPEST-D mission was to validate the performance of a CubeSat microwave radiometer designed to study precipitation events on a global scale. The TEMPEST constellation of 6U CubeSats is designed to sample convective precipitation events, from cloud formation, through ice formation and precipitation to cloud dissipation. 4)
The TEMPEST-D project is to increase the TRL (Technology Readiness Level) of the millimetre-wave radiometer instrument from 6 to 9. 5)
The TEMPEST-D mission success criteria for a 90-day mission after on-orbit commissioning are as follows:
1) To demonstrate the feasibility of differential drag measurements required to achieve the desired time separation of 6U-Class satellites deployed together in the same orbital plane.
2) To demonstrate cross-calibration with 2 K precision and 4 K accuracy between TEMPEST-D millimetre-wave radiometers and the NASA/JAXA GPM/GMI or the Microwave Humidity Sounder currently in orbit on two NOAA satellites and two ESA/EUMETSAT satellites.
TEMPEST-D 1 is a partnership among CSU, JPL and spacecraft provider BCT (Blue Canyon Technologies Inc.) of Boulder, CO. BCT has recently been awarded a contract to build, test, and operate a new 6U-class satellite. BCT delivered the 6U spacecraft, ready for instrumentation, for the TEMPEST-D project, led by CSU (Colorado State University), Fort Collins, CO. TEMPEST-D is supported by NASA’s Science Mission Directorate, Earth Science Division and is managed by NASA’s ESTO (Earth Science Technology Office). NASA/JPL(Jet Propulsion Laboratory) provided the five-channel millimetre-wave radiometer instrument. 6)
BCT integrated the TEMPEST-D payload with the 6U spacecraft bus and performed environmental testing of the complete spacecraft. The spacecraft operated from BCT’s Mission Operations Center in Boulder, Colorado. BCT’s 6U spacecraft is a high-performance CubeSat that includes an ultra-precise attitude control system that allows for accurate knowledge and fine-pointing of the satellite payload.
ADCS (Attitude Determination and Control Subsystem): BCT uses the XACT-50 (fleXible ADCS Cubesat Technology-50) for 6U CubeSats. The XACT-50 improves the capability of XACT by incorporating larger reaction wheels and torque rods.
Spacecraft Pointing Accuracy
±0.003º (1σ) for 2 axes; ±0.007º (1σ) for 3rd axis
5 years (LEO)
1.23 kg, 10 x 10 x 7.54 cm (0.75U)
Electronics Input Voltage
RS-422, RS-485 & SPI
≥10º/s (14 kg, 6U CubeSat)
The complete TEMPEST-D flight system will be delivered to NanoRacks for launch integration in the autumn of 2017, spacecraft mass: 6 kg).
The TEMPEST-D CubeSat was launched to the ISS on 21 May 2018 (08:44 UTC) on ELaNa 23 of NASA. The launch vehicle was the Antares 230 with Cygnus CRS OA-9E, also known as Orbital Sciences CRS Flight 9E, the tenth planned flight of the Orbital ATK unmanned resupply spacecraft Cygnus. The launch site was MARS (Mid-Atlantic Regional Spaceport), Wallops Island, VA, USA. 8) 9)
Orbit: Near circular orbit, altitude of ~400 km, inclination = 51.6º.
The ELaNa 23 (Education Launch of Nanosatellites 23) initiative payloads of NASA on OA-9 are: 10)
• HaloSat (Soft X-ray Surveyor), a 6U CubeSat of the University of Iowa, Iowa City, Iowa.
• TEMPEST-D 1 (Temporal Experiment for Storms and Tropical Systems Technology - Demonstration 1) , a 6U CubeSat of CSU (Colorado State University), Fort Collins, CO.
• EQUiSat – a 1U CubeSat of Brown University, Providence, R.I.
• MemSat, a 1U CubeSat of Rowan University, Glassboro, N.J.
• CaNOP (Canopy Near-IR Observing Project), a 3U CubeSat of Carthage College, Kenosha, WIS, USA.
• RadSat (Radiation-tolerant SmallSat Computer System), a 3U CubeSat of MSU (Montana State University), Bozeman, Montana.
• RaInCube (Radar In a CubeSat), a 6U CubeSat of NASA/JPL (Jet Propulsion Laboratory), Pasadena, CA.
• SORTIE (Scintillation Observations and Response of the Ionosphere to Electrodynamics), a 6U CubeSat of ASTRA (Atmospheric & Space Technology Research Associates), Boulder, CO.
