Microwave Sensors

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1.16

Microwave Sensors

RV Leslie, Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA, United States © 2018 Elsevier Ltd. All rights reserved.

1.16.1 1.16.2 1.16.2.1 1.16.2.1.1 1.16.2.1.2 1.16.2.1.3 1.16.2.1.4 1.16.2.1.5 1.16.2.2 1.16.2.2.1 1.16.2.2.2 1.16.2.2.3 1.16.2.2.4 1.16.2.2.5 1.16.3 1.16.3.1 1.16.3.1.1 1.16.3.1.2 1.16.3.1.3 1.16.3.1.4 1.16.3.1.5 1.16.3.2 1.16.3.2.1 1.16.3.2.2 1.16.3.2.3 1.16.3.2.4 1.16.4 1.16.4.1 1.16.4.1.1 1.16.4.1.2 1.16.4.2 1.16.4.3 1.16.4.4 1.16.5 1.16.5.1 1.16.5.1.1 1.16.5.1.2 1.16.5.2 1.16.5.2.1 1.16.5.2.2 1.16.5.3 1.16.5.3.1 1.16.5.3.2 1.16.5.4 1.16.5.4.1 1.16.5.4.2 1.16.5.4.3 1.16.5.5 1.16.5.5.1 1.16.5.5.2 1.16.5.5.3 1.16.6 1.16.6.1 1.16.6.1.1 1.16.6.1.2

Introduction Microwave Radiation Electromagnetic Waves Maxwell’s equations Media Wave equations and Poynting power Polarization Surface interactions Thermal Radiation and Radiative Transfer Emission and brightness temperature Radiative transfer equation Absorption Scattering Surface Emissivity Sensing Techniques Collecting Radiation Antenna fundamentals Aperture Synthetic apertures Spatial resolution Swath Measuring Radiation System design Total power radiometer Dicke radiometer Polarimetric radiometer Mechanisms of Retrievals Passive Remote Sensing Atmosphere Surface Active Remote Sensing Terrestrial and Jovian Planets Radioastronomy Calibration Data Processing Data product ﬂow Correction factors Calibration Techniques Periodic absolute calibration Dicke switching Performance Metrics Radiometric calibration accuracy Radiometric calibration precision Calibration Standards Calibration targets Cosmic background Internal Calibration Prelaunch Characterization Spatial response Spectral response Linearity Veriﬁcation and Validation Instrument Veriﬁcation Instrument performance Electromagnetic interference

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1.16.6.2 1.16.6.2.1 1.16.6.2.2 1.16.6.2.3 1.16.6.2.4 1.16.6.2.5 References

1.16.1

Data Product Validation Ground truth comparisons Inter-instrument comparisons Vicarious validation NWP and radiosonde validation Data maturity

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Introduction

Remote sensing in the microwave or millimeter wave spectrum (approximately 300 MHz–300 GHz) has an enduring and critical role for a wide range of applications. Radar is the most famous microwave remote-sensing application, but for most people in the developed world, a microwave is an appliance in their kitchen for heating food (which does use microwave radiation). Modern society also relies heavily on microwaves for geolocation (e.g., GPS) and communication such as Wi-Fi, mobile phone networks, and satellite communications. This chapter provides a comprehensive study of microwave remote sensing fundamentals for passive applications (i.e., listening or measuring naturally emitted microwave energy) with appropriate connections to the active applications (i.e., generating and then measuring the return microwave energy). For more in-depth information on active microwave sensors used in radar applications, see the chapter on Radar Sensors. Microwave remote sensing applications include monitoring the Earth from space (e.g., US NOAA Joint Polar-orbiting Satellite System), monitoring near-by planets using space probes (e.g., NASA’s Mariner 2), and even distant galaxies in radio astronomy (e.g., Arecibo Observatory). This chapter concentrates on the monitoring the Earth, but much of the instrumentation is applicable to the other applications. A few application examples of microwave sensors include measuring temperature and humidity for weather forecasting, planning disaster relief after severe weather, long-term climate change, and mapping soil moisture for agriculture. The chapter starts with the ﬁrst principles of electromagnetic waves and radiative transfer. The second section describes the instrumentation that collects and quantiﬁes the microwave radiation. The third section covers physical mechanisms of retrieving information from the microwave radiation. The fourth section describes quantifying the performance and calibrating the instrumentation. The ﬁnal section explains the instrument’s veriﬁcation and validation techniques. To impart the breath of the applications of microwave remote sensing, Fig. 1 presents a graphical depiction that maps typical microwave systems with common applications. The ﬁrst primary distinction between microwave remote-sensing systems is whether the system generates the microwave radiation (i.e., active) or whether it uses natural sources of microwave radiation (i.e., passive). The next main distinction for the passive systems is whether the system is design to measure a three-dimensional data product (e.g., vertical temperature) or a two-dimensional data product (e.g., soil moisture). Systems designed for three-dimensional data products are called sounders, while two-dimensional data product systems are called radiometers. The design distinction between the sounder and radiometer is that the radiometer’s microwave frequencies are chosen to be largely transparent through the atmosphere, while the sounder’s frequencies receive radiation from the atmosphere. Two-dimensional data products typically measure phenomenology near or at the Earth’s surface, which requires the microwave radiation to go unimpeded through the atmosphere. The main distinction for the active systems is the manner of collecting the microwave radiation with either a single aperture or a collection of apertures that can be conﬁgured to make a much larger “synthetic” aperture. The aperture size typically drives the spatial resolution, i.e., geographical footprint on the ground considered the source of the microwave radiation. Signal processing allows synthetic apertures to general images with much ﬁner spatial resolution than practical real apertures, but at a cost of complexity. Active systems are much heavier and consume much more power because they need to include a transmitter and be able to perform the complex algorithms. The remote-sensing active systems are generally in three categories of altimeters, scatterometers, and imaging radars. Even though both altimeters and scatterometers can create an image of their direct measurements, imaging radars need special processing to construct their image (which is at a much ﬁner spatial resolution). There are ﬂeets of environment observing satellites with microwave sensors for both scientiﬁc research and operational monitoring to help with a wide range of applications ranging from agriculture and hydrology, climate and atmospheric studies, severe weather prediction, military, and disaster relief. Microwave measurements are one of the most important data sources for reducing forecast error in weather modeling (English, 2006). There are exciting new frontiers of microwave sensors, which includes hyperspectral microwave sounding (Blackwell et al., 2011), passive synthetic antennas for sounding (Tanner et al., 2007) from a geostationary orbit, and having constellations of small satellites with microwave sensors to study tropical storms (Blackwell, 2015), measure wind speed from reﬂections of GPS satellites off of the ocean, and measure the refraction of GPS signals through the atmosphere to retrieve the atmospheric state (Ruf et al., 2013; Cook et al., 2015). These are the frontier of microwave remotesensing sensors.

1.16.2

Microwave Radiation

This section provides an introduction to the underlying principles of microwave radiation that is fundamental to understanding microwave sensors. The section starts with the theory of electromagnetic waves (EM) and how the waves behave and couple

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Fig. 1 Mapping of microwave system designs to principal applications. Dashed lines are systems that use synthetic apertures and solid lines are real apertures. Colors represent the passive sounders (green), passive radiometers (red) and active systems (blue).

with the environment. In atmospheric passive remote sensing, EM radiation can be considered a collection of EM waves that is stochastic (i.e., random) and unpolarized, but active systems use coherent EM waves that are still radiation. The primary parameter of EM radiation is more often the amount of energy carried in the EM waves. The stochastic energy (or power as energy per unit time) in the EM radiation is either the signal in radiometry, or a source of noise in active sensors. Some applications in radiometry gain information by knowing the amount of energy in different polarizations (e.g., sea surface wind direction). The section continues with describing the basics of how microwave EM radiation interacts and generated in nature (i.e., thermal radiation and radiative transfer). As pointed out in “Introduction” section, a big distinction in microwave sensors is between the active sensor, i.e., sensor that emits and then receives EM radiation, and the passive sensor that receives EM radiation from natural sources.

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Fig. 2

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EM waves spectrum. (source: https://commons.wikimedia.org/wiki/File:EM_spectrum.svg)

1.16.2.1

Electromagnetic Waves

Electromagnetic (EM) waves are the foundation of remote sensing because sensors collect and quantify the characteristics of the EM radiation coming from the physical environment or the reﬂections from a man-made source. This section reviews the fundamentals of EM waves, but there are extensive material available in the reference section. This section is applicable to all frequencies of EM waves (see Fig. 2 for a classiﬁcation of the EM waves versus frequency and wavelength), but we will concentrate on the properties of the microwave portion of the spectrum. More comprehensive texts can be found in Staelin, 1994 and Cheng, 2014.

1.16.2.1.1

Maxwell’s equations

James Clerk Maxwell (1831–1879) uniﬁed static electrical and magnetic phenomena into the dynamic electromagnetic waves, and he postulated that light was an EM wave and therefore radio waves must exist as EM waves at different frequencies (i.e., longer wavelengths) (Maxwell, 1865). The theory of EM waves was proven by the experimental work of Heinrich Hertz (1857–1894), and he developed the ﬁrst dipole antenna transmitter and rudimentary receiver (Hertz, 1893). Later, Hertz had the fundamental unit of frequency unit named after him. Maxwell’s work showed mathematically how electric and magnetic ﬁelds were coupled waves and how they could transfer energy through vacuum using 20 equations and 20 unknowns. In Table 1, Oliver Heaviside (1850–1925) reworked Maxwell’s equations while developing vector analysis to give us the form we are most familiar with today. The form presented in Table 1 is the general differential form with four unknowns that is independent of the media (i.e., the matter that the EM waves travel in). The next section describes how the media impacts these equations and then a solution that fulﬁls these equations.

1.16.2.1.2

Media

Whether the sensor is active or passive, the microwave radiation must pass through free space (i.e., vacuum), the Earth’s atmosphere, or both. Sometimes the EM waves travel round trip in active scenarios or even in the passive case if it is cosmic background radiation reﬂecting off of hydrometeors (e.g., hail in a thunderstorm). We will discuss more about the transfer of energy in the media during the upcoming section on radiative transfer. Table 1

Maxwell’s equations

Law

Concept

Differential form

Notes

Electric Gauss’ Law

Charges create electric ﬁelds

V$D ¼ r

Magnetic Gauss’ Law Faraday’s Law of Induction Ampere’s Law with Maxwell’s Modiﬁcation

No free magnetic charges Time varying magnetic ﬂux will create an electric ﬁeld Electric current and time-varying electric ﬂux will create a magnetic ﬁeld

V$B ¼ 0 vB VE ¼ vt vD VH ¼ þJ vt

D is the electric displacement ﬁeld (C/m2) and r is electric charge density (C/m3) B is the magnetic ﬂux density (tesla; T) E is the electric ﬁeld (V/m) H is the magnetic ﬁeld [A/m] and J is electric current density (A/m2)

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To solve Maxwell’s equations, we need to determine how the media relate the electric displacement ﬁeld (D) to the electric ﬁeld (E) and the magnetizing ﬁeld (or magnetic ﬂux density; D) to the magnetic ﬁeld (H). They are related by the constitutive relations: D ¼ ε$E B ¼ m$H ε is the permittivity of the media in units of farads per meter and m is the relative permeability of the media in units of henries per meter. They can be further separated into a product of an unitless multiplicative factor (e.g., for permittivity it is called the dielectric constant) and the value in vacuum, when the media is made of the same matter (i.e., homogenous), isotropic (i.e., behaves the same in all directions), time-invariant (i.e., does not change on appropriate time scales), and the material acts on the ﬁelds in a linear fashion (i.e., not nonlinear). ε ¼ εr ε0 m ¼ mr m0 The 0 subscript represents the value in vacuum and the r is the relative value, which is a unitless multiplicative factor. The relative value has a variety of forms to handle the multitude of conditions of the media. The other forms consist of polarizable, anisotropic (i.e., direction dependent), inhomogeneous, and dispersive (i.e., frequency dependent) to name a few of the major categories (Kong, 1990).

1.16.2.1.3

Wave equations and Poynting power

The next step is to discuss how Maxwell’s equations can be manipulated to produce a wave equation fulﬁlling all the electromagnetic wave requirements set out by Maxwell’s four equations. The wave equation is then solved to produce a function (i.e., a solution) that can be used to describe the upcoming characteristics such as polarization and how the EM behaves when the media changes (e.g., reﬂections). Using Faraday’s law, Ampere’s Law without current density, and Electric Gauss’s Law without charge (along with constitutive relationship and a vector identity), the differential wave equation is (a bar above indicates a vector) V2 E m0 ε0

v2 E ¼0 v2 t

A general solution is given as Eðr; t Þ ¼ E0 f ut k$r , where omega is the angular frequency (radians/second), r is the Cartesian vector (m), and k is the propagation constant (or wave number in units of 1/m). Substitution into the above wave equation produces the dispersion relationship k 2 ¼ u2 m 0 ε0 A common solution is E ¼ b x E0 cosðut kzÞ, which the dispersion relationship gives the velocity of electromagnetic waves as c¼

u 1 meters ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 2:998x108 k m 0 ε0 sec

Entering the electric ﬁeld solution above to Faraday’s Law gives the corresponding magnetic ﬁeld: E0 cosðut kzÞ h0 qﬃﬃﬃﬃ where h0 is the wave impedance of free space and is equal to mεo0 . The example is a special case known as the uniform plane wave where the electric and magnetic ﬁelds are uniform, i.e., share the same form in the x-y plane. The Poynting vector, which characterizes the direction and magnitude of power ﬂow, is deﬁned as the cross product of the electric and magnetic ﬁelds, which has the plane wave solution of H¼b y

S¼E H¼b z

E20 cos2 ðut kzÞ W=m2 h0

Note that in this orientation and assumption, the electric ﬁeld is in the x direction, the magnetic ﬁeld is in the y direction, and the power (and therefore the wave) moves in the forward z direction. To get the time-average or instantaneous power, 1 S ¼ T

ðT

1 1

S ¼ Re Sdt ¼ E H ¼ Re E H 2 2

0

The vectors with the underbar denote a complex number, which for the uniform plane waves assumption is not applicable but will be needed for some polarizations in the next section.

