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--- instruments:hatpro:hatpro [2016/05/24 15:57] – stefan
+++ instruments:hatpro:hatpro [2018/07/23 12:51] – andreas
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 **HATPRO** (//Humidity and Temperature Profiler//) is a microwave radiometer [[http://en.wikipedia.org/wiki/Remote_sensing|remote sensing]] instrument detecting thermal emission from the [[http://en.wikipedia.org/wiki/Atmosphere| atmosphere]]. We currently operate three HATPRO devices:
+  * [[instruments:foghat:foghat|FOGHAT]] in [[sites:iquique|Iquique]] in the Atacama desert
   * [[instruments:tophat:tophat|TOPHAT]] at [[sites:joyce|JOYCE]] near (Julich)
-  * [[instruments:sunhat:sunhat|SUNHAT]] on [[sites:barbados|Barbados]]
   * [[instruments:snohat:snohat|SNOHAT]] at the [[sites:ufs|Schneefernerhaus observatory]] (Mt. Zugspitze)
+  * [[instruments:sunhat:sunhat|SUNHAT]] on [[sites:barbados|Barbados]]
 ===== Introduction =====
+Microwave radiometers are very sensitive receivers designed to measure thermal electromagnetic radiation emitted by material media like the atmosphere. They are usually equipped with multiple receiving channels in order to derive the characteristic emission spectrum of the atmosphere or extraterrestrial objects. Microwave radiometers are utilized in a variety of environmental and engineering applications, including weather forecasting, climate monitoring, [[https://en.wikipedia.org/wiki/Radio_astronomy|radio astronomy]] and radio propagation studies.
-The atmosphere in the [[https://en.wikipedia.org/wiki/Microwave|microwave spectral range]] (MW) between 1 and 300 GHz is semi-transparent. This means its components like dry gases, water vapor, or [[https://en.wikipedia.org/wiki/Precipitation#Hydrometeor_definition|hydrometeors]] interact with MW radiation but overall even the cloudy atmosphere is not completely opaque in this frequency range. Microwave radiometers are very sensitive receivers usually equipped with multiple receiving channels in order to derive the characteristic emission spectrum of the atmosphere. Microwave radiometers are utilized in a variety of environmental and engineering applications, including weather forecasting, climate monitoring, [[https://en.wikipedia.org/wiki/Radio_astronomy|radio astronomy]], as well as monitoring of land and ocean surface properties.
+Using the [[https://en.wikipedia.org/wiki/Microwave|microwave spectral range]] (MW) between 1 and 300 GHz provides complementary information to the visible and infrared spectral range. Most importantly, the atmosphere and also vegetation is semi-transparent in the MW [1]. This means its components like dry gases, water vapor, or [[https://en.wikipedia.org/wiki/Precipitation#Hydrometeor_definition|hydrometeors]] interact with MW radiation but overall even the cloudy atmosphere is not completely opaque in this frequency range.
 For weather and climate monitoring, microwave radiometers are operated from space [1] [2] as well as from the ground [3]. As [[https://en.wikipedia.org/wiki/Remote_sensing|remote sensing]] instruments, they are designed to operate continuously and autonomously often in combination with other atmospheric remote sensors like for example [[https://en.wikipedia.org/wiki/Millimeter_cloud_radar|cloud radars]] and [[https://en.wikipedia.org/wiki/Atmospheric_lidar|lidars]]. They allow to derive important meteorological quantities such as vertical temperature and humidity profile, columnar water vapor amount, or columnar liquid water path with a high temporal resolution in the order of seconds to minutes under nearly all weather conditions.
@@ Line 12: / Line 14: @@
 {{:instruments:sunhat:p1040071.jpg?400|}} \\
-[[http://www.radiometer-physics.de/rpg/html/Home.html|RPG]] HATPRO-SUNHAT at the [[http://barbados.zmaw.de|Barbados Clouds Observatory]].
+Fig. 1: [[http://www.radiometer-physics.de/rpg/html/Home.html|Humitity and Temperature Profiler]] (HATPRO-SUNHAT) at the [[http://barbados.zmaw.de|Barbados Clouds Observatory]].