• CubeRTT (CubeSat Radiometer Radio Frequency Interference Technology) Validation Mission, a 6U CubeSat of OSU (Ohio State University), Columbus, Ohio.
• AeroCube-12A and -12B, a pair of 3U CubeSats of the Aerospace Corporation, El Segundo, CA, to demonstrate a technological capability of new star-tracker imaging, a variety of nanotechnology payloads, advanced solar cells, and an electric propulsion system on one of the two satellites (AC12-B).
• EnduroSat One, a 1U CubeSat of Bulgaria, developed by the Space Challenges program and EnduroSat collaborating with the Bulgarian Federation of Radio Amateurs (BFRA) for the first Bulgarian Amateur Radio CubeSat mission.
• Lemur-2, four 3U CubeSats (4.6 kg each) of Spire Global Inc., San Francisco, CA.
• June 22, 2021: TEMPEST-D, a small satellite that helped pioneer novel remote-sensing technologies, successfully ended its nearly three-year mission.
- Steven Reissing, the Principal Investigator of the mission at Colorado State University, said “We couldn’t be happier. Tempest-D exceeded nearly every measure of success wwe set when designing this mission. It continued to collect valuable scientific data until its last days in orbit and greatly exceeded our expectations.”
• March 22, 2021: The TEMPEST-D mission is still operational according to Steven C. Reising of Colorado State University.
• September 4, 2019: A new view of Hurricane Dorian shows the layers of the storm, as seen by an experimental NASA weather satellite that's the size of a cereal box. TEMPEST-D reveals rain bands in four layers of the storm as Hurricane Dorian approaches Florida on Sept. 3, 2019. The multiple vertical layers show where the strongest convective "storms" within the hurricane are pushing high into the atmosphere, with pink, red and yellow corresponding to the areas of heaviest rainfall. 11)
- Known as a CubeSat, TEMPEST-D (Temporal Experiment for Storms and Tropical Systems Demonstration) uses a miniaturized version of a microwave radiometer - a radio wave instrument used to measure rain and moisture within the clouds. If TEMPEST-D can successfully track storms like Dorian, the technology demonstration could lead to a train of small satellites that work together to track storms around the world. CubeSats are much less expensive to produce than traditional satellites; in multiples, they could improve our global storm coverage and forecasting data.
- TEMPEST-D is led by Colorado State University in Fort Collins and managed by JPL in partnership with Blue Canyon Technologies in Boulder, Colorado, and Wallops Flight Facility in Virginia. The mission is sponsored by NASA's Earth Ventures program and managed by the Earth Science Technology Office at NASA Headquarters in Washington. The radiometer instrument was built by JPL and employs high-frequency microwave amplifier technology developed by Northrop Grumman.
• September 3, 2019: The Advanced Rapid Imaging and Analysis (ARIA) team at NASA's Jet Propulsion Laboratory in Pasadena, California, created this flood map (Figure 5) depicting areas of the Bahamas that are likely flooded (shown by light blue pixels) as a result of Hurricane Dorian. 12)
• August 29, 2019: Several instruments and spacecraft from NASA's Jet Propulsion Laboratory in Pasadena, California, have eyes on Hurricane Dorian, capturing different types of data from the storm. 13)
- The weather-observing satellite TEMPEST-D captured imagery of Hurricane Dorian off the coast of Puerto Rico in the early morning hours (local time) of Aug. 28, 2019. At a vantage point of 400 km above the storm, the CubeSat used its miniaturized radio-wave-based instrument to see through the clouds, revealing areas with heavy rain and moisture being pulled into the storm.
- TEMPEST-D is a technology-demonstration mission led by Colorado State University and managed by JPL in partnership with Blue Canyon Technologies and Wallops Flight Facility in Virginia. The mission is sponsored by NASA's Earth Ventures program and managed by the Earth Science Technology Office. The radiometer instrument was built by JPL and employs high-frequency microwave amplifier technology developed by Northrop Grumman.
- The AIRS instrument aboard the Aqua satellite senses emitted infrared and microwave radiation from Earth. The information is used to map such atmospheric phenomena as temperature, humidity, and cloud amounts and heights. In Figure 8, the large purple area indicates very cold clouds carried high into the atmosphere by deep thunderstorms. These clouds are also associated with heavy rainfall. Blue and green indicate warmer areas with shallower rain clouds, while the orange and red areas represent mostly cloud-free air.