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1.16.2.1.4

Polarization

Polarization is deﬁned by the angle of the EM wave’s E-ﬁeld as the wave propagates in time and space. The solutions to the wave equations from “Wave Equations and Poynting Power” section can have the E-ﬁeld changing magnitude in the same twodimensional plane or make a corkscrew path through a three-dimensional space. In a three-dimensional Cartesian space, Sir George Gabriel Stokes (1819–1903) designed the Stokes parameters in a Stokes vector to represent the EM radiation under unpolarized, partial-polarized, and fully polarized conditions. EM radiation from natural sources like soil and molecules in the atmosphere are unpolarized, meaning the electric ﬁelds are oriented in no systematic way. Active sensors, and some passive sensors, gain information for their application by quantifying the amount of energy in different polarizations. Some active systems will transmit radiation in one polarization, but measure the power of the transmitted polarization and the orthogonal polarization as well to discern characteristics of the target. For passive applications, measuring the energy at different polarizations indicates the surface properties because natural radiation sources reﬂect off the surface. For example, polarimeter radiometers (radiometers measuring more than one polarization) can determine wind direction by measuring the amount of energy reﬂected based on the instrument’s orientation relative to the ocean wavefronts. For more details see Skou and Le Vine (2006a) or Ulaby and Long (2014a). Table 2 has the Stokes parameter description and equations for the electric ﬁelds and the brightness temperature. Notice that the electric ﬁeld is in units of power, and the brightness temperature uses an approximation coming up referred to as the Rayleigh–Jeans which relates intensity (i.e., power per area) to brightness temperature (“Emission and brightness temperature” section). The Cartesian basis unit vector designations x and y can be replaced with the common horizontal and vertical nomenclature. The 45 degrees refer to a 45 degress rotation of the Cartesian basis. The L and R refer to special cases where the electric ﬁelds in the basis coordinates are out of phase that causes the path in the z direction to make a corkscrew pattern, which is called a circular polarization in the x-y plane. The direction of the circular or elliptical pattern in the x-y plane is the handedness and can be either right (R) or left (L) handed following the IEEE right hand convention in respect to the direction of propagation (z). A couple of examples can help show the utility of the Stokes vector. A horizontally polarized wave (i.e., all in the x direction) will have the Stokes vector of [1 1 0 0], which the I of 1 is just the total power and is always present and the Q of 1 is positive and equal to the I (i.e., total power) that all the power is in the horizontal or x direction. A vertically polarized wave would simply change the sign of the Q to show there was no power in the horizontal or x direction. Finally, the unpolarized Stokes vector would have no power in Q, U, or V and would represented as [1 0 0 0]. This means for a coherent (nonrandom) plane wave that I2 ¼ Q2 þ U2 þ V 2 . The Stokes vector can completely characterize a polarized coherent EM wave. If the EM wave is partially polarized and therefore random, then I2 Q2 þ U2 þ V 2 and represents the time-average values.

1.16.2.1.5

Surface interactions

The previous sections kept the discussion in homogenous media, but remote sensing frequently estimates geophysical properties or conditions from information on the boundaries of media, for example, the atmosphere and ocean. There are ever increasingly complex models for the interaction of EM waves with boundaries or surfaces, but reﬂections are an important characteristic whether it is cosmic background radiation scattering off of rain or scatterometers transmitting EM waves off the ground. The EM energy impinging on an interface between two media can be either reﬂected off or transmitted through the boundary. The conservation of energy requires the sum of the reﬂected and transmitted to be equal to 1. This section will only cover some of the major points of boundaries and EM waves that will be pertinent in the following sections. There are two standard approaches to representing EM waves in textbooks: (1) the ray representing the direction of the power (i.e., propagation constant; k) or (2) the phase front contour of equal ﬁeld strength, which is perpendicular to the propagation constant. To gain intuition, this section will use the same common example in textbooks for normal incidence (i.e., direct) radiation and oblique incidence as shown in Fig. 3. Maxwell’s equations dictate that the electric ﬁeld tangential to the plane dividing the different media must be equal (i.e., phase matching condition), which combined with the fact that the incident and reﬂected waves are in the same media gives Snell’s law of reﬂection. Furthermore, Snell’s law of refraction (i.e., transmission) deﬁnes the relationship between incident/reﬂected angle and the transmitted angle: sinqi hb k t ¼ ¼ sinqt ha k i

Table 2

Stokes vector

Stokes Designation

Description

S0 or I

Represents the total power

S1 or Q

Difference between the two orthogonal dimensions

S2 or U

Real part of the cross-correlation

S3 or V

Imaginary part of the cross correlations

In terms of E fields h i 2 2 1 h0 jEx j þ jEy j h i 2 2 1 h0 jEx j jEy j

2 h0 Re Ex $Ey

2 h0 Im Ex $Ey

In terms of brightness temperature 1 2 ðTx

þ Ty Þ

1 2 ðTx

Ty Þ

1 2 ðT45 1 2 ðTL

T45 Þ

TR Þ

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Fig. 3

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Cartoon representation of incident EM waves between two different media.

At the critical or polarizing angle, sin qt ¼ 1 (or qt ¼ 90 degrees along the boundary interface) which makes the critical angle equal to sin1 ðhb =ha Þ. We are going to go directly to the Fresnel reﬂection and transmission coefﬁcients for horizontal polarization (also known as transverse electric plane waves) and vertical polarization (transverse magnetic plane waves) as that nomenclature has been already introduced. Following the ﬁeld equations for fulﬁlling the tangential boundary (i.e., phase matching) conditions, an expression for the reﬂection and transmission used in the electric and magnetic ﬁeld equations. Next, we will discuss the more useful terms for the power reﬂection and transmitted. qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 Erh0 cosqi ðεb =εa Þ sin qi qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ rh ¼ i ¼ Eh0 cosq þ ðε =ε Þ sin2 q i i b a ε 1 2 ε b 2 εba cosqi εa sin qi Erv0 rv ¼ i ¼ 1 2 ε Ev0 εb 2 εba cosqi εa sin qi = =

sh ¼ 1 þ rh sv ¼ ð1 þ rh Þ

cosqi cosqr

In terms of power, the magnitude squared of the reﬂection coefﬁcient is the reﬂectivity (plotted in Fig. 4), and with the conservation of energy, the transmissivity plus the reﬂectivity is equal to one. It can be confusing to understand the difference between the

Fig. 4

Reﬂectivity of water and dry land.

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commonly used term reﬂectivity and the reﬂectivity coefﬁcient. The relative permittivity of the water is 81, while dry land is only 3. There will be more discussion in the next section when we try to retrieve geophysical parameters like soil moisture. More information on the details of surface models can be found in Ulaby and Long (2014a).

1.16.2.2

Thermal Radiation and Radiative Transfer

It is mathematically cumbersome to use the ﬁrst principles of Maxwell’s equations to represent EM radiation in most remote-sensing applications, and the discipline of radiometry does not primarily rely on solving EM waves through media for remote-sensing applications. Instead, remote sensing tracks the energy of the radiation in our environment. We will often return to the material in “Basic mechanisms of electromagnetic waves” section, but we will need additional mathematical tools offered through the study of radiative transfer, or the energy transfer of EM waves through a media (Fante, 1981). Thermal radiation is electromagnetic radiation that originates from the temperature of an object. The nature of the emitted thermal radiation is governed by Planck’s law of blackbody radiation (see Fig. 5). A black body is an object that absorbs all electromagnetic radiation, i.e., none is reﬂected. Kirchhoff’s law states that in full or local thermodynamic equilibrium, the black body’s absorption of radiation equals its emission of radiation (Stephens, 1994). Many objects are considered “grey bodies,” which absorb and reﬂect electromagnetic radiation.

1.16.2.2.1

Emission and brightness temperature

Matter emits electromagnetic energy or radiation. A theoretical body of matter that absorbs all incident radiation is called a blackbody. The intensity emitted by a body at uniform temperature, T, is deﬁned by Kirchhoff’s law:

W If ¼ ka $Bf ðT Þ 2 m $Hz$Ster The absorption coefﬁcient, ka, has a value between 0 and 1 and is frequency dependent. Having ka ¼ 0 means that the matter neither emits nor absorbs electromagnetic energy at a particular frequency, while a ka ¼ 1 is the theoretical blackbody. Max Planck derived a radiation formula for radiation intensity in units of power per area-hertz-steradian. Planck’s radiation law is as follows

2hf 3 W 2 Bf ðT Þ ¼ 2 hf =kT c e 1 m $Hz$Ster with T, temperature in kelvin; f, frequency in Hertz; h, Planck’s constant; k, Boltzmann’s constant; c, speed of light in the medium. P xk x The power series expansion ex ¼ N k¼0 k! can be approximated when ðx 1Þ as ðe ¼ 1 þ xÞ. This approximation is the Rayleigh– Jeans limit and gives

2kT W Bf ðT Þ ¼ 2 m2 $Hz$Ster l only when hf kT. This is true in the microwave region of the electromagnetic spectrum for temperatures greater than 50 K.

Fig. 5 Planck radiation law (light grey) with Rayleigh–Jeans approximation (dark grey). Right axis is the frequency of the radiation, and the left axis is the source temperature. A few temperatures were replaced with examples.

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Fig. 6

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Radiance simulation ﬂowchart and list of input parameters.

A very common term in microwave remote sensing is brightness temperature. Kirchhoff’s law is in units of intensity, and when intensity is expressed in units of temperature, then it is termed brightness temperature. Rayleigh–Jeans law can be rearranged to give the equivalent temperature for a given intensity: Tb ¼

ka Bf ðT Þ$l2 If $l2 ¼ 2k 2k

This equation is only appropriate if all the conditions for the Rayleigh–Jeans limit are met. Figure 5 illustrates the Planck’s law and the Rayleigh-Jeans approximation.

1.16.2.2.2

Radiative transfer equation

The radiative transfer equation, RTE, deﬁnes the physics of the thermal radiation between a source, an intervening medium, and a receiver. In this section, the RTE is deﬁned for an incremental piece of atmosphere. “Passive remote sensing” section will extend the equation to a scenario where the terrestrial atmosphere is the medium, the earth’s surface is the source, and spacecraft is the receiver. A more in-depth explanation of radiative transfer can be found in Chandrasekhar, 1960; Armstrong and Nicholls, 1972. Fig. 7 shows the geometry of a planar-stratiﬁed atmosphere, with the surface of the earth at the bottom. The antenna is pointing toward the surface from somewhere within the atmosphere. The equation starts with the exchange of radiation in an incremental piece of the atmosphere (ds in Fig. 6) is dIf ¼ dIemission þ dIextinction þ dIscattering The dIextinction comes from Lambert’s law, which states dIextinction ¼ ae $If ds

Fig. 7

Illustration of a planar stratiﬁed atmosphere assumption.

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The ae is the extinction coefﬁcient and it is the sum of the absorption coefﬁcient, ka, and the scattering coefﬁcient, ks. Kirchhoff’s law states that, in thermodynamic equilibrium, emission is equal to absorption, and therefore: dIemission ¼ ka $Bf ðT Þds Furthermore, the dIscattering term is electromagnetic energy that is scattered into the direction of the incremental distance ds, as opposed to s term in the extinction equation where the energy is scattered away from the ds direction. The source of the electromagnetic energy that is scattered into the ds direction could have many sources, which are lumped into the scattering source function (Js). The scattering source function equation is ð ð 1 Js ¼ jðs; s0 ÞBf ðT; s0 ÞdU 4p 4p

which determines the contributions of the scattered energy from all directions (’s) in 4p steradians. Bf (T, ’s) is the incident radiation from the ’s direction, and j(s, ’s) is the phase function. The brightness temperature simulations typically use the Henyey–Greenstein model (Henyey and Greenstein, 1941) for the phase function. The dIscattering is dIscattering ¼ ks $Js ds The distance along the s direction can be approximated as z $ sec(q) (see Fig. 7). The optical depth, or opacity, is deﬁned as ð z00 sðzÞ ¼ ae ðzÞ dz z

sðsÞ ¼ secðqÞ sðzÞ Combining the results: dIf ¼ ka Bf ðT Þ ae If þ ks Js ds For now, the rest of the radiative-transfer-equation derivation will ignore scattering, but the precipitating numerical solution will pick it up again in the next section. Multiplying both sides by es(z) afterwards and integrating from z0 to z00 in the above equation results in the intensity at the antenna: ð z00 0 00 00 If ðz00 Þ ¼ If ðz0 Þ$e½sðz Þsðz ÞsecðqÞ þ secðqÞBf ðzÞe½sðzÞsðz ÞsecðqÞ ae ðzÞdz z0

As an exercise to describe common terminology, we integrate both sides of the equation, while temporarily ignoring emission between distance z0 and z00 , gives the transmittance and opacity of the atmosphere.

1.16.2.2.3

Absorption

In the Earth’s atmosphere, the absorption of radiation originates because of molecular constituents (e.g., N2, 02, and H20). Molecular constituents have three mechanisms to absorb incident electromagnetic radiation, that is, energy can be stored in electronic states, vibrations between atoms, and the rotation of the atoms around their center of gravity. These absorption mechanisms depend on the wavelength of the incident radiation. Visible and ultra-violet wavelengths are absorbed when electrons are excited to a higher electron state (and emitted when they are released to a lower state). The mid- to near-infrared wavelengths are absorbed by vibrations of the interatomic spacing (e.g., vibration of diatomic molecules). Microwave and far-infrared frequencies are mainly absorbed by rotational transitions of molecules. The mechanisms are related to the wavelength of the excitation, for example, electronic states generating the EM waves with the smallest wavelength and the larger rotational transitions the longer microwave EM waves. Radiative transfer models typically model each energy storage mechanism in what is called a line-by-line model (Liebe, 1992; Smith, 2002). Hydrometeors can also absorb electromagnetic energy. A hydrometeor is condensed atmospheric water vapor, and, if the hydrometeor is large enough, it will scatter microwave electromagnetic energy. The absorption of hydrometeors follows the same reasoning as the scattering presented in “Scattering” section. For a more in-depth explanation, please see Ulaby and Long (2014a), Stephens (1994), Janssen (1993a), and Armstrong and Nicholls (1972).

1.16.2.2.4

Scattering

The volume scattering coefﬁcient (ks) determines the power scattered within the atmosphere (units of Nepers/m). The scatterers (e.g., rain drops) have no coherent phase relationship, because they are assumed to be randomly distributed within the volume.