 ===== History of microwave radiometer measurements =====
+First developments of microwave radiometer were dedicated to the measurement of radiation of extraterrestrial origin in the 1930s and 1940s [1]. The first operational microwave radiometer was designed by [[https://en.wikipedia.org/wiki/Robert_H._Dicke|Robert H. Dicke]] in the Radiation Laboratory of Massachusetts Institute of Technology to better determine the temperature of the microwave background radiation. This first radiometer worked at a wavelength 1.25 cm and was operated at the Massachusetts Institute of Technology. Dicke also first discovered weak atmospheric absorption in the MW using three different radiometers (at wavelengths of 1.0, 1.25 and 1.5 cm).
-The first operational microwave radiometer was designed by [[https://en.wikipedia.org/wiki/Robert_H._Dicke|Robert H. Dicke]] in the Radiation Laboratory of Massachusetts Institute of Technology to better determine the temperature of the microwave background radiation. This first radiometer worked at a wavelength 1.25 cm and was operated at the Massachusetts Institute of Technology. Dicke also first discovered weak atmospheric absorption in the MW using three different radiometers (at wavelengths of 1.0, 1.25 and 1.5 cm).
+Soon after satellites were first used for observing the atmosphere, MW radiometers became part of their instrumentation. In 1962 the [[https://en.wikipedia.org/wiki/Mariner_2|Mariner-2 mission]] was launched by NASA in order to investigate the surface of Venus including a MW radiometer for water vapor and temperature observations. In following years a wide variety of MW radiometers were tested on satellites. The launch of the [[https://en.wikipedia.org/wiki/Scanning_multichannel_microwave_radiometer|Scanning Multichannel Microwave Radiometer]] (SMMR) in 1978 became an important milestone in the history of radiometry. It was the first time a conically scanning radiometer was used in space; it was brought in space on board of the NASA [[https://en.wikipedia.org/wiki/Nimbus_program|Nimbus satellite]] [4]. The launch of this mission gave the opportunity to image the Earth at a constant angle of incidence that is important as surface emissivity is angular dependent. In the beginning of 1980, new multi-frequency, dual-polarization radiometric instruments were developed. Two spacecraft were launched which carried instruments of this type: Nimbus-7 and [[https://en.wikipedia.org/wiki/Seasat|Seasat]]. The Nimbus-7 mission results allowed to globally monitor the state of ocean surface as well as surface covered by snow and glaciers. Today, microwave instruments like the Advanced Microwave Sounding Unit [[https://en.wikipedia.org/wiki/Advanced_Microwave_Sounding_Unit|AMSU]], Special Sensor Microwave Imager / Sounder [[https://en.wikipedia.org/wiki/SSMIS|SSMIS]] are widely used not only onboard different satellites.
-Soon after satellites were first used for observing the atmosphere, MW radiometers became part of their instrumentation. In 1962 the [[https://en.wikipedia.org/wiki/Mariner_2|Mariner-2 mission]] was launched by NASA in order to investigate the surface of Venus including a MW radiometer for water vapor and temperature observations. In following years a wide variety of MW radiometers were tested on satellites. The launch of the [[https://en.wikipedia.org/wiki/Scanning_multichannel_microwave_radiometer|Scanning Multichannel Microwave Radiometer]] (SMMR) in 1978 became an important milestone in the history of radiometry. It was the first time a conically scanning radiometer was used in space; it was brought in space on board of the NASA [[https://en.wikipedia.org/wiki/Nimbus_program|Nimbus satellite]] [4]. The launch of this mission gave a unique opportunity to image the Earth at a constant angle of incidence. In the beginning of 1980, new multi-frequency, dual-polarization radiometric instruments were developed. Two spacecraft were launched which carried instruments of this type: Nimbus-7 and [[https://en.wikipedia.org/wiki/Seasat|Seasat]]. The Nimbus-7 mission results allowed to globally monitor the state of ocean surface as well as surface covered by snow and glaciers. Today, radiometers are widely used not only onboard different satellites but also as ground-based instruments integrated in worldwide observational networks.
+Ground-Based radiometer for the determination of temperature profiles were first explores in the 1960s [4] and have since themn strongly improved in terms of reduced noises and the ability to run unattended in 24/7 mode within worldwide observational networks [5]. Review articles [[http://www.ursi.org/files/RSBissues/RSB_310_2004_09.pdf|[6] ]], [7] and a detailed online [[http://cfa.aquila.infn.it/wiki.eg-climet.org/index.php5/Microwave_radiometer|handbook]] [8] are available.
