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| An '''atmospheric sounding''' is a measurement of vertical distribution of physical properties of the [[atmosphere|atmospheric]] column such as [[atmospheric pressure|pressure]], [[temperature]], [[wind speed]] and [[wind direction]] (thus deriving [[wind shear]]), liquid water content, [[ozone]] concentration, pollution, and other properties. Such measurements are performed in a variety of ways including [[remote sensing]] and [[in situ#Earth and atmospheric sciences|in situ]] observations.
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| The most common in situ sounding is a [[radiosonde]], which usually is a [[weather balloon]], but can also be a [[rocketsonde]].
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| Remote sensing soundings generally use passive [[infrared]] and [[microwave]] [[radiometer]]s:
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| * airborne instruments
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| * surface stations
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| * Earth-observing satellite instruments such as [[Atmospheric Infrared Sounder|AIRS]] and [[Advanced Microwave Sounding Unit|AMSU]]
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| There is even a sounder at Mars: the [[Mars climate sounder]] on the [[Mars Reconnaissance Orbiter]]
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| ==Direct methods==
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| Sensors that measure atmospheric constituents directly such as thermometers, barometers and humidity sensors can be sent aloft on balloons, rockets or [[dropsonde]]s. They can also be carried on the outer hulls of ships and aircraft or even mounted on towers. In this case, all that is needed to capture the measurements are storage devices and/or [[transponder]]s.
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| ==Indirect methods==
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| The more challenging case involves sensors, primarily satellite-mounted, such as [[radiometers]], optical sensors, [[radar]], [[lidar]] and [[ceilometer]] as well as [[sodar]] since these cannot measure the quantity of interest, such as temperature, pressure, humidity etc., directly. By understanding emission and absorption processes, we can figure out what the instrument is looking at between the layers of atmosphere.
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| While this type of instrument can also be operated from ground stations or vehicles—optical methods can also be used inside in situ instruments—satellite instruments are particularly important because of their extensive, regular coverage. The [[Advanced Microwave Sounding Unit|AMSU]] instruments on three [[NOAA]] satellites, for instance, can sample the entire globe at better than one degree resolution in less than a day.
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| We can distinquish between two broad classes of sensor: ''active'', such as [[RADAR]], that have their own source, and ''passive'' that only detect what is already there. There can be a variety of sources for a passive instrument including scattered radiation, light emitted directly from the sun, moon or stars—both more appropriate in the visual or ultra-violet range, as well light emitted from warm objects which is more appropriate in the microwave and infrared.
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| ===Viewing geometry===
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| An atmospheric limb sounder tracks the sun, moon, a star, or another transmitting satellite through the planet limb or edge of the atmosphere as they get [[occultation|occultated]] behind the Earth. In contrast, a [[nadir]]-looking atmospheric sounder looks down through the atmosphere at the surface. The [[SCIAMACHY]] instrument operates in all these modes.
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| ==Atmospheric inverse problem==
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| {{split section|date=October 2013}}
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| ===Statement of the problem===
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| The following applies mainly to passive sensors, but has some applicability to active sensors.
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| Typically, there is a vector of values of the quantity to be retrieved, <math>\vec x</math>, called the '''state vector''' and a vector of measurements, <math>\vec y</math>. The state vector could be temperatures, ozone number densities, humidities etc. The measurement vector is typically counts, radiances or brightness temperatures from a radiometer or similar detector but could include any other quantity germain to the problem.
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| The '''forward model''' maps the state vector to the measurement vector:
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| :<math>
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| \vec y = \vec f (\vec x)
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| </math>
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| Usually the mapping, <math>\vec f</math>, is known from physical first principles, but this may not always be the case. Instead, it may only be known [[empirical]]ly, by matching actual measurements with actual states. Satellite and many other [[remote sensing]] instruments do not measure the relevant physical properties, that is the state, but rather the amount of radiation emitted in a particular direction, at a particular frequency. It is usually easy to go from the state space to the measurement space—for instance with [[Beer's law]] or [[radiative transfer]]--but not the other way around, therefore we need some method of [[inverse problem|inverting]] <math>\vec f</math> or of finding the '''inverse model''', <math>\vec f^{-1}</math>.
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| ===Methods of solution===
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| If the problem is [[linear]] we can use some type of matrix inverse method—often the problem is [[ill-posed]] or [[Numerical instability|unstable]] so we will need to [[regularization (mathematics)|regularize]] it: good, simple methods include the [[normal equation]] or [[singular value decomposition]]. If the problem is weakly nonlinear, an iterative method such [[Newton-Raphson]] may be appropriate.
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| Sometimes the physics is too complicated to model accurately or the forward model too slow to be used effectively in the inverse method. In this case, [[statistical]] or [[machine learning]] methods such as [[linear regression]], [[neural networks]], [[statistical classification]], [[kernel estimation]], etc. can be used to form an inverse model based on a collection of ordered pairs of samples mapping the state space to the measurement space, that is, <math>\lbrace \vec x: \vec y \rbrace</math>. These can be generated either from models—e.g. state vectors from dynamical models and measurement vectors from radiative transfer or similar forward models—or from direct, empirical measurement. Other times when a statistical method might be more appropriate include highly [[nonlinear]] problems.
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| ==List of methods==
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| * [[Differential absorption spectroscopy]]
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| * [[Isoline retrieval]]
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| * [[Optimal estimation]]
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| ==See also==
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| * [[Inverse problems]]
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| * [[Collocation (remote sensing)]]
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| * [[Thermodynamic diagrams]]
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| * [[Skew-T log-P diagram]]
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| * [[Atmospheric sounder]]
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| ==References==
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| * {{cite book | author=Egbert Boeker and Rienk van Grondelle | title=Environmental Physics | edition=2nd| year=2000 | publisher=Wiley}}
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| * {{cite book
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| | author=Clive D. Rodgers
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| | title=Inverse Methods for Atmospheric Sounding: Theory and Practice
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| | year=2000
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| | publisher=World Scientific
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| }}
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| ==External links==
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| * [http://weather.uwyo.edu/upperair/sounding.html University of Wyoming Atmospheric Soundings]
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| {{DEFAULTSORT:Atmospheric Sounding}}
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| [[Category:Atmospheric thermodynamics]]
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| [[Category:Diagrams]]
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| [[fr:SkewT]]
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| [[ja:Skew-T log-P図]]
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| [[pl:sondaż atmosferyczny]]
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