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Also, the density of scatterers is assumed to be low enough that particles do not overshadow one another. These two assumptions lead to this equation, from Ulaby and Long (2014a): ð r¼N ks ¼ pðr ÞQs ðr Þdr r¼0

where p(r) is the drop-size distribution, which is the number of drops per m3 per unit increment of r with dimensions of m 4, and Qs(r) is the scattering cross-section of a sphere of radius (r) with dimensions of m2. A commonly used example of modeling p(r) is described in Marshall and Palmer (1948). Scattering efﬁciency, xs ¼ Qs/pr2, and the parameter c, c ¼ 2pr/lo, can be used to rearrange the scattering coefﬁcient equation as: ð l3 N 2 c pðcÞxs ðcÞdc ks ¼ o 2 8p o Mie (1908) found the solution for the scattering (xs) and absorption (xa) efﬁciencies for a dielectric sphere of radius, r. The complete solutions are in Ulaby and Long (2014a), and the equation for the scattering efﬁciency is repeated here: xs ðn; cÞ ¼

N 2 X ð2l þ 1Þ jal j2 þ jbl j2 2 c l¼1

The variables are the complex index of refraction (n) and the Mie coefﬁcients (al and bl). For a more in-depth explanation of the theory behind hydrometeor scattering, please see Janssen (1993a) and Ulaby and Long (2014a). Fig. 8 plots the scattering efﬁciency as a function of hydrometer diameter at several microwave frequencies. The phase of the hydrometer also impacts the scattering, which is also shown in the ﬁgure. Deirmendjian developed an iterative procedure for calculating the Mie coefﬁcients. When |n c| 1, the Mie coefﬁcients are calculated using the Rayleigh approximation, and the particular algorithm used by the atmospheric model is from Wiscombe (Deirmendjian, 1969; Wiscombe, 1980). Actual measurement of scattering from a convective cell is shown in Fig. 9 from an airborne passive microwave radiometer (Blackwell, 2001; Leslie, 2004). The smaller the wavelength, the scattering signature is larger from cosmic background radiation. Fig. 6 has the various input parameters used to simulate the radiances. An example numerical solution can be found in Rosenkranz (2002).

1.16.2.2.5

Surface Emissivity

The surface emissivity deﬁnes the amount of power that is absorbed or emitted by the surface material. Not all material is a blackbody, but considered “grey” because it reﬂects and absorbs radiation. To represent these materials, the brightness temperature is the transmissivity (introduced in “Surface interactions” section) multiplied by physical temperature of the material. Tv εv ðqi Þ ¼ 1 jrv j2 $T ¼ B T

Fig. 8

Mie scattering of water spheres in two phases.

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Fig. 9

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Radiance perturbations due to a convective cell. (Leslie, 2004)

Under thermal equilibrium, the fraction of radiation absorbed is also the fraction radiated; therefore the brightness temperature from the surface is: TBv ¼ εv ðqi Þ$T ¼ 1 jrv j2 $T

1.16.3

Sensing Techniques

The previous sections introduced the nature of thermal electromagnetic radiation and the geophysical mechanisms that are used to retrieve a geophysical parameter, i.e., a data product. This section covers the major techniques of how to design an instrument that measures the microwave radiation. As expected, microwave instrumentation is different compared to other parts of the spectrum. For example, the microwave wavelengths do not require the smooth mirrors like the visible wavelengths and can redirect radiation with a precision wire grid.

1.16.3.1

Collecting Radiation

The ﬁrst section will explain the standard technique to couple radiation from the environment to the instrument to be quantiﬁed, i.e., measured. These techniques are the same for active or passive instruments, and even for other applications like communication. The primary limitation for both passive and active sensors is the directional discrimination of upwelling radiation with a reasonably sized antenna; active sensors have the added complication of obtaining adequate return signal. These limitations can conﬂict with the required timeliness and coverage for some data product of interest. Three common characteristics of sensor architectures are the ground swath, horizontal spatial resolution, and revisit rate. The ground swath is bounded by the maximum spatial extent of the sensor’s measurements will point from the platform. For example, an aircraft sensor could point its antenna to the left and right sides of the aircraft as the aircraft moves in the forward direction, and the swath would be the distance between the maximum left measurement and the maximum right measurement. The horizontal spatial resolution is determined by the microwave frequency, size of the antenna, and the distance between the platform and targeted phenomenology. The revisit rate is primarily due to the platform ﬂight path and the number of platforms. These characteristics are dominated not only by the choice of platform, but also by the sensor’s antenna design and mechanism to scan the antenna (can be steered mechanically or electronically). Attributes of a radiometer include the antenna’s directional response, the spectral response, radiometric calibration accuracy, and the radiometric sensitivity. Within the microwave spectrum, it is common to express power in terms of brightness temperature using the Rayleigh–Jeans approximation (see “Emission and brightness temperature” section). The antenna temperature is the power measured from the antenna and can be modeled as: ðþ 1 Dðq; fÞ$TB ð f ; q; fÞ dU df ðkelvinsÞ TA ¼ 4p The antenna temperature integrates the brightness temperature, Tb, over the entire gain pattern of the antenna, D(f, q, f). Therefore, D(f, q, f) gives the directional response of the radiometer’s antenna. The next sections will discuss the gain pattern of the antenna. Fig. 10 is an example of mapping the radiance into an antenna pattern’s footprint on the surface. The radiance data is from a NOAA cross-track radiometer called the Advanced Microwave Sounding Unit.

1.16.3.1.1

Antenna fundamentals

This section will derive the brightness temperature equation from the “collecting radiation” section. Oscillating electric and magnetic ﬁelds induce a current on an antenna. The alternating current propagates down a transmission line to induce a voltage in the instrument. The voltage is proportional to the characteristics of the EM waves, which allows the determination of amplitude and polarization of the incoming radiation. The design cycle of an antenna is primarily centered around collecting the targeted

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Fig. 10 AMSU brightness temperature projected onto the surface within the antenna pattern’s FWHM footprint. This channel has a center frequency of 50.3 GHz, which is considered a window channel. The ocean and land have different surface emissivity.

frequency of electromagnetic waves from the correct direction. Due to reciprocity, the characteristics of transmitting are the same as receiving. This section will cover important antenna characteristics. The “Microwave Radiation” section left off with speciﬁc intensity (which other ﬁelds of study like physics calls spectral radiance). In “Wave equations and Poynting power” section, the timeaveraged or instantaneous power in the Poynting vector was introduced. For antennas, this function can be separated out to a term containing the variables of range, R; frequency, f; and power/amplitude, P in the Smax term and all the angular dependence into the normalized radiation intensity F. SðR; f ; P; q; 4Þ ¼ Smax ðR; f ; PÞ $ Fðq; 4Þ

W m2 $Hz

Normalized radiation intensity is dimensionless and represents the directional response that the antenna will receive or transmit energy. Fig. 11 is the normalized radiation pattern for a common antenna used at microwave frequencies called a corrugated circular horn (Balanis, 1982). The F(q,f) are the same on the left- and right-hand sides but plotted in different ways. The left-hand side is

Fig. 11

An example normalized radiation pattern of a corrugated circular horn antenna.

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a three-dimensional representation as a linear function of angle, while the right-hand side is a plot in spherical coordinates and a better illustration of the radiation pattern in three-dimensions (except the power scale to see the ﬁne details). Antenna theory uses a tool called a pattern (or beam) solid angle, Up. It represents the spherical surface area of the normalized radiation pattern into a single value in steradians. The solid angle of a normalized radiation pattern is: þ Up ¼ F ðq; fÞ dU The pattern solid angle has a minimum value if the antenna receives/transmits energy in all directions (i.e., isotropic), which is 4p. By deﬁnition, the maximum value of F(q,f) is one, and if some directions (i.e., angles) were not equal to the maximum during the normalization, they were less than one. This leads into another antenna property called directivity, which is the isotropic pattern solid angle divided by the antenna’s pattern solid angle: D ¼ 4p=Up Directivity, D, is also dimensionless but goes in the opposite direction of pattern solid angle as a higher directivity means a narrower normalized radiation pattern. Next, the power received by an antenna is considered. The total power radiated by a source is: þ þ Prad ¼ R2 SðR; f ; P; q; fÞ dU ¼ R2 Smax ðR; f ; P Þ F ðq; fÞdU ¼ R2 Smax ðR; f ; P ÞUp If we combine the directivity and the total radiated power, we can show another deﬁnition of directivity: D¼

4pR2 Smax Prad

In practical antenna and transmitters, the power radiated is not the power of the transmitter, and the difference is captured in the radiation efﬁciency, xr, where the antenna gain is the product of the radiation efﬁciency and directivity. For an unrealistic case of a lossless antenna (i.e., no power is dissipated in the antenna), the radiation efﬁciency is equal to unity. xr ¼

Prad 4pR2 Smax ; G ¼ xr $D ¼ Pt Pt

Now the discussion will move toward receiving power through an antenna, which due to the reciprocity theorem of electromagnetics, the receiving radiation pattern is the same as the transmitting radiation pattern. An antenna has a physical area, which may or may not represent how well it receives energy, for example, a small dipole antenna (i.e., wire) receives much more energy than its cross-sectional area would suggest while a dish antenna receives energy closer to the physical area of the aperture. The effective area metric Ae (m2) is deﬁned as the ratio of the power that the antenna intercepts divided by the power density (i.e., Watts divided by Watts per meter squared). It can be shown (Ulaby and Long, 2014a) that this ratio is proportional to a couple of other metrics discussed so far: Ae ¼

l2 l2 D¼ ¼ ha Aphy 4p Up

The power received is directly proportional to the source aperture area and the receiver aperture area, but inversely proportional to the square of the range as the solid angle as illustrated in Fig. 12. The ﬁgure shows that the power through the receiving aperture is the speciﬁc intensity of the source times the area of the source multiplied by the solid angle of the receiving aperture. In this

Fig. 12 Illustration showing a transmitting or source aperture and a receiving aperture (Adapted from Ulaby, F. T. and Long, D. G. (2014a). Microwave radar and radiometric remote sensing. Ann Arbor: The University of Michigan Press.).

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simplistic example, the solid angle is the receiving aperture divided by the distance squared. The source properties are orange and the receiving properties are blue. Note that the R2 term is in the solid angle. If we return to the differential spectral power from the equation in Fig. 12, dPR ¼ If $Ae $Fðq; fÞ dU and have a closed integral over 4 p steradians, the equation below shows the relationship of the power measured by the instrument and the directional sensitivity of the antenna. The speciﬁc intensity is replaced with brightness temperature (assuming the RayleighJeans approximation): þ ð þ 2kT Fðq; fÞ dU PR ¼ Ae If Fðq; fÞ dU ¼ Ae df l2 After making the appropriate substitutions in the last equation, it is important to consider a closed system that has uniformed brightness temperature in all directions shows the direct linear relationship between brightness temperature and power: PR ¼ 2kTB

Ae Up ¼ 2kTB l2

which is useful for instrumentation and characterizing noise power. Passive microwave radiometers are essentially noise power meters. The Boltzmann’s constant (in units of J/K) is k, and B is the frequency bandwidth. This is the same equation for the power of a resistor in thermal equilibrium. Furthermore, an antenna’s terminal can be represented as an antenna radiation resistance that has a power as a function of its physical temperature. Now returning to derive the antenna temperature equation, we return to an earlier power received equation using speciﬁc intensity. In the case of the remote sensing, the incoming radiation is not uniform and is a function of direction or angle, and the power measured is related to the scene speciﬁc intensity by ðþ l2 Dðq; fÞ$Ið f ; q; fÞ dU df PR ¼ 4p And if the speciﬁc intensity is replaced with the Rayleigh–Jeans approximation and the linear relationship between power and an equivalent black body temperature, which in this case is termed the antenna temperature, TA, the relationship becomes: ðþ l2 2k Dðq; fÞ$ 2 TB ð f ; q; fÞ dU df PR ¼ 2kTA ¼ 4p l TA ¼

1.16.3.1.2

1 4p

ðþ Dðq; fÞ$TB ð f ; q; fÞ dU df

Aperture

At microwave frequencies, the most common antenna is an aperture. Typically, it is a horn antenna, but it is also common to point a small aperture antenna, or feedhorn, at a parabolic reﬂector or “dish.” As seen in the last subsection, the antenna’s directivity is inversely proportional to the physical aperture size, but proportional to the square of the wavelength. To make the directivity ﬁner, the aperture or frequency has to increase (wavelength decrease). An “academic” or theoretical antenna is a square aperture (side length of l) with an uniform E-ﬁeld (Eo) illuminating it, which provides relatively easy math to represent the radiation intensity. 2 2 jEo j2 A2phy W jEðR; f ; q; 4Þj2 jEo j Aphy 2 p l sin ð q Þ SðR; f ; q; 4Þ ¼ ¼ $ F ð q; 4 Þ ¼ $ sinc l m2 $Hz 2h 2hl2 R2 2hl2 R2 The normalized radiation intensity of the square aperture with the limited E-ﬁeld produces a sinc function pattern (i.e., the Fourier transfer of a boxcar is a sinc function). The larger the lengths of the square, the narrower the sinc function. The red curve in Fig. 13 is an example. Antenna pattern have several attributes. The beamwidth is deﬁned as the angle that subtends the points from half the antenna pattern’s maximum value, and it is called Full Width Half Max (FWHM) or Half Power Beamwidth (HPBW). This attribute represents the direction of a majority of the radiation received by the antenna. Ideally, there would be no sidelobes (or backlobes) to allow the antenna aperture to discriminate ﬁne angular extent. This can be problematic when the brightness temperature scene has a large contrast such as a land sea boundary. A correction to remove systematic bias due to sidelobes can be derived, but at the design stage, an instrument characteristic called beam efﬁciency is calculated to try to quantify directivity of the antenna. The beam efﬁciency is an antenna attribute that helps measure how much radiation is within the mainlobe, which tries to quantify the contribution of radiation between the mainlobe and the sidelobes. There are many ways to demarcate the boundary, but the typically way is at the ﬁrst null in the antenna pattern. The beam efﬁciency is deﬁned as the solid angle contribution of the mainlobe divided by the total power in the 4p steradians. Typically beam efﬁciency requirement is 0.95 or 95%. Fig. 13 has three types of apertures with varying sidelobe levels. The ﬁrst is a hypothetical square aperture that is illuminated with a uniform electric ﬁeld, which has the highest sidelobe level along with the narrowest FWHM that is proportional to 0.88 l/L (L is the length of the square). The next lower sidelobe was a circular aperture with a uniformly illuminated electric ﬁeld, which has

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Fig. 13

A slice of the antenna radiation pattern of three kinds of antenna.

a FWHM proportional to l/D (D is the diameter of the circle). There was a trade with these apertures beween sidelobe level and beamwidth. These two are academic antennas, and there are many details to designing a practical antenna, but the ﬁnal antenna is commonly used in passive microwave remote sensing for its low sidelobes. It is a circular horn antenna with ridges lining the inside of the horn that effectively tampers the edges of the electric ﬁeld, which reduce the sidelobes. Each of these steps to reduce sidelobes (i.e., increase beam efﬁciency) required the diameter or area of the aperture to increase to maintain the same FWHM. This is the tradeoff between aperture size, beamwidth, and beam efﬁciency.