+Here we could keep the graphic from the original article
+https://en.wikipedia.org/wiki/Microwave_radiometer#/media/File:Radiometer_227629main_ostm-AMR-RSA.jpg
+Fig. 2
 =====  Principle of operation =====
-Solid matter (e.g. the earth's surface, ocean, sea ice, snow, vegetation) but also gases emit and absorb MW radiation. The atmospheric components emit and absorb MW radiation in different ways: Atmospheric gases provide specific absorption features (Fig. 1) which allow to derive information about their vertical profile. Examples for such absorption features are the oxygen absorption complex (magnetic dipole transitions) around 60 GHz which is used to derive temperature profiles or the water vapor absorption line around 22.235 GHz (dipole rotational transition) which is used to observe the vertical profile of humidity. Other significant absorption lines are found at 118.75 GHz (oxygen absorption) and at 183.31 GHz (water vapor, used for water vapor profiling under dry conditions). Weak absorption features due to ozone are used for stratospheric [[http://link.springer.com/article/10.1023%2FA%3A1010406601571|ozone density and temperature]] profiling [7].
+Solids, liquids (e.g. the earth's surface, ocean, sea ice, snow, vegetation) but also gases emit and absorb MW radiation. Traditionally, the amount of radiation a microwave radiometer receives is expressed as the equivalent blackbody temperature also called [[https://en.wikipedia.org/wiki/Brightness_temperature|brightness temperature]] (TB). In the microwave range several atmospheric gases inhibit [[https://en.wikipedia.org/wiki/Rotational_spectroscopy|rotational lines]]. They provide specific absorption features (Fig. 3) which allow to derive information about their abundance and vertical structure. Examples for such absorption features are the oxygen absorption complex (caused by magnetic dipole transitions) around 60 GHz which is used to derive temperature profiles or the water vapor absorption line around 22.235 GHz (dipole rotational transition) which is used to observe the vertical profile of humidity. Other significant absorption lines are found at 118.75 GHz (oxygen absorption) and at 183.31 GHz (water vapor absorption, used for water vapor profiling under dry conditions or from satellite). Weak absorption features due to ozone are also used for stratospheric [[http://link.springer.com/article/10.1023%2FA%3A1010406601571|ozone density and temperature]] profiling.
+Besides the distinct absorption features of molecular transistion lines, there are also non-resonant contributions by hydrometeors (liquid drops and frozen particles). Liquid water emission increases with frequency, hence, measuring at two frequencies, typically one close to the water absorption line (22.235 GHz) and one in the nearby window region (typically 31 GHz) dominated by liquid absorption provides information on both the columnar amount of water vapor and the columnar amount of liquid water separately (two-channel radiometer). The so-called „water vapor continuum“ is arises from the contribution of far away water vapor lines.
- In addition to gaseous absorption, scattering, absorption, and emission also originate from hydrometeors in the atmosphere.
+Larger rain drops as well as larger frozen hydrometeors (snow, graupel, hail) also scatter microwave radiation especially at higher frequencies (>90 GHz). These scattering effects can be used to distinguish between rain and cloud water content exploitinh polarized measurements [9] but also to constrain the columnar amount of snow and ice particles from space [10] and from the ground [11].
+{{:instruments:hatpro:mwr_5.png?600|Microwave spectrum: The black lines show the simulated spectrum (in brightness temperatures TB) for a ground-based receiver; the colored lines are the spectrum obtained from a satellite instrument over the ocean measuring at horizontal (blue) and vertical (red) linear polarization. Solid lines indicate simulations for clear-sky (cloud-free) conditions, dotted lines show a clear-sky case with a single layer liquid cloud. The vertical lines indicate typical frequencies used by satellite sensors like the [[https://en.wikipedia.org/wiki/Advanced_Microwave_Sounding_Unit|AMSU]] radiometer.}} \\
+Fig. 3: Microwave spectrum: The black lines show the simulated spectrum (in brightness temperatures TB) for a ground-based receiver; the colored lines are the spectrum obtained from a satellite instrument over the ocean measuring at horizontal (blue) and vertical (red) linear polarization. Solid lines indicate simulations for clear-sky (cloud-free) conditions, dotted lines show a clear-sky case with a single layer liquid cloud. The vertical lines indicate typical frequencies used by satellite sensors like the [[https://en.wikipedia.org/wiki/Advanced_Microwave_Sounding_Unit|AMSU]] radiometer.
