A Continuous Wave Radar Receiver Consists of

Radar

Nadav Levanon , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

X.A Continuous Wave Radar

A continuous wave (CW) radar, as its name implies, emits a continuous signal. It must therefore receive the returned signal while transmitting. The unavoidable leakage between transmitter and receiver means that the weak reflected signal may have to compete with the strong directly received transmission. Separation between the two must be based on parameters other than intensity.

The CW design is found in radars that emphasize velocity measurement, such as police radars or artillery muzzle velocity radars. The Doppler shift provides the means to separate the transmitted signal from the received signal. The long signal duration enables high-resolution velocity measurement. For a CW radar to be able to measure range too, the transmitted signal must be marked on the time axis. Such marking is usually implemented through periodic phase or frequency modulation. The modulation also helps to separate the target-reflected signal from the directly received signal. Still, it is important to minimize the direct reception, which is why CW radars usually use two separate antennas, a transmitting one and a receiving one.

A major advantage of CW radars is pointed out in Eq. 7, which shows that the SNR is a function of the average transmitted power during target illumination. A pulse radar needs high peak power to achieve sufficient average power, while in a CW radar the peak power is equal to the average power. This is why CW radars use low-power transmitters, based on low-voltage solid state devices rather than on high-voltage vacuum tubes.

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Ground Penetrating Radar Systems and Design

Steven Koppenjan , in Ground Penetrating Radar Theory and Applications, 2009

3.6.1.1 Stepped-frequency technique – synthesized pulse

A stepped-frequency CW radar incorporates an RF source or a direct digital synthesis (DDS) source, and DSP. The source is stepped between a start frequency, f ₀, and a stop frequency, f_{N − 1}, in equal, linear increments. It is important to note that for a swept FM-CW radar, the source is swept from f _min to f _max and linearly sampled on the fly. In either case, the radar is continuously transmitting. A return signal is formed by mixing the received signal with a portion of the transmitted one. This return signal is digitized at each step and stored. After each complete sweep of N steps, a Fourier transform is performed to convert the data from the frequency domain to the time domain. This is the process of creating the synthesized pulse.

Range information is based on the time-of-flight principle, which is a phase path difference measurement. This concept is outlined with reference to Figure 3.8. Two paths are defined: 2–3–4–5–6 and 7–8. There is an associated phase, θ _rf and θ _lo, with each path, respectively. When the phase path lengths are equal, θ _rf  = θ _lo, the length of 7–8 is equal to that of 2–3–5–6 (transmit is directly connected to receive). The phase paths of 7–8 and 2–3–4–5–6 are not equal when a target is present. A phase difference, ψ, occurs as a result of the time-of-flight difference and can be expressed as follows:

Figure 3.8. Simplified diagram of the stepped-frequency radar technique.

(3.11) $\psi =(2\text{π}f)\tau =(2\text{π}f)d/c$

where f  =   frequency (Hz),   τ =   two-way time of flight (s), d  =   two-way distance to the target 3–4–5, and c  =   speed of light.

If a single frequency, f ₀, from the RF source, 1, is power divided with one side transmitted and the other side connected to the receive mixer, the received signal at 6 is

(3.12) $r(0)=\text{cos}\left(2\text{π}{f}_0(t+{\tau }_0)+{\theta }_{\text{rf}}\right)=\text{cos}\left(2\text{π}{f}_{0}t+{\theta }_{\text{rf}}+{\psi }_0\right)$

and the output of the mixer, 9, will be

(3.13) $v\left(0\right)=A_0\cos \left(2\text{π}{f}_{0}t+{\theta }_{\text{lo}}\right)\cos \left(2\text{π}{f}_{0}t+{\theta }_{\text{rf}}+{\psi }_0\right)$

where ψ ₀ is the phase associated with the target path length, d (3–4–5) for f ₀. A ₀ is the amplitude of the return. If the phase lengths are preset so that θ _rf  = θ _lo, then v(0) reduces to

(3.14) $v(0)=A_0\text{cos}\left(2\text{π}{f}_{0}t\right)\text{cos}\left(2\text{π}{f}_{0}t+{\psi }_0\right)$

Using a trigonometric identity

(3.15) $v(0)=\frac{A_0}{2}\text{cos}({\psi }_0)+\frac{A_0}{2}\text{cos}(2\text{π}(2f_0)t+{\psi }_0)$

If v(0) is low-pass filtered with a cutoff frequency of f ₀, then the output of the filter, 10, will be

(3.16) $v(0)=\frac{A_0}{2}\text{cos}\left({\psi }_0\right)$

Since the target's distance is fixed, the phase path, ψ ₀, at a given frequency is also fixed. Thus v(0) is a constant, which is represented by a DC voltage. This DC voltage can be sampled with a low-speed ADC; thus, v(0) is now represented as v[0], the sampled version at f ₀. If the RF source is stepped by an amount Δf to a higher frequency, f ₁, such that f ₁  = f ₀ + Δf, the phase path length, ψ ₁, is longer. Then the sampled output of the low-pass filter, v[1], is

(3.17) $v[1]=\frac{A_1}{2}\text{cos}\left({\psi }_1\right)$

When the RF source is stepped in equal, linear increments of Δf from (f ₀ to f ₁ to f₂ to … f_{N − 1}), the output voltages (v[0], v[1], v[2], …, v[N−1]) resemble a sampled sine wave, as shown in Figure 3.9. This is due to the periodic nature of the phase. This sequence is the radar return signal and can be expressed as follows:

Figure 3.9. Sampled sine wave.