- AIRS, in conjunction with the Advanced Microwave Sounding Unit (AMSU), provides a 3D look at Earth's weather and climate. Launched into Earth orbit in 2002, the AIRS and AMSU instruments are managed by JPL under contract to NASA.
- NASA's CloudSat satellite provided a 3D animation after passing over Dorian, still a tropical storm at the time, near Puerto Rico. CloudSat uses an advanced cloud-profiling radar that "slices" through clouds, enabling us to see their height, their different layers and the areas where the heavier bands of rain are found within the storm system.
• July 30, 2019: TEMPEST-D (Temporal Experiment for Storms and Tropical Systems—Demonstration), a 6U CubeSat, is still providing precise images of global weather—exceeding the expectations of even its engineers. 14)
- TEMPEST-D is about the size of an Oxford dictionary and was deployed from the International Space Station last July carrying a miniaturized microwave radiometer. Measuring at five frequencies, TEMPEST-D can see through clouds to reveal the interior of storms where raindrops and ice crystals form.
- The project is led by principal investigator Steven Reising, professor of electrical and computer engineering, whose team developed the satellite supported by an $8.2 million grant from NASA's Earth Science Technology Office.
- "TEMPEST-D is the first weather satellite on a CubeSat to image the interior of storms on a global basis," said Reising, who heads the project in collaboration with co-investigator V. "Chandra" Chandrasekar, University Distinguished Professor in electrical and computer engineering. "We have shown that the quality of our data is at least as high as that from large operational radiometers in orbit."
- Chandra is a veteran of multiple large weather satellite missions. "This mission has been wildly successful—beyond our dreams," he said. "It was just supposed to demonstrate the technology of the radiometer and orbital maneuvers. Then it started taking data, and people were saying, "Wow!".... It's looking at hurricanes and producing very high-quality global data—very much like a big mission."
Demonstrating future technologies
- TEMPEST-D is intended as a proof-of-concept for next-generation Earth-observing technologies that are orders of magnitude smaller and lower cost than traditional satellites operated by federal agencies.
- The ultimate goal is to send not just one but a constellation of six to eight CubeSats like TEMPEST-D into space. The satellites would fly in a train, watching storms develop every few minutes. Such fine temporal resolution would offer unprecedented views inside storms—such as those that threaten the Atlantic Basin and the eastern U.S. every year—to monitor how they develop every few minutes over a 30-minute period. Such a mission could also improve scientists' understanding of cloud processes and the influence of surrounding water vapour.
- Christian Kummerow, director of CSU's Cooperative Institute for Research in the Atmosphere, is also a co-investigator on TEMPEST-D. He worked with Reising to develop new techniques to retrieve cloud and precipitation information of interest to atmospheric scientists.
- NASA mission: TEMPEST-D is led by CSU and managed by NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California, in partnership with Boulder-based Blue Canyon Technologies. The ground station is operated by NASA Wallops Flight Facility in Virginia. The mission is sponsored by NASA's Earth Ventures program and managed by the Earth Science Technology Office. The radiometer instrument was built by JPL and employs extremely high-frequency microwave amplifier technology developed by the Northrop Grumman Corporation.
• September 20, 2018: TEMPEST-D took its first images of Hurricane Florence on 11 September, just hours after its instrument was turned on. The 6U CubeSat carries a state-of-the-art miniaturized microwave radiometer, an instrument that sees through the thick clouds to reveal the hidden interior of storms. 15)
- The image taken by TEMPEST-D captures Florence over the Atlantic Ocean, revealing the eye of the storm surrounded by towering, intense rain bands. The green areas highlight the extent of the rain being produced by the storm, with the most intense rain shown in yellow and red. The TEMPEST-D data is contrasted with a visible image of Florence that shows the familiar cyclone-shaped clouds of the storm but doesn't reveal what's inside.
- TEMPEST-D's mission is to test new, low-cost technology that could be used in the future to gather more weather data and help researchers better understand storms. The level of detail in the small-satellite image is similar to what existing weather satellites produce.
- "We were challenged to fit this instrument into such a small satellite without compromising data quality and were delighted to see it work right out of the box," said Sharmila Padmanabhan, who led the instrument development at NASA's Jet Propulsion Laboratory in Pasadena, California.