-{{ :instruments:hatpro:mwr_5.png?600 |Microwave spectrum: The black lines show the spectrum from the view of a ground-based receiver, the colored lines the spectrum from a satellite over the ocean measuring at horizontal (blue) and vertical (red) polarization. Solid lines indicate a clear sky case, dotted lines the clear sky case with liquid cloud added. Some weather satellites have AMSU sensors on board and measure at the corresponding vertical lines.}} \\
-Microwave spectrum: The black lines show the spectrum from the view of a ground-based receiver, the colored lines the spectrum from a satellite over the ocean measuring at horizontal (blue) and vertical (red) polarization. Solid lines indicate a clear sky case, dotted lines the clear sky case with liquid cloud added. Some weather satellites have AMSU sensors on board and measure at the corresponding vertical lines.
 ===== Design =====
+A microwave radiometer consits of an antenna system, microwave radiofrequency components (frontend) and a backend for signal processing at intermediate frequencies (Fig. 5). The atmospheric signal is very weak and the signal needs to be amplified by around 80 dB. Therefore often heteorodyne techniques are used to convert the signal down to lower frequencies that allow the ise of commercial amplifiers and signal processing. Increasingly low noise amplifiers become available at higher frequencies, i.e. up to 100 GHz, making heteorodyne techniques obsolete. Thermal stabilization is highly important to avoid receiver drifts.
+Usually ground-based radiometers are also equipped with environmental sensors (rain, temperature, humidity) and GPS receivers (time and location reference). The antenna itself often measures through a window made of foam which is transparent in the MW (light blue material in Fig. 1) in order to keep the antenna clean of dust, liquid water and ice. Often, also a heated blower system is attached the radiometer which helps to keep the window free of liquid drops or dew (strong emitters in the MW) but also free of ice and snow.
-Basically, the radiometers have the general form of the design. Radiometer is consisted of few blocks: antenna system, microwave radiothermal receiver, recording and storage devices and radioengineering system for the transmission of obtained data to the processing step. Here is short description of several major blocks of radiometers:
+{{:stuff:mwr_design.png|Schematic diagram of a microwave radiometer}} \\
+Fig. 4: Schematic diagram of a microwave radiometer using the [[https://en.wikipedia.org/wiki/Heterodyne|heterodyne]] principle.
+After being received at the antenna the radiofrequency signal is downconverted to the intermediate frequency (IF) with the help of a stable local oscillator signal. After amplification with a Low Noise Amplifier (LNA) and band pass filtering the signal can be detected in full power mode, by splitting or splitting it into multiple frequency bands with a spectrometer. For high-frequency calibrations a Dicke switch is used here.
-  - The antenna block receives radiation propagating in free space. This module transforms these electromagnetic waves into the oscillation modes guided in a transmission line.
+===== Calibration =====
-  - Radiometric receiving device consists of a high-frequency amplifier, a quadratic device and a low-frequency filter. The function of a high-frequency amplifier is to amplify the received signal in every frequency band.
+The calibration of MWRs sets the basis for accurate measured TB and therefore, for accurate retrieved atmospheric parameters as temperature profiles, integrated water vapor and liquid water path. The simplest version of a calibation is a so-called „hot-cold“ calibration using two reference blackbodies at known, but different, „hot“ and „cold“ temperatures, i.e. assuming a linear relation between input power and output voltage of the detector. Knowing the physical temperatures of the references, their TB can be calculated and directly related to detected voltages of the radiometer, hence, the linear relationship between TB and voltages can be obtained.
-  - Recording and storage devices – these parts of the system are made for recording the measured parameters.
-Also, depending on the particular characteristics of each instrument, the radiometer can be equipped with additional devices (for instance: rain, temperature and humidity sensors, GPS-receiver etc).
+The temperatures of the calibration targets should be chosen such that they span the full measurement range. Ground-based radiometers usually use an ambient temperature target as „hot“ reference. As a cold target one can use either a liquid nitrogen cooled blackbody (77 K) [1] or a zenith clear sky TB that was obtained indirectly from radiative transfer theory [Paper Westwater]. Satellites use a heated target as „hot“ reference and the cosmic background radiation as „cold“ reference. To increase the accuracy and stabiltity of MWR calibrations further calibration targets, such as internal noise sources, or Dicke switches (Fig. 4) can be used.