1.16.3.1.3

Synthetic apertures

In the previous section, the “rule of thumb” was given that the beamwidth is proportional to the ratio of wavelength over aperture diameter, but the area of the aperture can be made up of smaller antennas to synthesize a much larger equivalent aperture area. Furthermore, by controlling the amplitude and phase of the EM waves either coming from (receiving) or excited (transmitting), the synthetic aperture can steer the mainlobe to point in different directions. Returning to the “Antenna Fundamentals” section on the separating out the input parameters to the instantaneous power of an antenna, an array of antenna can further separate out the normalized radiation intensity, F(q,f), into the two separate factors: (1) the single antenna’s normalized radiation intensity and (2) the impact of the array. The impact of the array is commonly called the array factor, and the single antenna is the element factor. 2 N1 jEo j2 A2phy jEo j2 A2phy W X jji jkiLcosðqÞ Ai e e SðR; f ; q; 4Þ ¼ 2 2 $ Fðq; 4Þ$AFðqÞ ¼ 2 2 $ Fðq; 4Þ$ m2 $Hz 2hl R 2hl R i¼0 There are now three multiplicative terms that represent the amplitude (i.e., power), element angular distribution of a single aperture or antenna, and the array angular distribution. For the linear array in Fig. 14, the array factor is only a function of theta and only changes the element factor in that direction so that mainbeam’s beamwidth only narrows in the line of antennas and remains the beamwidth of the individual antenna (or element) unchanged in the perpendicular direction. Each individual antenna has a different amplitude (Ai) and phase (ji). The array factor, AF, angular sensitivity is the distance between the antenna or iLcos(q) (see upper left in Fig. 14) and the receiver induced j phase change. Changes in A can alter the shape AF and the phase, j, can alter the direction of the mainlobe, allowing for electronic beam steering. In this case, the element factor needs to be wide enough for all the AF to steer the beam within it. There is an example in Fig. 14 with an individual antenna having a 1 GHz frequency and a 0.1 m square aperture, which is uniformly illuminated and a side length of D (0.1 m in the example in Fig. 14). The resulting element factor is shown in the red curve and does not discriminate very well. The upper right ﬁgure is a polar plot of the case where there are a total of three smaller antennas where the red curve is the element factor and the blue is the array factor. The product, which is the normalized radiation intensity, is shown as a dashed black line. This synthesized aperture is not much better than before. The element is 0.1 m wide, and the antenna spacing, L, is half wavelength or 0.15 m apart. The new equivalent length is 0.3 m instead of 0.1 m. When we go to 15 antennas spaced half wavelength apart, or 2.1 m, the beamwidth is much narrower and is shown in bottom right-hand side. To illustrate the point of aliasing, the lower left-hand side has only three antennas, but they are spaced farther apart to have the three cover the same distance as the 15, but the sampling is too sparse and the AF has three peaks or mainlobes. This simple example can be extended to two dimensions with a Y or T formation instead of a line in this example. The ﬁrst spaceborne example is on the

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Fig. 14 Synthesized aperture using smaller apertures. The yellow is the net effect of the single antenna radiation intensity or element factor multiplied by the array factor.

European Space Agency’s Soil Moisture and Ocean Salinity (SMOS) satellite. The passive microwave synthetic aperture is called the Microwave Interferometric Radiometer with Aperture Synthesis (MIRAS) (McMullan et al., 2008).

1.16.3.1.4

Spatial resolution

Spatial resolution (or horizontal cell size) is a measurement’s geographical area on the ground that the upwelling radiation originates from. This section discusses how we determine the radiation collected and not the accuracy of the geolocation. Spaceborne and airborne measurements quantify the geodetic location of the energy received by projecting the antenna’s FWHM footprint on to the Earth’s surface. The 3-dB footprints can project a circle or more often an ellipse. For a conical scanner, the major and minor axis of the elliptical footprint stays consistent across the scan, but the cross-track scanner will have the cross-track axis (vs. the along or down track axis) increase as the scan angle increases. Therefore, the cross track has very unequal spatial resolution across the scan. Even though the cross track scanner might have a larger swath width, the utility of the most oblique measurements is limited due to the increased spatial resolution. Fig. 15 has FWHM footprints projected on to the surface as examples. The top two are cross-track patterns with two degrees of overlap. The bottom pattern is the conical scanning footprints. Most modern instruments will collect data as the system is integrating, which effectively smears the antenna pattern in the scan direction for both cross-track and conical scanners. The nomenclature calls the FWHM beamwidth as the Instantaneous Field of View (IFOV). The Effective Field of View (EFOV) is the resulting spatial resolution of the smeared antenna pattern, which is also deﬁned as the effective beamwidth as the angle subtended between the effective antenna pattern’s half power points. Finally, a new antenna pattern can be comprised of measurements already taken. By summing weighted nearby measurements, which effectively makes a composite antenna pattern out of the original antenna patterns, a new antenna pattern can be formed. This is often termed the Composite Field of View (CFOV). One technique is called the Backus–Gilbert technique that minimizes a cost function between trying to ﬁt the new composite antenna pattern to a target antenna pattern or reducing the instrument noise through increased averaging (Fig. 16). (Samra et al., 2010)

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Fig. 15 Examples of footprints projected onto the Earth’s surface with the contours representing the 3-dB beamwidth of the antenna’s radiation pattern.

Fig. 16 Cartoon example of a composite ﬁeld of view. The original or native antenna patterns are shown on the left and they are multiplied by scalar value and summed together to form a new antenna pattern. (From Samra, J. E., Blackwell, W. J. and Leslie, R. V. (2010). Spatial ﬁltering and resampling of multi-resolution microwave sounder observations. In: 2010 IEEE International Geoscience and Remote Sensing Symposium, pp. 2964– 2967.)

1.16.3.1.5

Swath

The geographic coverage requirement is dictated by the data product. Some data products require global measurements, and others might need speciﬁc geographical locations. It is difﬁcult for most microwave applications to be persistent over a single geographic area, and most platforms with microwave remote sensing instruments ﬁnd the best platform to be satellites in Low Earth Orbit (LEO). LEO typically gives the best balance of altitude and geodetic revisit on the ground. Passive microwave radiometers have primarily two scanning techniques to take measurements underneath the spacecraft depending on the principal data product. Sounders typically use a “cross-track” conﬁguration because of the simplicity and the fact that the targeted radiation is unpolarized (i.e., random). Cross-track systems are deﬁned as systems that take measurements perpendicular to the spacecraft’s forward motion or “ground track.” The feedhorns are pointed at a rotating reﬂector that projects the measurements to the left and right of nadir and also allows for calibration measurements when not looking downward. Moving just the reﬂector is typically the easiest technique to steer the antenna pattern, but it does cause the polarization of the antenna system to change as a function of rotation angle because the feedhorn is decoupled from the rotating reﬂector. Passive microwave imagers typically use the “conical scanning” technique where the feedhorn is ﬁxed with the reﬂector along with the receiver, but now the entire radiometer is rotated. This allows for better control of the polarization across the swath. Imagers are used for measuring surface properties such as soil moisture or wind direction where the polarization contains information about the data product. See Fig. 17 for a description of two operational satellites (one cross-track and the other conical). Fig. 18 has an example swath for each. There are advantages and disadvantages of each. Cross-track systems advantages include easier implementation, which combined with sounder’s higher frequencies (i.e., smaller aperture) allows the calibration to measure the system from “end to

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Fig. 17 Examples of operational passive microwave spaceborne instruments and their scan patterns on the Earth’s surface. ATMS (Kim et al., 2014) is on the left and SSMIS is on the right (Kunkee et al., 2008a).

Fig. 18

Projections on the ground (also known as 3-dB footprints) for the two main scanning geometries in passive microwave remote sensing.

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end” by having the rotating reﬂector view the external calibration targets. The lower frequencies used on conical-scanners (i.e., atmospheric window channels that are sensitive to surface properties) require large aperture s( meters), which are implemented with large meters-long deployed main reﬂectors. These large reﬂectors cannot view targets and must have the calibration targets cover just the feedhorns. Cross-track systems can have wider swath widths, which mean that a single scan will have measurements with a wider distance between the furthest left-hand side measurement to the furthest right-hand side measurement. This advantage is diminished by a disadvantage of the cross track system that have large footprint sizes at the edge of the swath. Finally, the rotation rotate of the two systems is different. The cross track usually has the advantage with a longer scan period, which allows longer integration time to take measurements (i.e., reduce measurement noise). (Charlton and Klein, 2006)

1.16.3.2

Measuring Radiation

This section reviews the techniques for measuring the power incident on the antenna. The incident power is converted to a quantiﬁed metric such as a voltage or digital number (also called a count). “Calibration” section covers converting or calibrating the digital number back into a radiance, or more commonly at microwave frequencies a brightness temperature. There are a number of receiver architectures used to measure radiation, and each has advantages and disadvantages. Before describing the architecture, we will cover the system design around the performance and science requirements.

1.16.3.2.1

System design

This section presents a hypothetical system design to illustrate the design process. The ﬁrst design consideration is whether the instrument must generate the microwaves or will it use the passive radiation of the environment. The science parameter of interest (e.g., temperature proﬁle or soil moisture) may have a readily available passive geophysical mechanism discussed in “Mechanisms of Retrievals” section that can be measured without the need of an active source. Typically, the passive signature or sensitivity of the geophysical parameter is too small to measure, and therefore the sensor requires more radiation than nature emits, and the sensor needs to measure the active system’s backscatter of radiation. Or the sensors need to measure a characteristic of the EM waves that is important for the retrieval like polarization (e.g., wind direction). While other retrievals need to measure the phase of the EM waves (e.g., radar signatures). The next step is a frequency plan consisting of the radiometric channels for passive instruments or transmit frequency of active instruments. Active instruments choose frequencies that can be efﬁciently generated (e.g., power) and is relatively transparent to the Earth’s atmosphere, weather, or vegetation, but interactions with the targeted phenomenology. An example is soil moisture which requires a frequency that penetrates the vegetation or tree canopy but will scatter from moist soil more than dry soil. A passive retrieval example is temperature proﬁles that require channels with sensitivity to the atmosphere. Passive instruments are vulnerable to other microwave radiation in their passbands and even though there are designated frequency bands for passive radiometry, and some instruments still emit out-of-band radiation that can cause interference. The Radio Frequency Interference (RFI) from other sources in the environment will inﬂuence some design decisions. Once the channel set or frequency is chosen, the antenna system can be designed to collect the radiation in a particular acquisition pattern. Typically, an antenna is rotated instead of the instrument or the platform (e.g., spacecraft), but the forward motion of the platform is utilized. More on the various acquisition patterns were presented earlier in this section. Now the system architecture can be designed around the frequency plan, geophysical phenomenology, and the RFI environment.

1.16.3.2.2

Total power radiometer

Radiometers measure the power received through the antenna within a speciﬁed bandwidth. The fundamental radiometer is termed “total power,” because it measures the power through the antenna along with the self-generated power of the sensor. The power radiated by nature is very weak so the radiometer needs to apply approximately 60 dB of power gain for proper detection. A basic schematic of a standard total-power radiometer is shown in Fig. 19. Kraus (1966), Rohlfs and Wilson (1996), Ulaby and Long (2014a), and Skou Le Vine (2006a) Typically, the total-power radiometer uses a superheterodyne conﬁguration to downconvert the microwave frequencies from the antenna to a more manageable intermediate frequency (IF). This is analogous to an AM

Fig. 19 A generic block diagram of a total power radiometer with a down conversion from the RF input frequency to an intermediate frequency before detection.

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Fig. 20 A ﬂowchart of the signal through the block diagram. (Adapted from Staelin, D. H. (2003). 6.661 receivers, antennas, and signals. (MIT OpenCourseWare: Massachusetts Institute of Technology), https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-661-receiversantennas-and-signals-spring-2003/index.htm (Accessed July 10, 2017). License: Creative commons BY-NC-SA.)

radio receiver. The manageability refers to the capabilities of the technology to implement ﬁlters, ampliﬁers, and detectors. As technology advances, the performance of components at higher frequencies is improving, which allow the microwaves to be directly ampliﬁed and detected; referred to as direct detect architecture. The sounder, also called a spectrometer, further separates the IF into bands or channels that measure separate parts of the atmosphere (i.e., weighting functions) to be discussed further in “Atmosphere” section. Note that the ﬁgure only shows one “channel.” After the bandpass ﬁlter, a square law device converts the incident power on the device to a proportional voltage. The square law device used is typically a tunnel diode or Schotty detector, which are very linear to incident power. The detector’s output voltage from each channel is converted to a digital signal, after ampliﬁcation and ﬁltering, by an analog-to-digital converter. Through digital signal processing, the signal is integrated (equivalent to a lowpass ﬁlter) and expressed as “counts.” In Figs. 20, there are graphical representations of the signal as it progresses through the block diagram in Fig. 19. The ﬁnal output of the total-power radiometer is a voltage that is proportional to the incident power from the antenna, but also the receiver noise temperature. The receiver noise temperature is added noise to the signal from the receiver’s components, which is related to the receiver’s physical temperature and termed thermal or Johnson–Nyquist noise. Thermal noise is the dominate noise contributor for microwave receivers (unlike optical receivers that are shot noise limited). As shown in the “Antenna fundamentals” section, the power is linearly related to temperature if the Rayleigh–Jeans approximation holds since the radiometer’s voltage is linearly proportional to the incident power: Vout y kGBðTA þ Trec Þ It is more evident now on the utility of having the radiance in units of kelvins as well as the receiver noise. The new part of the above equation is the instrument’s gain factor, G. It is unitless and unfortunately varies in time due to two factors: thermal changes of the instrument will change the gain (e.g., ampliﬁers) and second is a phenomenon in ampliﬁers called ﬂicker or “1 over f” noise, which represents the noise power spectrum having an inverse relationship to the frequency (unlike thermal noise which has a ﬂat spectrum). The gain is always large and also a function of the frequency as the ampliﬁers and bandwidth changes throughout the block diagram. Calibration consists of solving for the antenna temperature and estimating the resulting parameters: TA y

Vout Trec kGB

It is easy to recognize that variations in the gain can be mistaken as changes in antenna temperature. In the next section, we will discuss the sensitivity or precision and the accuracy that we can measure the antenna temperature.