- Shrinking weather satellites could one day help scientists provide more frequent updates on developing storms. "TEMPEST-D paves the way for future missions where we can afford to fly many of these miniaturized weather satellites in constellations. Such a deployment would enable us to watch storms as they grow," said Steven Reising, the principal investigator for TEMPEST-D at Colorado State University.
- TEMPEST-D is a technology-demonstration mission led by Colorado State University and managed by NASA/JPL, in partnership with Blue Canyon Technologies and Wallops Flight Facility, Virginia. The mission is sponsored by NASA's Earth Ventures program and managed by the Earth Science Technology Office. The radiometer instrument was built by JPL and employs high-frequency microwave amplifier technology developed by Northrop Grumman Corporation.
• July 13, 2018: NanoRacks successfully completed the 14th CubeSat Deployment mission from the Company’s commercially developed platform on the International Space Station. Having released nine CubeSats into low-Earth orbit, this mission marks NanoRacks’ 185th CubeSat released from the Space Station and 217th small satellite deployed by NanoRacks overall. 16)
- The CubeSats deployed were launched to the Space Station on the ninth contracted resupply mission for Orbital ATK (now Northrop Grumman Innovation Systems) from Wallops Island, Virginia in May 2018.
- NanoRacks offered an affordable launch opportunity, payload manifesting, full safety reviews with NASA, and managed on-orbit operations in order to provide an end-to-end solution that met all customer needs.
- The satellites deployed were: CubeRRT, EQUiSat, HaloSat, MemSat, RadSat-g, RainCube, TEMPEST-D, EnduroSat One, Radix (the last two entries are commercial CubeSats).
- The CubeSats mounted externally to the Cygnus spacecraft from the May 2018 launch are scheduled to be deployed on Sunday, July 15th, pending nominal operations.
MM Radiometer (Millimeter-wave Radiometer)
The MM radiometer was built by NASA/JPL and performed continuous measurements at five frequencies, 89, 165, 176, 180 and 182 GHz. The five-frequency radiometer is based on the direct-detection architecture, in which the RF input to the feed horn is amplified, bandlimited, and detected using Schottky diode detectors. 17) The use of direct-detection receivers based on InP HEMT MMIC LNA front ends substantially reduces the mass, volume and power requirements of these radiometers. 18) Input signals are bandlimited using waveguide-based bandpass filters to meet the radiometer bandwidth requirements of 4±1 GHz at centre frequencies of 89 and 165 GHz, as well as 2±0.5 GHz at 176, 180 and 182 GHz centre frequencies (Ref. 5).
The TEMPEST-D instrument design is based on a 165 GHz to 182 GHz radiometer design inherited from RACE and an 89 GHz receiver developed under the ESTO ACT-08 and IIP-10 programs at CSU (Colorado State University) and JPL. All receivers were jointly developed by JPL and the Northrop Grumman Corporation. The TEMPEST reflector scanning and calibration methodology have been adapted from the ATMS (Advanced Technology Microwave Sounder). This methodology has been validated on the Global Hawk unmanned aerial vehicle (UAV) using the HAMSR (High Altitude MMIC Sounding Radiometer) instrument. 19)
The TEMPEST-D instrument occupied a volume of 3U (normally defined as 34 cm x 10 cm x 10 cm) and is designed for deployment in a 6U CubeSat. The instrument was mounted on a temperature-controlled bench that interfaces with the spacecraft structure using thermally isolating spacers. Figure 13 shows the mechanical layout of the instrument components on the instrument bench.
The TEMPEST-D radiometer performed cross-track scanning, measuring the Earth scene between ±45° nadir angles, providing an 825 km wide swath from a 400 km nominal orbit altitude. Each radiometer pixel was sampled for 5 ms. The radiometer performed end-to-end calibration during each rotation of the scanning reflector. The radiometer observes both cosmic background radiation at 2.7 K and an ambient blackbody calibration target (at approximately 300 K) every 2 seconds, for a scan rate of 30 RPM. A schematic representation of the TEMPEST-D observing profile over a 360° reflector scan and the resulting output data time series are shown in Figure 14.
The TEMPEST-D flight model radiometer instruments (two copies, FM1 and FM2) have been designed, fabricated and integrated at JPL. Figure 15 shows the TEMPEST-D instrument, including the scanning reflector (top left), dual-frequency feed horn, originally developed under a NASA ESTO Advanced Component Technology (ACT-08) program (centre left), and the four radiometer channels from 165 to 182 GHz, including front-ends, power divider, bandpass filter bank and detectors. Measurements of the receiver bandpass and linearity of each of the five frequency channels have been performed at JPL.