-{{ :instruments:hatpro:mwr_4.png?400 |Schematic presentation of the transmission of information from data to natural object (from Atmosphere to radio-frequency amplifier). Noise resistor and amplifier represent the emission reception parts [8].}}
 =====   Retrieval of temperature and water vapor profiles   =====
+The retrieval of physical quantities (e.g. temperature or water vapor profiles) is not straight-forward and comprehensive retrieval algorithms (using inversion techniques like [[https://en.wikipedia.org/wiki/Optimal_estimation|optimal estimation]] approach) have been developed.
-Temperature profiles can be obtained by measuring the radiation intensity, or brightness temperature, at points along the side of the oxygen feature at 60 GHz. By scanning downward from line center onto the wing of the line, the instrument can obtain altitude information. Emission at any altitude is proportional to local temperature and density of oxygen; therefore the temperature profile can be retrieved.
+Temperature profiles are obtained by measuring along the oxygen absorption complex at 60 GHz. The emission at any altitude is proportional to local temperature and density of oxygen. Unlike water vapor, oxygen is relatively homogeneously distributed within the atmosphere and around the globe. Thanks to the relatively well known vertical profile of oxygen concentration, the TB signals can be directly used to derive the unknown temperature profile. Signals at the center of the absorption complex are dominated by the atmosphere closest to the radiometer (only the first hundred meters above the instrument). Moving more into the window region, the signal is a superposition from close and more distant regions of the atmosphere. The combination of several channels contains therefore information about the vertical temperature distribution. A similar approach is used to derive vertical profiles of water vapor utilizing the absorption line at 22.235 GHz.
-Water vapor profiles can be obtained by observing the intensity and shape of emission from pressure broadened water vapor lines. The water vapor line at 22 GHz is a narrow line at high altitudes and is pressure broadened at low altitudes. The intensity of emission is proportional to vapor density and temperature. Scanning the spectral profile and mathematically inverting the observed data provides water vapor profiles.
-The process of inverting the measured brightness temperature, TB_meas, in order to retrieve the profiles of atmospheric parameters (temperature, water vapor density, and cloud liquid density), generally requires an initial-guess for these profiles. The guess profiles are then corrected based on the difference of TB_meas and TB_guess, (obtained via forward-model and the guess profiles), i.e., ΔTB=TB_meas- TB_guess. The process can be repeated until ΔTB is minimized. When inverting for a particular quantity, e.g., temperature profile, the measurement frequency, or the so-called spectral channel, is chosen in such a way that the sensitivity of the measurements is maximized with respect to the perturbations in that parameter. However, there is always some influence on the measurements from other parameters, i.e., effect of water vapor and clouds on the temperature sounding, etc. As a result, for accurate retrieval, it is best to make simultaneous use of temperature, water vapor, and the cloud liquid channels, thereby, taking into account the influence of all these profiles together, on the measured brightness temperature.
-Along with measurements at several frequency channels, angular scans of the atmosphere provide additional information especially for the boundary layer studies.
@@ Line 57: / Line 60: @@
 | {{ :instruments:hatpro:table_3.png?nolink&300 |}} | {{ :instruments:hatpro:table_4.png?nolink&300 |}} | \\
-Time series on the 14th of April 2015 for (a) the brightness temperatures measured in 7 different frequencies on the MWR in the K (right) and V (left) bands, (b) Integrated Water Vapor and Liquid Water Path, (c) Temperature profiles from 0 to 5 km, (d) Absolute humidity profiles from 0 to 5 km.
+Time series from the 14th April 2015 for (a) brightness temperatures measured at 7 different frequencies in the K (right) and V (left) bands, (b) retrieved vertically Integrated Water Vapor (IWV) and cloud Liquid Water Path (LWP), (c) temperature profiles from 0 to 5 km, (d) absolute humidity profiles from 0 to 5 km.
 ===== MWRnet =====
-[[http://cetemps.aquila.infn.it/mwrnet/|MWRnet]] is a network established in 2009 connecting people working with ground-based microwave radiometers. MWRnet aims to facilitate the exchange of information in the MWR user community fostering the participation to coordinated international projects. In the long run, MWRnet’s mission aims at setting up operational software, quality control procedures, data formats, etc. similar to other successful networks such as  [[http://www.earlinet.org/ | EARLINET]],  [[http://aeronet.gsfc.nasa.gov/| AERONET]],[[http://www.metoffice.gov.uk/science/specialist/cwinde/profiler/| CWINDE]].