1.16.3.2.3

Dicke radiometer

The sensitivity to changes in gain is a drawback to the total-power radiometer, which the Dicke switching technique attempts to address, but with a disadvantage of reduced sensitivity. Before describing the implementation of Dicke switching (Dicke, 1946),

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Fig. 21 A Dicke radiometer conﬁguration is shown with the Dicke switch between the antenna and receiver front end and a demodulator before A/D converter.

named after Robert Dicke who invented the technique, let us show how the instrument’s output voltage is now related to the instrument and antenna temperatures: Vout y kGB TA Tref For the Dicke radiometer, the voltage is proportional to the difference of the antenna temperature and a new reference temperature, and the receiver temperature, Trec, is no longer in the equation. Now if we have gain variations, they will not multiply against the system temperature (i.e., the sum of Ta and Trec), but only the difference of TA and Tref. There are options at what temperature to set the reference temperature at, but if Tref is a ﬁxed temperature, a good temperature would be close to TA if we wanted to be less sensitive to gain variations. This is termed the unbalanced Dicke radiometer. To totally eliminate gain variations, the receiver could vary Tref to match the TA, but it would make Vout useless for determining TA anymore. Instead, the information on TA would be in the feedback required to set Vout to zero, that is, to make Tref equal to TA. These are called balanced Dicke radiometers (Skou and Le Vine, 2006a). The mechanism that makes the output voltage proportional to the difference of the antenna and reference temperature is the rapid switching of the reference temperature before the receiver (i.e., before of the gain) and the modulator after the detector (see Fig. 21). The switching frequency has to be sufﬁciently fast enough that the gain does not change and is shorter than the integration time. The integration adds the scene TA plus Trec and Tref plus Trec together, but not before the demodulator, after the detector, applies a negative sign to the reference measurement, which effectively removes the Trec.

1.16.3.2.4

Polarimetric radiometer

The previous two radiometers have been for applications that only needed the horizontal or vertical polarizations of the surface (maybe at a ﬁxed off-nadir angle) or for sounders that were measuring unpolarized radiant from the atmosphere. They are classiﬁed as incoherent receivers since they do not measure the phase informtion, because the geophysical radiation does not have information in the phase because it is random. Phase information is important for synthetic aperture systems even though the geophysical radiation is random to synthesize or electronically steer the aperture. Some geophysical parameters like surface wind direction can be estimated from the Stokes brightness temperature measurements presented in the “Polarization” section. Scatterometers typically use measurements from different scan angles to get equivalent polarization diversity as the instrument passes over the ocean. Refer to Table 2 for the Stokes parameters that can completely characterize polarized radiation. There are two categories of polarimeters (Skou and Le Vine, 2006a): (1) use the antenna to separate the polarizations and use incoherent, or total-power, detection of the power or (2) coherent methods that manipulate the phase information of two orthogonal polarization measured by the antenna. In Table 2, the brightness temperature column shows the polarizations measured in the antenna system, and this technique is used in the passive microwave WindSat to measure wind speed and direction (Gaiser et al., 2004). The U and V are derived from the simultaneous measurement of the positive 45 degrees, negative 45 degrees, left-hand circular, and right-hand circular polarizations. The coherent methods perform the U and V as the direct cross correlation of vertical and horizontal measures per the “E ﬁeld” column in Table 2 (Piepmeier and Gasiewski, 2001). The U or real part of the cross correlation is called the “inphase” measurement and the V or imaginary part of the cross correlation is called the “quadrature” measurement, which will be discussed further in the next section. The coherent cross correlation in polarimeters is accomplished with a correlation radiometer, which a simpliﬁed block diagram is shown in Fig. 22. The vertical and horizontal are typical total-power radiometers, and their sum and difference give the ﬁrst and second Stokes parameters. The correlator can be implemented in analog using phase shifters and mixers or digitized and computed in a processor. The correlator will multiply the two signals together and integrate them, but the imaginary part will have a phase shift of 90 before multiplying. The Stokes parameter I is the sum of TV and TH, parameter Q is the difference of TV and TH. U is the real part of the cross-correlation, and V is the imaginary part. This is the general correlation radiometer for computing the Stokes parameters used for ocean wind speed and direction, but the receiver is more complex and requires

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Fig. 22

457

Simpliﬁed polarimetric radiometer with coherent detection of the third and fourth Stokes parameter.

additional calibration for the correlator (Lahtinen et al., 2003). More details on the receivers can be found in Skou and Le Vine (2006a), Rohlfs and Wilson (1996).

1.16.4

Mechanisms of Retrievals

This section explains the physical mechanisms and how the physical parameters can be retrieved using microwave remote sensing. An instrument is designed to measure the particular physical phenomena to best estimate or retrieve a physical property such as temperature, precipitation, soil moisture, wind direction. An instrument’s design from its spectral response (i.e., which part of the microwave spectrum), how it couples with the environment (i.e., antenna), and its accuracy and precision are all optimized to retrieve a speciﬁc geophysical parameter.

1.16.4.1

Passive Remote Sensing

The ﬁrst section will concentrate on our Earth’s mechanisms of passive remote sensing the atmosphere, and second section on land, ocean, and ice.

1.16.4.1.1

Atmosphere

Passive microwave remote sensing of the atmosphere produces a crucial data product for the weather forecast community. Modern forecasting use Numerical Weather Prediction models (Bell et al., 2010) that use the data to reduce the forecast error. With the proper design, a single measurement from an atmospheric sounder can be used to retrieve the vertical temperature proﬁle or the vertical water vapor proﬁle. As the instrument scans or points in different directions, a three-dimensional temperature or humidity structure can be measured. The vertical sampling is accomplished by carefully choosing the channel set (i.e., the number of channels, their center frequencies, and bandwidths) to be near the frequencies that the atmospheric constituents (i.e., molecules) store and emit microwave radiation. Fig. 23 shows a simulation of the atmospheric transmittance of the 1976 U.S. standard atmosphere (a representative atmosphere from seasonal and global measurements) that used a “line-by-line” model of the absorption as function of frequency (“Absorption” section). The y-axis is the zenith opacity (see opacity deﬁnition at the end of the “Radiative transfer equation” section), which is the opacity from the surface to the top of the atmosphere. The zenith opacity illustrates the transparency of the atmosphere versus frequency. The various valleys are transparent windows in between molecular absorption peaks. Based on the instrument’s application, channels can be either “window” channels that allow radiation to be freely passed through the atmosphere without the atmosphere either contributing its own radiation or attenuating the radiation. These windows are used by applications interested in reaching the surface or outer space such as radio astronomy, soil moisture, or communications. The opacity peaks are used to gain information about the atmosphere. In the microwave part of the spectrum, diatomic oxygen has a multitude of absorption lines around 50–60, 118.75, and 425.76 GHz that are strong enough to sound the atmosphere to retrieve temperature. Diatomic oxygen is relatively uniform in the atmosphere, which makes it a prime choice to measure the amount of radiation coming from the oxygen

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Fig. 23 Absorption through the entire standard atmosphere. Peaks are at energy states, typically rotational energy states at microwave frequencies, for primary molecular constituents like diatomic oxygen and water vapor.

which is proportional to the temperature of the oxygen and therefore the temperature proﬁle. Water vapor follows the same phenomenology, but water vapor is not uniform in the atmosphere, and varies greatly. A second transmittance curve, shown in Fig. 23 as a dashed line, has the water vapor removed from the standard atmosphere. It clearly shows which absorption lines are due to water vapor. Those water vapor lines can sound the atmosphere’s water vapor, if there is sufﬁcient amount of water vapor in the scene. The water vapor channels progressively measure deeper into the water vapor as there becomes more water vapor to measure. When we measure higher power levels of microwave radiation at frequencies near the water vapor absorption lines, we know that the radiation is due to the presence of water vapor and not a temperature increase of another constituent like diatomic oxygen. The other important phenomena to recognize are the impact of the water vapor continuum (Shine et al., 2012) that starts in the microwave region and continues throughout the infrared until the visible, but with some windows. The higher-frequency diatomic oxygen lines are obfuscated by the water vapor continuum, which limits their utility for sounding temperature proﬁles. Sounding of the atmosphere relies on a phenomenon called pressure broadening. Collisions of the molecular constituents add random phase shifts to the rotational moments of the molecules. This effectively broadens the spectral lines as a function of pressure. Since atmospheric pressure is a function of altitude, the shape of the line is much wider near the surface where the pressure is the highest. For either temperature or water vapor sounding, to “sound” deeper into the atmosphere a channel’s spectral bandwidth and center frequency are chosen off of the absorption line. If you chose a frequency close to the line, then the molecules at the highest altitudes will be measured by a spaceborne instrument, but if you move off the line, only the radiation at the lower altitude will be measured as the radiation will transfer relatively unimpeded through the upper atmosphere because the oxygen at that pressure will not store energy at those frequencies because the lower pressure does not broaden the line. Next we will adapt the material from “Emission and brightness temperature” section to be used in an airborne or spaceborne microwave application. We will consider “clear air” or an atmosphere without hydrometeors that would scatter microwave radiation.

The ﬁrst step is to replace the intensity (If) with the brightness temperature. Next, the position at the surface is set to zero (z0 ¼ 0) and (z00 ¼ top of atmosphere, TOA). We are going to jump to the answer and then back out how we got there. In Fig. 24, the upwelling radiation to the instrument has four contributions: Tb ¼ TbA þ TbB þ TbC þ TbD

l

A is the surface brightness temperature through the atmosphere into outer space B is the brightness temperature of the constituents (e.g., diatomic oxygen) in the atmosphere going up into the instrument l C is the same atmospheric constituents, but the energy that goes downward and is reﬂected off of the surface and back up to the instrument (and through the atmosphere again) l D is the deep space (i.e., cosmic background) radiation that goes through the atmosphere, reﬂects off the surface (or rain) and back through the atmosphere into the instrument l

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Fig. 24

459

A depiction of the various sources of radiation in an airborne or spaceborne application.

Next we will describe each contribution in detail. The surface contribution is the radiation from the earth, trees, water, etc., but some of that radiation is absorbed by the atmosphere (e.g., oxygen or clouds) before it reaches the instrument. The surface’s radiance, using Kirchhoff’s law of thermal radiation (see “Surface Emissivity” section), is the surface’s emissivity multiplied by the surface’s physical temperature (Ts), but the surface’s radiation is attenuated by the transmittance of the atmosphere (see “Radiative transfer equation” section). TbA ¼ εs $Ts $esð0;TOAÞ The next contribution is the radiation from the atmosphere going directly into the instrument. Here the Planck’s radiation is replaced with the physical proﬁle, T(z), under the Rayleigh–Jeans approximation. ð TOA ka ðzÞ$T ðzÞ$esðz;TOAÞ dz TbB ¼ 0

The third contribution is same as the second but reﬂected off the surface unless the surface has an emissivity of one (i.e., absorbs all incident energy). The radiation is attenuated by the reﬂection or kept the same if the reﬂectivity is one (e.g., metal), but it will be attenuated by the intervening atmosphere. TbC ¼ ð1 εs Þ$TbB $esð0;TOAÞ The last contribution is the radiation from behind the instrument, which is typically just cosmic background radiation, TC, but at some frequencies it can include the Sun (if at the right angle). This radiation has to converse the atmosphere twice (one downward and then upward) and be reﬂected off the surface (typically water, but hydrometers in the atmosphere can scatter the cosmic background radiation back into the instrument). TbD ¼ ð1 εs Þ$Tcosmic $e2sð0;TOAÞ Combining the contributions gives (opacity, tau, with input of altitude z is from z to TOA): Tb ¼ Tbu þ Tbsurf þ ð1 εs ÞTbd esð0ÞsecðqÞ Tbsurf ¼ εs $Tsurface : Tbd ¼ Tcosmic esð0Þ secðqÞ þ secðqÞ Combining the integrals at nadir gives: Tb ¼ εs Tsurf esð0Þ þ rs Tcosmic e2sð0Þ þ

ð z00

ð z00 0

T ðzÞae ðzÞe½sð0ÞsðzÞsecðqÞ dz:

0

ae ðzÞ 1 þ rs e2½sð0ÞsðzÞ esðzÞ T ðzÞ dz:

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Everything within the integral, except the temperature proﬁle, can be placed into a term called a weighting function. W ðzÞ ¼ ae ðzÞ 1 þ rs e2½sð0ÞsðzÞsecðqÞ esðzÞsecðqÞ : If extinction coefﬁcient is large enough to ignore the contributions of the surface and cosmic background, then the equation can be written as a Fredholm integral equation of the ﬁrst kind: Tb ¼

ð z00

W ðzÞT ðzÞdz:

0

This is the principal equation behind proﬁle sounding and illustrated in Fig. 27. Fig. 25 is an example of a channel set to retrieve water vapor proﬁles and cloud ice. This design uses double-sidebands, so the image on the left is mixed with the image on the right to create a single band at the intermediate frequency (i.e., superheterodyne) and therefore a single radiance value. The channel at 205 GHz is a single sideband channel. This channel is more sensitive to the scattering from very small cloud ice particles aloft that are very high in the atmosphere. Using the radiative transfer model and the channel information from Fig. 25, the water vapor weighting functions are shown in the left-hand side of the Fig. 26. For temperature weighting functions near uniformly mixed constituents (e.g., diatomic oxygen), the reliability represents the relationship between channels measuring temperature proﬁles. The radiation emitted from the water vapor is still a function of the physical temperature of the water vapor, but unlike the uniformly mixed diatomic oxygen, water vapor can be absent from the measurement. Instead of showing temperature weighting functions of water vapor channels, it is more useful to plot their water vapor burden. The temperature weighting functions are a function of altitude in either pressure or height, but water vapor burden is a function of water vapor areal density to represent the sounding into the column of water vapor (see right-hand side of Fig. 26).