Both TEMPEST-D flight model instruments have been integrated with the XB1 6U spacecraft avionics and bus at BCT, as shown in Figure 16. The TEMPEST-D flight model radiometer and spacecraft bus have passed electromagnetic self-compatibility tests in an anechoic chamber designed for EMI (Electromagnetic Interference) testing.
The TEMPEST-D flight model radiometer instrument has passed vibration testing to GEVS (General Environmental Verification Standard ) levels at JPL. Figure 17 shows the TEMPEST-D flight model instrument in the configuration for vibration testing. The receiver characteristics have been measured and compared for both pre- and post-vibration testing. The next steps for the flight model radiometer instrument are TVAC (Thermal Vacuum) testing and antenna radiation pattern testing at JPL.
1) Anne Ju Manning, ”Small satellites to pave way for future space-borne weather observations,” CSU, Dec. 2015, URL: http://source.colostate.edu/
2) Steven C. Reising, Todd C. Gaier, Christian D. Kummerow, Sharmila Padmanabhan, Boon H. Lim, Shannon T. Brown, Cate Heneghan, Chandrasekar V. Chandra, Jon Olson, Wesley Berg, ”Temporal Experiment for Storms and Tropical Systems Technology Demonstration (TEMPEST-D): Risk Reduction for 6U-Class Nanosatellite Constellations,” EGU ( European Geosciences Union) General Assembly 2016, Vienna, Austria, April 17-22, 2016, Vol. 18, paper: EGU2016-11622, URL of abstract: http://meetingorganizer.copernicus.org/EGU2016/EGU2016-11622.pdf
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5) Steven C. Reising, Christian D. Kummerow, V. Chandrasekar, Wesley Berg, Jonathan P. Olson, Todd C. Gaier, Sharmila Padmanabhan, Boon H. Lim, Cate Heneghan, Shannon T. Brown, John Carvo, Matthew Pallas, ”Temporal Experiment for Storms and Tropical Systems Technology Demonstration (TEMPEST-D) Mission: Enabling Time-Resolved Cloud and Precipitation Observations from 6U-Class Satellite Constellations,” Proceedings of the 31st Annual AIAA/USU Conference on Small Satellites, Logan UT, USA, Aug. 5-10, 2017, paper: SSC17-III-01, URL: http://digitalcommons.usu.edu
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12) ”Flooding from Dorian Seen from Space,” NASA/JPL, 3 September 2019, URL: https://www.jpl.nasa.gov/spaceimages/details.php?id=PIA23360
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16) ”NanoRacks Completes 14th CubeSat Deployment Mission from International Space Station,” NanoRacks, 13 July 2018, URL: http://nanoracks.com/14th-cubesat-deployment-from-iss/
17) D. E. Dawson, A. L. Lee, D. P. Albers, O. Montes, T. C. Gaier, D. J. Hoppe, B. Khayatian, ”InP HEMT low-noise amplifier-based millimeter-wave radiometers from 90 to 180 GHz with internal calibration for remote sensing of atmospheric wet-path delay,” IEEE MTT-S International Microwave Symposium Digest, Montreal, Quebec, Canada, 17-22 June 2012,
18) P. Kangaslahti, E. Schlecht, J. Jiang, W. R. Deal, A. Zamora, K. Leong, S. C. Reising, X. Bosch, M. Ogut, “CubeSat Scale Receivers for Measurement of Ice in Clouds,” Proceedings of the 14th Specialist Meeting on Microwave Radiometry and Remote Sensing of the Environment (MicroRad 2016), Espoo, Finland, 11-14 April 2016, pp. 42-47, DOI: 10.1109/MICRORAD.2016.7530501
19) Sharmila Padmanabhan, Todd C. Gaier, Steven C. Reising, Boon H. Lim, Robert Stachnik, Robert Jarnot, Wesley Berg, Christian D. Kummerow, V. Chandrasekar, ”Radiometer payload for the temporal experiment for storms and tropical systems technology demonstration mission,” Proceedings of IGARSS 2017 (IEEE International Geoscience and Remote Sensing Symposium), Fort Worth, Texas, USA, July 23–28, 2017
The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: ”Observation of the Earth and Its Environment: Survey of Missions and Sensors” (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates (email@example.com).