+[[http://cetemps.aquila.infn.it/mwrnet/|MWRnet]] is a network established in 2009 of scientists working with ground-based microwave radiometers. MWRnet aims to facilitate the exchange of information in the MWR user community fostering the participation to coordinated international projects. In the long run, MWRnet’s mission aims at setting up operational software, quality control procedures, data formats, etc. similar to other successful networks such as [[http://www.earlinet.org/ | EARLINET]],  [[http://aeronet.gsfc.nasa.gov/| AERONET]],[[http://www.metoffice.gov.uk/science/specialist/cwinde/profiler/| CWINDE]].
 {{ :instruments:hatpro:mwr_3.png?400 |Distribution of ground based microwave radiometers across the globe by type [3]}} \\
@@ Line 68: / Line 71: @@
 ===== References =====
+[1] Microwave Remote Sensing—Active and Passive”. By F. T. Ulaby. R. K. Moore and A. K. Fung. (Reading, Massachusetts: Addison-Wesley, 1981 and 1982.) Volume I: Microwave Remote Sensing Fundamentals and Radiometry.
+[2] Thermal Microwave Radiation: Applications for Remote Sensing, C. Matzler, 2006, The Institution of Engineering and Technology, London, Chapter 1.
+[3] Westwater, Edgeworth Rupert, 1970: Ground-Based Determination of Temperature Profiles by Microwaves. PH.D. Thesis, UNIVERSITY OF COLORADO AT BOULDER, Source: Dissertation Abstracts International, Volume: 32-02, Section: B, page: 1134.
+[4] Passive Microwave Remote Sensing of the Earth, Physical Foundations, Eugene A. Sharkov, Springer-Praxis Books in Geophysical Sciences, Chapter 14: Passive microwave space missions
+[5] http://cetemps.aquila.infn.it/mwrnet/main_files/whatisMWRnet.html
+[6] Westwater, E.R., C. Mätzler, S. Crewell (2004) A review of surface-based microwave and millimeter-wave radiometric remote sensing of the troposphere. Radio Science Bulletin, No. 3010, September 2004, 59-80,
+[7] Westwater, E. R., S. Crewell, C. Mätzler, and D. Cimini, 2006: Principles of Surface-based Microwave and Millimeter wave Radiometric Remote Sensing of the Troposphere, Quaderni Della Societa Italiana di Elettromagnetismo, 1(3), September 2005, 50-90.
+[8] Final report of the COST action EG-Climet, http://cfa.aquila.infn.it/wiki.eg-climet.org/index.php5/Microwave_radiometer
+[9] Czekala et al. (2001), Discrimination of cloud and rain liquid water path by groundbased polarized microwave radiometry, Geophy. Res. Lett., DOI: 10.1029/2000GL012247
+[10] Bennartz, R., and P. Bauer (2003), Sensitivity of microwave radiances at 85–183 GHz to precipitating ice particles, Radio Sci., 38(4), 8075, doi:10.1029/2002RS002626.
+[11] Kneifel et al. (2010), Snow scattering signals in ground-based passive microwave radiometer measurements, J. Geophys. Res., DOI: 10.1029/2010JD013856
-  - http://juno.wisc.edu/spacecraft_instruments_MWR.html
-  - http://noaasis.noaa.gov/NOAASIS/ml/avhrr.html
-  - http://cetemps.aquila.infn.it/mwrnet/main_files/whatisMWRnet.html
-  - Thermal Microwave Radiation: Applications for Remote Sensing, C. Matzler, 2006, The Institution of Engineering and Technology, London, Chapter 1.
-  - Eugene A. Sharkov, “Passive Microwave Remote Sensing of the Earth”, Physical Foundations, Springer-Praxis Books in Geophysical Sciences, Chapter 14: Passive microwave space missions
-  - Cimini et al., 2009
-  - Klein and Gasiewski, 2000
-  - Eugene A. Sharkov, “Passive Microwave Remote Sensing of the Earth”, Physical Foundations, Springer-Praxis Books in Geophysical Sciences, Chapter 3: Microwave radiometers: functions, design, concepts, characteristics [http://www.iki.rssi.ru/asp/pub_sha1/pub_sha1.htm]
-  - http://fas.org/irp/imint/docs/rst/Sect14/Sect14_4.html