1.16.4.1.2

Surface

Passive microwave remote sensing of the surface is a special case of the atmospheric remote sensing. First, surface remote sensing requires the atmosphere to be transparent, which dictates that the frequencies are low (i.e., wavelength long). This means that there is little to no contribution from B and C in the spaceborne radiative transfer equation above. The dominant radiation contribution switch as the atmospheric remote sensing concentrated on B as the primary source of signal, and the other contributions only make the retrieval more difﬁcult by varying the radiance without adding information on the geophysical parameter being retrieved (e.g., temperature). Now the surface emissivity (i.e., ocean salinity) and temperature are the primary geophysical parameters being retrieved. We discussed the EM wave interaction with the surface in “Surface interactions” section, but now need to provide a deeper explanation of how microwave radiation interactions with the surface. There are two properties of the media that characterize how EM propagate through a boundary between two types of media. There were the permittivity and permeability, but a third property characterized the loss of the material, which attenuates the EM waves as their travel through the media. For most remote-sensing applications, the permittivity is the driving property.

Fig. 25

An example channel set to sound water vapor.

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Fig. 26

Resulting temperature weighting functions and water vapor burden from example channel set in Fig. 25.

Fig. 27

Illustration of the weighting function.

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In “Microwave Radiation” section, Fig. 4 plotted the reﬂectivity for two different media transitions. One was modeled water and another was dry land. The difference of these two media was in the relative permittivity, i.e., dielectric constant. A more complete description of the permittivity is the complex permittivity, or dielectric constant of the media is: js εeff ¼ εr ε0 1 uεr ε0 The s is the conductivity (siemens/meter), which as an imaginary number will attenuate the electric ﬁeld solution. The surface emissivity has several key characteristics that determine its value: ﬂat or rough (also known as specular or Lambertian), lossless or lossy (conductivity), homogenous or heterogeneous (dielectric constant). Models are theoretically or empirically derived for various surfaces from soil to sea ice with varying degrees of complexity. From these models, an instrument can be design to provide maximum sensitivity based on frequency, off-nadir angle, and polarization. The emissivity of the ocean is a function of temperature, roughness due to surface winds, and the salinity, which can all be retrieved with microwave remote sensing (Ulaby and Long, 2014a). For example, soil moisture is retrieved by both active and passive L-band instruments, but each has their own advantages based on surface characteristics. Passive upwelling radiation has higher sensitivity to soil moisture as long as the vegetation over the soil has limited water content (due to large changes in dielectric constant verse moisture), but typically coarse spatial resolution at the relatively low frequency with a reasonable aperture. Active L-band radar can gain very ﬁne resolution using synthetic aperture, but due to surface roughness and vegetation scattering, which reduces the backscatter and therefore the sensitivity (Ulaby and Long, 2014a). Another example comes from retrieving ocean characteristics. Active and passive microwave instruments can measure ocean wind speed by measuring the backscattering of either the active coherent microwave signal in the case of the radar or the reﬂection of the cosmic background radiation for the passive system (both rely on the change in reﬂectivity because of the winds). Furthermore, both active and passive can determine the wind direction by measuring how the winds impact the polarization differently (Ulaby and Long, 2014a). A ﬁnal example is snow coverage or vegetation coverage. For these applications, the brightness temperature term in the spaceborne radiative transfer equation is expanded to include the additional layer. The B term now includes another media layer on the surface that has similar properties as the atmosphere. TbA ¼ εs $Ts $esð0;TOLÞ þ TL $ 1 esð0;TOLÞ þ rL $esð0;TOLÞ $TL $ 1 esð0;TOLÞ $esð0;TOAÞ The ﬁrst term is the emission of the surface under the coverage (TOL is top of layer), but attenuated by the transmittance of the coverage. The next term is the physical temperature of the coverage (TL) times one minus the transmittance, which can be derived from the ﬁrst equation from the “Atmosphere” section if we treat the layer as a special case of an atmospheric layer and assuming the coverage is homogenous, uniform temperature, and no scattering (Woodhouse, 2006a). The ﬁnal summed term is the coverage radiance reﬂecting off the surface (rL) and then reduced by its own transmittance. The transmittance multiplied against all the summed terms is the atmosphere between the coverage and instrument, but the frequencies used in surface retrievals make this term very close to one. There are other complexities, which include the cosmic background radiation reﬂecting off both the coverage and possibly the surface underneath. Sun glint can be a problem at certain angles, but those are usually minimized by orbit selection (Woodhouse, 2006a).

1.16.4.2

Active Remote Sensing

Active remote sensing requires transmitting coherent EM wave at a target, and the target can vary from celestial objects or pointed toward the ground. The active system has two additional characteristics that the passive does not typically measure: (1) the time it takes for the transmitted EM wave to return (or arrive if the receiver and transmitter are in different locations) to the receiver and (2) the phase information of the returned EM wave. Both active and passive are interested in the polarization in some applications, but radar gains additional information from the Doppler shift. Since EM waves travel at the speed of light, the duration between the transmission and receipt of the EM wave can determine the range, which the altimeter is an essential application of this type of radar (RAdio Detection And Ranging, but is no longer capitalized). Scatterometers measure the strength and polarization of the returned EM wave, which interacts with the target through scattering (i.e., not absorption/ emission). The ﬁnal category is the imaging radars that are designed to leverage the Doppler shift to greatly increase the ground resolution. As the examples in the last section on passive surface remote sensing suggest, active remote sensing uses frequencies that penetrate the atmosphere, but the transparent atmospheric frequencies are typically the lower microwave frequencies and easier to generate sufﬁcient power levels. When an active system illuminates the ground, there are two principal characteristics used in active remote sensing: (1) the time series of the return waveform’s amplitude and (2) any Doppler frequency shift due to either a moving instrument platform or target. Radar can have “super” resolution within the main antenna footprint by binning the return signals duration and frequency shift, which is utilized by SAR. A good reference for active microwave remote sensing can be found with Woodhouse (2006a).

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1.16.4.3

463

Terrestrial and Jovian Planets

The same principles presented here can be applied to the other terrestrial and Jovian planets. The atmospheric chemistry is very different and the frequency plan must accommodate the molecular constituents of alien planets. This has been accomplished on several missions to nearby planets (Taylor, 1972; Janssen, 1993a).

1.16.4.4

Radioastronomy

Microwave radiometry began in the ﬁeld of astronomy, which spun off the ﬁeld of radioastronomy. In 1933, Karl Jansky, an employee of Bell Laboratories was investigating sources of interference to transatlantic radio telephone service. He identiﬁed nearby and distant thunderstorms along with a steady hiss of unknown origin. Jansky concluded that the hiss was radiation coming from the Milky Way, and it was conﬁrmed by Grote Reber in 1937 when Reber built the ﬁrst radio telescope in his backyard in Wheaton, IL. In 1965, Arno Penzias and Robert Wilson accidentally measured the cosmic background radiation with the Horn Antenna while working at Bell Telephone Laboratories in Holmdel, NJ, which won them the Nobel Prize in 1978. The discovery of cosmic background radiation helped support the Big Bang theory. The cosmic background radiation provides a stable and convenient calibration source for spaceborne instruments. Radioastronomy also studies many sources in the universe that emit radio and microwave emissions. Examples of cosmic sources include quasars, pulsars, masers. The ﬁeld typically calls their antennas and instruments radio-telescopes. Their radiometric signatures are so faint and the angular extent so small that the receivers are cooled to liquid hydrogen temperatures ( 20 K) and interferometric antenna arrays that simulate antenna thousands of miles wide (Rohlfs and Wilson, 1996).

1.16.5

Calibration

The sensing technique section ended with digital numbers that were proportional to the geophysical parameter of interest but were not converted to the units of radiance (e.g., brightness temperature). This section covers standard techniques to convert (i.e., calibrate) the raw digital numbers to a radiance or correlation coefﬁcient.

1.16.5.1

Data Processing

This section describes some of the standard practices and nomenclature in processing microwave remote-sensing data. Organizations like National Aeronautics & Space Administration (NASA), National Ocean and Atmospheric Administration (NOAA), and European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) have standardized the data ﬂow. Table 3 gives the data product levels and describes the attributes (e.g., https://science.nasa.gov/earth-science/earth-science-data/data-processinglevels-for-eosdis-data-products). Table 3

NOAA & NASA data product designations

Designation

Designation

Description

Level 0

Raw Data Record (RDR)

Level 1a

Temperature Data Record (TDR)

Level 1b

Sensor Data Record (SDR)

Level 2

Environmental Data Record (EDR) or Climate Data Record (CDR) N/A N/A

Basic telemetry (i.e., raw digital numbers) from the instrument and platform with communication headers removed, but contains calibration and engineering unit conversion information Native-resolution instrument data that has been calibrated, i.e., convert the raw digital number to radiances or housekeeping telemetry (e.g., voltages or temperatures). The data has been time-referenced and geolocated. Some products have the calibration or georeferencing coefﬁcients appended, but not applied. The radiances have not been corrected for antenna pattern artifacts (e.g., sidelobes) Not all products have this level, but it is very similar to 1a, but with additional correction factors. This typically includes the conversion from antenna temperature to brightness temperature This is the geophysical data product retrieved from the Level-1 data. Geophysical data products mapped to a common grid Model output or results from analyses of lower-level data (e.g., variables derived from multiple measurements).

Level 3 Level 4

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1.16.5.1.1

Data product flow

Instrumentation has a progression or ﬂow of data from the most fundamental data coming from the instrument to the ﬁnal data product used by the end users (e.g., NWP data assimilation). Table 3 provides the progression of the data. Level 0, or raw data, consists of the instrument data, platform data, and engineering and calibration conversion coefﬁcients. Typically, Level 0 contains all the necessary information to bring the data to Level 1 but reserves the ability of the end user to execute their own Level 1 algorithms (e.g., calibration or geolocation). Level 0 data from microwave instruments are similar to other wavelengths and include the science data (e.g., radiometric counts or in-phase and quadrature components), housekeeping (e.g., voltage monitoring), and calibration data (e.g., onboard temperature measurements of calibration targets). The platform (e.g., spacecraft bus) provides the orientation of the bus through geodetic coordinates (i.e., latitude, longitude, and altitude), attitude references (e.g., yaw, pitch, roll Euler angles in a rotation matrix or a quaternion), absolute time reference (i.e., GPS time). Level 1 data is calibrated (e.g., radiance or power), timestamped to Coordinated Universal Time, and geolocated at the instrument’s native spatial resolution. Level 1 includes designations of letters, typically a through c (e.g., Level 1a), but the deﬁnitions of the letters are dependent on the instrument and organization. For passive microwave instruments, Level 1a is typically the antenna temperature measured by the instrument, and the Level 1b has the artifacts of the antenna pattern removed to produce the scene’s brightness temperature. For active microwave instrument, Level 1a is the instrument counts and Level 1b is the calibrated reﬂected power. Instruments have Level 1 Algorithm Theoretical Basis Document (ATBD) that describes the calibration procedure. Level 2 is the geophysical parameter, which is usually the most useful to the end users. Level 2 has its own ATBD that describes the physics on how the radiance or power is converted to the geophysical parameter (e.g., rain rate) and the particular algorithm used to estimate the geophysical parameter. Level 2 is typically still at the native spatial resolution of the instrument. Level 3 takes the native spatial resolution of the geophysical parameter and relocates the measurement to a standardized grid to make colocation with other instruments easier. Level 4 can consist of analysis of the Level 3 data from multiple instruments for the same geophysical data product. As the data progresses through the levels, less of the native or raw data is included because the utility may diminish for users of the higher levels. For example, an instrument housekeeping voltages used to determine instrument’s health are not needed in Level 1 data products, but some attributes of the instrument may be useful to end user to indicate the data product’s quality level. Higher levels will have quality ﬂags indicating if there were any anomalies discovered by the algorithms. For example, a calibration algorithm of a passive microwave radiometer might have momentary lunar intrusion in its view of deep space (i.e., calibration reference) that required the calibration algorithm to use less space view measurements and therefore decreasing the performance of the calibration reference. The end user may decide to remove that measurement from their algorithm.

1.16.5.1.2

Correction factors

Error can have both systematic bias and random ﬂuctuations. All attempts are made to remove systematic bias that can be quantiﬁed before launch and used to apply corrections in the data product algorithms. Common corrections include compensating for the instrument’s nonlinearity. Another is contamination of the measurement by the sidelobes. For an example with more details, see Weng (2013). A common microwave data product correction is the conversion of antenna temperatures to brightness temperatures (the primary difference between Level-1a and Level-1b in Table 3).

1.16.5.2

Calibration Techniques

There are several options for calibration that have advantages and disadvantages based on the application. Some applications need to be compact, while others require long-term stability. We will discuss a few of the techniques that are commonly used. Not presented is the calibration of the passive microwave sensor with a synthetic aperture, but a detailed description can befound in Brown et al. (2008). Calibration of a polarimetric instrument can be found in Peng and Ruf (2008).

1.16.5.2.1

Periodic absolute calibration

A common calibration technique consists of using two targets of know radiance the radiometer periodically measures to calibrate the unknown scene radiance. The output voltage of the radiometer will vary even though the input radiance is the same because the gain of the radiometer changes with temperature and due to random ﬂuctuation due to ﬂicker noise (also called 1/f noise due to its power spectrum). These two factors require periodic calibration throughout the data collection. The two calibration radiances, or references, allow the calculation of a transfer function between the radiometric counts and antenna temperature (i.e., radiance). This is called a two-point calibration, which produces an afﬁne relationship. The linearity assumption breaks down for two reasons: (1) the inherent error of the Rayleigh–Jeans approximation of Planck’s radiation law and (2) practical radiometer’s output voltage is not completely a linear function of the input radiance. The breakdown of the Rayleigh–Jeans approximation is discussed in the next section under using the cosmic microwave background as a calibration standard. Fig. 28, on the right-hand side, is an illustration of the transfer function. On the left-hand side, a common form of the calibration equation on the top with a gain and offset. TC is the antenna temperature of the cold calibration measurement (usually deep space for space sensors) and TH is the hot calibration measurement. Each of the calibration measurements has a corresponding count measurement after measuring the cold and hot calibration sources (i.e., CC and CH). The lower left-hand side has a typical parabolic correction for nonlinearity. The TNL is derived from prelaunch calibration and discussed further in the upcoming “Prelaunch Characterization” section.

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Fig. 28

465

Calibration equations and calibration illustration.

A design decision must be made to pick two references to be used in the periodic calibration. Options for references are discussed in the next section. For spaceborne applications, the cosmic background radiation is a simple and accurate option for a cold reference. The standard option for the hot reference is an onboard calibration target. These precision calibration targets are highly accurate, but bulky. There are more compact calibration reference options that can be built into the receiver but typically require a compromise on calibration stability. The cross-track ATMS calibration algorithm is presented in Weng et al. (2013) and the conically scanning SSMIS (Wessel et al., 2008; Wentz and Draper, 2016).

1.16.5.2.2

Dicke switching

As discussed under the receiver architecture, a Dicke radiometer will modulate the output by alternating between the scene radiation and an internal reference. Modulating the internal reference into the signal path allows the trending of the receiver’s gain due to temperature changes and ﬂicker noise, but at the expense of using up time that could be used to reducing noise on the scene measurement. The unbalanced Dicke conﬁguration still needs to be periodically calibrated as the output is still proportional to the instrument gain times the difference between the antenna temperature and reference temperature. The balanced techniques can be much more stable and only require infrequent external calibrations. If the instrument ﬂies on an airborne platform, the external calibration can be as infrequent as before and after the ﬂight or series of ﬂights. The total-power radiometer will need frequent calibrations on the order of seconds (discussed further in the next section). A more in-depth calibration description of common Dicke-type radiometers can be found in Ulaby and Long (2014a) and Skou and Le Vine (2006a).

1.16.5.3

Performance Metrics

Instruments need performance metrics to determine if the design will meet the requirements of the application (i.e., the data products). Typical metrics consist of two statistics of the measurement error. One is the static error, which is the difference between the measurement and the actual value that is being measured. This error can have different names such as systematic error, bias, or accuracy. The static error is the consistent error the instrument will make for repeated measurements of the same input radiance. The other statistic captures the random part of the error, which is the part of the error that changes with each new measurement, even though the input radiance has not changed. The random error is also called the dynamic error, standard deviation, or precision. These error sources can be more complex, such that the static and dynamic metrics change with input levels, are time varying, or change with instrument temperature (Racette and Lang, 2005).

1.16.5.3.1

Radiometric calibration accuracy

Radiometric calibration accuracy is the systematic bias between the measured brightness temperature and the true brightness temperature. Instruments do not have a completely linear response to the input radiance, and most calibration techniques use two calibration measurements to produce a linear transfer function between counts and radiance. The resulting error is mitigated by characterizing the nonlinearity prelaunch and using a nonlinearity correction factor (with a assumption that the nonlinearity is quadratic). Some designs will use more than two calibration measurements on orbit, which allows a nonlinear transfer function. The other sources of accuracy error mainly deal with the calibration measurements and will be discussed in “Calibration Standards” section. Characterization of the accuracy is discussed in the “Prelaunch Characterization” section.

1.16.5.3.2

Radiometric calibration precision

In radio astronomy and remote sensing, a common radiometric sensitivity metric is Noise Equivalent delta Temperature, or NEdT, which is in units of kelvins. This metric measures the random uncertainty of the instrument to measure a brightness temperature. Kraus (1966) derived the equation for NEdT, and the intrinsic or theoretical limit of a total power radiometer is:

DTrms ¼

Voutrms vVout vTa

Ta þ Tr ¼ pﬃﬃﬃﬃﬃ ½Kelvin: Bs

The variables are Vout, the output voltage of the total-power radiometer; B, the bandwidth of the channel (Hertz); s, the boxcar integration time (second); Tr, the noise temperature of the receiver; and Ta is the antenna temperature. The receiver noise temperature is from the internally generated thermal noise. (Staelin, 2003)

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There are other contributors of NEdT. In Hersman and Poe (Hersman and Poe, 1981), NEdT has other independent components. They present it as: 2 DTrms ¼ d2sc þ d2cal þ d2gf :

The dsc is the ﬂuctuation due to broad-band “white” noise and is the lower theoretical limit in any total power radiometer. Typically, the calibration is considered “ideal” and only the dsc component is mentioned (i.e., the theoretical limit shown above), but calibration does introduce an additional source of error, dcal. The ﬁnal term, dgf, is due to the receiver gain ﬂuctuations and electronic 1/f noise. The total DTrms can be viewed in a “variance” space with each of these sources of noise as an orthogonal contributor. A superior calibration technique will reduce the total DTrms with signal processing. The voltage output when viewing a calibration target also has a random error (besides the scene measurements). The gain and offset in the calibration equation use counts with random noise from dsc. Therefore, the gain and offset estimates are noisy. The period between calibration–load measurements is tc. If the instrument’s gain and the target’s physical temperature were completely stable, then every measurement of the calibration load during data collection could be used in the estimate of the calibration target’s voltage, and therefore increase the accuracy of the estimate. This is not realizable because of varying receiver gain. Nonetheless, an estimate of the calibration output voltage will use several measurements of the calibration target from neighboring scans. This estimate of calibration voltage, or Vcal, is written mathematically as: X Vcal ¼ wðt ktc Þ$V ðktc Þ k ¼ 0; 1; 2; . k

with the proper constraint that

X

wðt ktc Þ ¼ 1

k

The w(tktc) are the weights of the calibration measurements. Hersman and Poe (Hersman and Poe, 1981) give this ﬁnal expression of DTrms when considering an imperfect calibration as sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 1 X 2 þ DTrms ¼ ðTa þ Tr Þ w ðt ktc Þ Bs Bs k and the

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 X 2 w ðt ktc Þ: Bs k

dcal ¼ ðTa þ Tr Þ

Using the propagation of errors technique in the calibration equation in Fig. 28 and replacing counts with their antenna temperature since the ratios are unitless, the calibration noise factor can also be presented as:

The closest calibration target will contribute the most noise to the scene measurement, but a TA midway between TH and TC would reduce the contribution of both by ¼. The reduced error between the two calibration targets is due to the fact the two measurements are uncorrelated. The power spectrum of the receiver noise has two primary components. There is a ﬂat “white” component that is due to dsc, or, in other words, the fundamental performance of the total-power radiometer. The other component is the gain ﬂuctuation, or 1/f noise. These components add to give a power spectral density that is represented by the curve in Fig. 29. Per Hersman & Poe, the calibration technique can be considered a transfer function, H(f), multiplied by the instrument’s power spectral density, Sr(f), which gives the DTrms as ðN ðDTrms Þ2 ¼ c2 Sr ð f ÞHð f Þdf ; 0

where c is a constant radiometer scale factor (kelvin/volt). The mathematical expression for the effective calibration ﬁlter is: 2 sinð pf s Þ sinð pf s Þ X s c j2pf ðtktc Þ wðt ktc Þe Hð f Þ ¼ pf ss pf sc k

where ss and sc are the integration time for the scene and calibration load, respectfully.

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The noise spectra can be separated into the ﬂat portion intrinsic to a total-power radiometer, Si(f), and the 1/f portion that is due to gain ﬂuctuations, Sg(f). The DTrms contribution due to gain ﬂuctuations is ðN d2gain ¼ c2 Sg ð f ÞHð f Þdf : 0

The period between calibrations, tc, is chosen to ﬁlter out as much gain-related noise as possible. It can be seen from Figs. 29 and 30, and the equation above that the calibration technique (H(f)) effectively ﬁlters out the gain-drift noise by reducing the contribution of Sg(f) in the DTrms equation. Therefore, it is important to choose w(t), the weights of the nearby calibration measures, to include as much information as possible for the Vcal estimation. Peckham (1989) published a paper on the optimal weights using the power spectral density. The calibration technique in Hersman & Poe uses a linear interpolation of the two nearest calibration points, which is the best of the simple techniques to reduce the effect of 1/f noise. Its transfer function is shown in red in Fig. 30. The red transfer function would be multiplied by the noise spectrum on the left-hand side of Fig. 29 and integrated across all frequencies to give a ﬁnal voltage or count. To reduce the thermal noise contribution, we used the Vcal from neighboring scans (þ/- 5 scans or w(t)), then the transfer function would be the black curve. While the black transfer function reduced the thermal variance of the calibration target, the transfer function allowed increase 1/f noise into the measurement and potentially canceled any net beneﬁt. The linear interpolation technique gives a weight function (w(t)) that is triangular in shape with the peak at the spot being calibrated and the two corners at the two nearest calibration points, which provides a better transfer function slope over the ﬂicker noise. The receiver conﬁgurations in “Measuring Radiation” section do not all have the same sensitivity. Faris (1967) presents the sensitivity of the correlation radiometer. Wait (1967) derives the sensitivity of the Dicke radiometer. For example, the Dicke conﬁguration spends integration time not measuring the scene brightness temperature and therefore degrades the sensitivity but increases the stability.

1.16.5.4

Calibration Standards

To implement the calibrations in “Calibration Techniques” section, sources of known or measurable radiance need to be used. These sources are using for calibrating frequently or characterizing the instrument before use. This section covers two main

Fig. 29

Advanced Technology Microwave Sounder power spectra and time series along with synthesized data. (Leslie et al., 2011)

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Fig. 30 Example of calibration transfer function using more scans (red in interpolating nearest calibrations and black is averaging þ/ 5 calibrations) and the impact on ﬂicker noise. The left dashed line is one over the calibration period (tc) and the right dashed line is one over the calibration target integration time (which reduces thermal noise) of the calibration measurement.

categories calibration standards: (1) sources measured using the antenna or a portion of the antenna system and (2) sources inside the receiver. The ﬁrst two sections cover the main standards measured “through the antenna” and the last explains the internal sources.

1.16.5.4.1

Calibration targets

It is natural to try to build a reference microwave blackbody target, i.e., material with an emissivity close to one, at microwave frequencies to calibrate a radiometer. If the emissivity is close to one and we know the physical temperature, the brightness temperature is its physical temperature (see “Surface Emissivity” section), which is an advantage of the microwave spectrum using the Rayleigh–Jeans approximation. In practice, it is difﬁcult to build a blackbody across a broad range of frequencies that can be kept thermally stable. There are two categories of calibration targets, with the traditional targets were made of foams or resin ﬁlled with carbon or iron in a pyramidal structure (Cox and Janezic, 2006) or the upcoming cavity targets (Murk et al., 2012). There are a number of sources of error that can be broadly separated between three issues: coupling the sensor’s antenna to the target, accurate measurement of the target’s physical temperature, and how the blackbody assumption breaks down. Efforts have been made to try to quantify the coupling error (Randa et al., 2005). An example of thermal gradients on the traditional target was found on the Special Sensor Microwave Imager/Sounder. Its target had an issue of solar heating of the onboard target that was not captured by the embedded temperature measurements (Kunkee et al., 2008b). A good analysis of the error sources can be found in Robitaille (2010). Efforts are being taken by the National Institute of Standards and Technology to standardize microwave calibration targets (Randa et al., 2004; Houtz et al., 2014). At this point, only the temperature sensors inside the calibration targets are NIST traceable.

1.16.5.4.2

Cosmic background

Space applications use a convenient source of consistent celestial radiation, which is strongest in the microwave part of the spectrum. A NASA mission has quantiﬁed the nearly isotropic source using the COsmic Background Explorer (COBE; https:// lambda.gsfc.nasa.gov/product/cobe/), and one of the COBE instruments was a passive microwave differential radiometer (Smoot et al., 1990). With the spatial resolution of environmental satellites (i.e., average a large solid angle of deep space), the cosmic background is a perfect blackbody with temperature of 2.73 K. Fig. 31 illustrates that the Rayleigh–Jeans approximation breaks down at low temperatures, and a frequency-dependent correction needs to be added to calibration algorithms using the cosmic background radiation.

1.16.5.4.3

Internal Calibration

There are three types of internal references: matched load, noise diode, and ColdFET. The external calibration targets have the advantage of calibrating all components starting with the antenna, but at the expense of being bulky and heavy. The primary passive internal calibration is called a matched load, which is a termination inside the receiver designed to have an impedance that has no reﬂections (i.e., absorbs radiation). Due to reciprocity, the matched load will generate radiation that is proportional to its

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Fig. 31

469

Example of the difference between Planck’s Law and Rayleigh–Jeans approximation.

physical temperature, which is measured by a precise temperature sensor and typically thermally temperature controlled. Some sensors will try to cool the matched load to have a different temperature and therefore radiance. Two active, or powered, internal references are noise diodes and so-called ColdFET. Noise diodes are semiconductors that generate microwave radiation that exceeds its physical temperature. The metric is called Excess Noise Ratio (ENR), which is the added power the noise diode injects into the system. The TP is the physical temperature of the diode, and the TN is the excess noise power added. Extensive calibrations can be found in Draper et al. (2015) and Brown et al. (2007), and a characterization of microwave avalanche noise diode can be found in Maya et al. (2003). ENR ¼

kBðTN TP Þ kBTP

ColdFETs are designs that terminate into a low-noise ampliﬁer. The impedence match is designed to make the termination represented by the receiver temperature of the ampliﬁer and not its physical temperature. Some designs can be as low as 50 K (Frater and Williams, 1981; Maya et al., 2002).

1.16.5.5

Prelaunch Characterization

There are characterizations of the instrument that can be done before it is delivered to the launch provider, which improve the onorbit performance and reduce the retrieval error when using the radiances. The characterization is completed at different stages of development, but typically characterizes the instrument from “end to end” or “through the antenna.” Depending on the instrument, “end to end” characterization might not be the most cost-effective option and effective use of resources.

1.16.5.5.1

Spatial response

The ﬁrst characterization is typically the spatial response of the instrument, and usually only the antenna subsystem. The antenna will be characterized on an antenna test range, which is typically a Compact Antenna Test Range (CATR). The range will have calibrated RF sources that project a collimated and coherent RF signal onto the antenna subsystem, or Antenna Under Test (AUT). The source or AUT will be rotated across orthogonal axes to produce the AUT’s antenna pattern. The main characteristics are the antenna’s electrical boresight, or antenna pattern peak in reference to a known location on the instrument. This allows for an exit vector to be determined to project the measurement onto the Earth’s surface by the data product’s geolocation algorithm. Furthermore, the antenna pattern’s beamwidth is measured to determine if the horizontal spatial resolution meets requirements. Finally, the antenna pattern’s sidelobes will be characterized and the beam efﬁciency metric is calculated. Further decision on these parameters is found in “Collecting Radiation” section. For a technique that uses the antenna pattern measurements to correct the calibration algorithm, see Weng et al. (2013).

1.16.5.5.2

Spectral response

The instrument’s response is not the same across all frequencies, which is by design (e.g., channel ﬁltering) but some of the unintended differences arise from the inconsistent gain is from the ampliﬁers and how the receiver components interact once assembled (i.e., mismatch). The detector effectively integrates across the bandwidth to produce a voltage that is proportional to the power

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within that bandwidth. Data assimilation and data product retrieval technique simulate the instrument’s radiance, but those simulations need to model how the microwave frequencies respond differently through the instrument before being integrated by the detector. Ideally, a special test to characterize the spectral response across the RF frequencies would be made from the antenna through the instrument to the detector’s output voltage that can be given to the user community as the instrument’s spectral response function (Kim et al., 2014).

1.16.5.5.3

Linearity

The instrument’s linearity is how well the radiometric count output represents the linear input of radiances over the expected range of inputs. The instrument transfer function between the radiometric counts to antenna temperatures is typically a quadratic response due to ampliﬁers entering into compression or when detectors are driven into their nonlinear region. To quantify this nonlinearity, passive microwave radiometers use precision calibration targets or other sources to measure the difference between the target’s equivalent blackbody radiance and the instrument’s calibrated radiance. Fig. 32 is an example plot of the prelaunch calibration accuracy veriﬁcation (Kim et al., 2014) that used precision external calibration targets (see “Calibration targets” section). The scene calibration target had its physical temperature varied as shown on the x-axis. The accuracy is the difference between the calibration antenna temperature of the external target and physical temperature (multiplied by the target’s emissivity). The limited range of scene target temperatures are extrapolated to cosmic background radiance ( 2.71 K) and used as a correction term in the algorithm (see Fig. 28 and “Periodic absolute calibration” section).

1.16.6

Verification and Validation

Designing and developing a microwave remote-sensing instrument also requires verifying the design and build before deployment. Early in the design phase, a plan to verify the data must be made. Veriﬁcation is testing that the new instrument has meet the design requirements. Validation is done after the instrument has been deployed to test the validity of the data product. It is standard to compare the instrument’s data against data termed “truth”, which, contrary to its name, has measurement errors of its own, but has lower known or different sources of error. Validating against a variety of truth data sets gives a combined assessment that can indicate the success of the data products. When a new microwave remote-sensing instrument is deployed it is also compared against other similar instruments to determine if its data products are “in family”, i.e., similar, with the others.

Fig. 32

Advanced technology microwave sounder radiometric accuracy. (Kim et al., 2014)

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1.16.6.1

471

Instrument Veriﬁcation

Instrument veriﬁcation process occurs during the assembly, integration, and testing and also into instrument’s early-stage deployment. Early in a program, a veriﬁcation plan is determined for each requirement that can be veriﬁed by inspection, demonstration, test, or analysis (BKCASE Editorial Board, 2016). This section describes some of the standard techniques for verifying microwave instruments and trending performance. When an instrument is delivered to a platform, a compliance matrix with all of the requirements is prepared to show the requirement, the veriﬁcation technique (e.g., demostration), and the technique’s results. During the design cycle, the instrument’s system engineers monitored the margin, or difference between the requirement and the current best estimate of the requirement. Based on trending the margins, the system engineer would then identify risk that the requirements won’t be met and take the appropriate corrective action, or justify a waiver of the requirement.

1.16.6.1.1

Instrument performance

The best way to determine the performance of a microwave receiver is the Y-factor method, which is common technique for measuring the noise ﬁgure of an RF ampliﬁer. The method calculates the receiver temperature (kelvins), which is the principal receiver characteristic in the noise equivalent delta noise (NEdT) equation. Two radiances are needed in the Y-factor method, which comes from a RF absorber (i.e., a nearly blackbody) at two physical temperatures as far apart as possible. If the absorber temperature is too close together, it is difﬁcult to measure the two different output voltages due to the intrinsic noise of the instrument. The easiest physical temperature is ambient temperature, but temperature below 0 C can cause ice to form on the absorber, which stops the absorber from being a black body because the ice is reﬂective. The standard practice is to have the absorber completely submerged into liquid nitrogen. The ambient absorber is assumed to be in thermal equilibrium with the room’s temperature, and the absorber in liquid nitrogen is assumed to be near the boiling point of liquid nitrogen. Care has to be taken to make sure ice does not form or that the level of the liquid nitrogen evaporates to reveal the absorber because is either eliminates the black body assumption or the radiances of the revealed absorber is not at liquid nitrogen temperature.

1.16.6.1.2

Electromagnetic interference

Electromagnetic interference (EMI) is a major issue for microwave instruments. They are susceptible to interference not only at the direct frequencies they measure but also at the downconverted Intermediate Frequencies (IF) used before detection. There are also the common issues of interference on the power circuits and signal voltages after the detector and before converting the signal’s voltage to a digital number. The sources of the interference can come from both inside and outside the instrument. Both inside and outside sources can interfere radiatively over free space, but internal interference sources can also occur over wires and structures (referred to as conductive interference). System engineers will plan out the possible interference in a frequency plan, which will inﬂuence design decisions across multiple microwave bands in a suite. The engineers will avoid having local oscillators with harmonics that are in the RF passbands of other channels in case there is local oscillator frequency will be measured from one band to another. Another important aspect are the communication frequencies on the instrument’s platform. Understanding the sources of external sources of radiative interference starts with the radio frequency allocation that protects parts of the frequency spectrum for science though international agreements. The US government governs the spectrum from 9 kHz to 300 GHz by allocating, authorizing, engineering, and enforcing the regulation (https://www.fcc.gov/engineering-technology/policy-and-rulesdivision/general/radio-spectrum-allocation). Even though the most, if not all, of the microwave spectrum used in remote sensing is protected, some instruments will not be completely compliant, and the passive microwave community is watching an ever increasing amount of EMI in their measurements (https://smap-archive.jpl.nasa.gov/science/wgroups/RFI/). External interference directly in the microwave spectrum the instrument is measuring is difﬁcult for an instrument to remove without additional design scope. For passive microwave applications, the detector is measuring changes in the noise ﬂoor and a coherent sinusoidal signal is measured by the detector as a increase in power that cannot be deciphered from the natural radiation background. There are techniques to design a more robust receiver which range from ﬂagging potential RFI corrupted measurements to binning the passband into separate subbands to detect and remove corrupted subbands Piepmeier et al. (2008, 2014). Internal sources of EMI can be switching power supplies, high-frequency digital signals, or even the local oscillator used for downconverting to IF. Most of these sources are mitigated by standard engineering practices or planning during the design phase. One of the most important design aspects is the electrical ground. The output voltages of detectors are very small and a clean ground potential is important before “video” ampliﬁcation. Differential measurements are ideal but often difﬁcult to implement.

1.16.6.2

Data Product Validation

Validation consists of comparing the data products against the remote sensing community’s standard. Validation occurs at several points in the data-processing chain and with a variety of validation techniques. For example, an atmospheric sounder would validate both the radiances and the temperature proﬁles. Furthermore, radiances can be validated against simulated radiances or against the radiances of other similar microwave instruments. It is difﬁcult to match two instruments temporally and with the same spatial ﬁdelity (i.e., pointing in the same direction with the same antenna pattern). Whether the community’s standard (i.e., a wellcalibrated heritage sensor that has been operated over an extended length of time), a new instrument, or simulated radiance, each measurement or simulation have different sources of error. Comparing a new instrument against several different validation

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techniques can provide a comprehensive evaluation. The rest of this section will highlight the more common validation techniques and ﬁnish with the data product maturity metric.

1.16.6.2.1

Ground truth comparisons

The ﬁrst data product validation discussed will be the geophysical parameters. This consists of measuring the geophysical parameter with another typically more accurate instrument that is usually sparsely distributed. This can be radiosondes (i.e., temperature, humidity, pressure sensors on high-altitude weather balloons), snow depth gauges, or buoys with water thermometers. As mentioned, these direct or in situ measurements are very sparse, but accurate. It is common to have a speciﬁc ﬁeld campaign with extra truth measurements to compare various data products against each other. Another source of truth measurements is the output of Numerical Weather Prediction (NWP) models. These complex and computationally intensive collection of models solve the time-varying geophysics of the atmosphere as they are interacting with the Earth’s surface. NWP models exist on scales varying from global, synoptic, and mesoscale. They are initialized with truth data from across the globe including surface weather stations on land or at sea on ships aircraft (airlines at cruising altitude and during takeoff and decent), weather balloons, automated sea buoys, surface weather radars, and both low earth orbit and geostationary satellite data. Furthermore, the simulations or analysis is frequently “nudged” back to match the latest truth measurements as the simulation progresses. The output of the NWP gives a wealth of truth data to validate the atmospheric data products of microwave remote-sensing instruments that have a high temporal sampling and spatial extent. It should be noted that microwave radiances are assimilated into the NWP models and reduce the forecast the most compared to other data sources. Finally, another truth source derives the atmospheric state from radio occultation of Global Navigation Satellite Systems (GNSS), e.g., GPS, signals. Using the GNSS constellation of transmitters, an on-orbit receiver measures the Doppler shift of the GNSS radio frequency signal as the atmosphere occults in between the satellites. The index of refraction of the atmosphere bends the radio frequency electromagnetic wave. The amount of bending, or index of refraction, is related to the temperature, water vapor, and pressure of the atmosphere at the tangent point. The GNSS temperature retrievals are assimilated into NWP models (Kuo et al., 2000) but can also be used as truth source for atmospheric temperature sounders (Zou et al., 2014).

1.16.6.2.2

Inter-instrument comparisons

Inter-instrument comparisons try to use the Sensor Data Records (SDRs), i.e., brightness temperatures to have all of the instrumentdependent characteristics to be calibrated out. Still, there will always be differences in the instrument that were not removed. There are also the temporal differences between the instruments’ measurements that will invariably cause radiances differences, and the measurements would not point in the same direction and with the same angular extent. These issues contribute a variable amount of error that the validation technique tries to minimize (Berg et al., 2016). A common radiance comparison technique between operational satellite systems is the Simultaneous Nadir Overpass (SNO) or “snow” technique (John et al., 2012). For polar-orbiting microwave cross-track instruments, the temporal difference between measurements at the polar regions is minimized, so nearly the same radiance can be measured. To further reduce the cross-track error due to measurements taken an oblique angle from different altitudes, the measurements taken closest to the nadir are compared. The drawback of the SNO technique is the limited range of radiances at the polar regions. The Double Difference Technique (DDT) tries to compare a larger range of radiances by mixing SNO with NWP output (John et al., 2013).

1.16.6.2.3

Vicarious validation

For transparent microwave channels, there is the option of vicarious calibrating against surfaces with consistent emissivities. If the channel does not interact with the atmosphere, i.e., the atmosphere is largely transparent, then the largest unknown in the radiative transfer equation is the surface emissivity. Some natural areas on the Earth have wide enough extent and natural emissivities that remain consistent (Mo, 2011; Saunders et al., 2013).

1.16.6.2.4

NWP and radiosonde validation

The ﬁnal common radiance validation uses a combination of a radiative transfer model and “truth” atmospheres like NWP model output or radiosondes. Common radiative transfer models for microwave sensors are the Radiative Transfer for TOVS or RTTOV (https://nwpsaf.eu/site/software/rttov/) and Community Radiative Transfer Model (CRTM: https://www.jcsda.noaa.gov/projects_ crtm.php). These are fast radiative transfer models that linearize the line-by-line models like TBSCAT (Rosenkranz, 2002). Saunders (2013) describes the technique to monitor satellite biases.

1.16.6.2.5

Data maturity

Operational microwave remote sensing instruments have data product maturity levels that indicate the level of validation to communicate to user community the readiness of the data product for operational use. Common data product maturity designations are the beta, provisional, and validated maturity levels. After the spacecraft checkout is complete, instrument activation and checkout begins. Instrument checkout is mainly an engineering checkout, but potentially it is the ﬁrst complete checkout of the data processing chain from the space segment down through the ground segment. Beta maturity is the most fundamental validation of the ground segment’s data products and consists of checking radiance values and the status of the quality ﬂags. Quality ﬂags are an important metric of the status of the data within a speciﬁc data granule. A granule consists of a predetermined number of measurements. Typically, a week or so after activation and checkout, the data

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product validation maturity advances to beta with the expectation of minimal validation and that the data product could still contain errors. This maturity level also includes the documentation of the performance to date, with any anomalies reported or remaining efforts required to maturity progression. The next level is provisional and requires a signiﬁcant amount of validation using the methods described above. The data validation does not have to cover all geographical or seasonal expectations but starts to change the qualitative validation of beta to a documented quantitative validation. Data can be used operationally at this point and is ready for scientiﬁc publications. The provisional level is typically gained 3–6 months after beta maturity. The ﬁnal maturity level is called “validated” and typically occurs a year after launch. This is a comprehensive evaluation over all conditions (i.e., full geographical coverage and all seasons). The data product has had user feedback and complete validation documentation including the remaining unresolved anomalies. The validation continues throughout the instrument’s lifetime to trend the performance.

See also: 1.17. Vicarious Calibration and Validation. 1.18. Remote-Sensing Missions and Sensors–Radar Sensors. 4.09. Snow Properties From Passive Microwave. 4.13. Surface Soil Freeze/Thaw State. 7.07. Fast Radiative Transfer Algorithms for Real-Time Sounder Applications.

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