(3.18) $\nu [n]=\frac{1}{2}{\displaystyle \sum _{i=0}^{N-1}\delta (n-i)A_i\text{cos}({\psi }_i)}$

where δ(n) is the dirac delta function or unit impulse. Rewriting this sequence, in a sampled sine wave format with frequency, ω, and amplitude, A, v[n] becomes

(3.19) $v[n]=A{\displaystyle \sum _{i=0}^{N-1}\delta \left(n-i\right)\text{cos}\left({\psi }_{i}n\right)}$

where ${\psi }_i={\omega }_i{\tau }_0=2\text{π}(f_i+n\Delta f){\tau }_0$ .

At each step, n, an ADC is performed on the DC voltage, v[n]. The data from all N steps are then converted into the time domain pulse response equivalent with a discrete Fourier transform (DFT):

(3.20) $V(k)=\{\begin{array}{ll}\frac{1}{N}{\displaystyle \sum _{n=0}^{N-1}\nu [n]{\text{e}}^{-\text{j}(2\text{π}/N)kn},}\hfill & 0\le k\le N-1\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array}$

Taking the DFT of Equation (3.19) yields

(3.21) $V(k)=\{\begin{array}{ll}\frac{A}{N}\frac{\text{sin}\{(k-\omega ){\Omega }_o[(N+1)/2]\}}{\text{sin}[(k-\omega ){\Omega }_o/2]},\hfill & 0\le k\le N-1\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array}$

where ${\Omega }_o=\text{2}\text{π}/N$ .

V(k) is plotted in Figure 3.10. Equation (3.21) is recognized as the discrete-time counterpart of the sinc function: sinc(x)   =   sin(x)/x, which is the Fourier transform of a continuous-time rectangular pulse. Notice that the sinc function is shifted (from 0) along the k axis by an amount equal to ω. This is a direct result of the sampled sine wave's frequency, ω, and in fact the range of a target is a function of ω. Closer targets produce smaller phase changes because the path, 3–4–5, is shorter. This results in low-frequency sine waves. More distant targets produce larger phase changes resulting in high-frequency sine waves. The amplitude of the sine wave is a function of the radar cross section of the target, the range, and the propagation loss of the ground.

Figure 3.10. Sinc function.

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Modeling wave pattern cycles using advanced interferometry altimeter satellite data

Maged Marghany , in Nonlinear Ocean Dynamics, 2021

10.3 Types of radar altimeter frequencies

There are two main components of radar altimeters: (i) frequency modulated continuous wave (FMCW) and (ii) pulse altimeters, which are a function of radar signals used. Two sorts of FMCW altimeters are generally used: broad-beamwidth and narrow-beamwidth types. Both FMCW altimeters are a function of antenna beamwidth. In contrast, the pulse altimeters are also known as short-pulse altimeters or pulse-compression altimeters, which are a function of intrapulse modulation. In addition, altimeters can also operate in optical bands, for instance, laser altimeters.

In other words, a simple continuous-wave radar device without frequency modulation has the disadvantage that it cannot determine target range because it lacks the timing mark necessary to allow the system to time accurately the transmit and receive cycle and to convert this into range. Such a time reference for measuring the distance of stationary objects can be generated using frequency modulation of the transmitted signal. In this method, a signal is transmitted, which increases or decreases in frequency periodically. When an echo signal is received, that change of frequency produces a delay Δt (by runtime shift), similar to the pulse radar technique. In pulse radar, however, the runtime must be measured directly. In FMCW radar, the differences in phase or frequency between the actual transmitted and the received signal are measured instead (Fig. 10.2).

Fig. 10.2. Ranging from an FMCW system.

For lower height measurements, a frequency modulated continuous wave radar (FMCW) can be used. This technology provides a better resolution but a lower maximum unambiguous height measurement at the comparable wiring effort, material 1 cavity of individual components in these systems. Often both technologies are used simultaneously [1–3].

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An Introduction to Atmospheric Gravity Waves

In International Geophysics, 2002

8.1.3.3 Frequency-Modulated Continuous-Wave Radar

Generally, Doppler radar returns are limited to temperature and humidity inhomogeneities on the scale of meters and to ranges greater than several hundreds of meters above the ground surface. The first restriction is imposed by the radar frequency, and the latter restriction is imposed by the fact that during the transmission of the radar pulse no signal can be received. However, to better understand the dynamics of the planetary boundary layer it is necessary to know the true thickness of thin radar backscatter layers and the processes generating these fine-scale refractive index inhomogeneities. The FM-CW radar developed by Richter (1969) makes these observations possible. To eliminate the need for radar pulses which limit the range, a continuous microwave frequency is transmitted and simultaneously received by an identical antenna closeby. In itself, this mode of operation would provide high spatial resolution, but no range information. To get range information, the transmitted frequency is linearly modulated between two frequencies over a time T_M . The received signal will be Doppler shifted by moving scatters, and when the transmitted and received signals are combined in real time, a sinusoidal beat frequency, f_b , is generated. The time delay, Δt, of the appearance of reflected signal is related to the distance of the scatter by

(8.3) $f_b=\frac{F}{T_M}\Delta t=\frac{2F}{c{T}_M}H,$

where F is the frequency excursion, c is the speed of propagation, and H is the height of the scatter (assuming the instrument is pointed upward). In the case of multiple returns, a spectrum analysis of the beat frequency allows the different targets to be resolved according to their range, and the amplitudes of the beat frequencies are measures of the reflection coefficients of the targets. Figure 8.3 taken during the CASES-99 field program (Poulos et al., 2001) illustrates the fine wave-like structures that can be revealed by FM-CW radar. The capability of FM-CW radar was enhanced in 1976 when Doppler capability was added (Chadwick et al., 1976; Strauch et al., 1976). This was accomplished by using a digital Fourier transform that preserved the phase and amplitude of spectral density of the radar signal obtained during each sweep. Monitoring the change in phase from sweep to sweep provides the Doppler information needed to estimate radial velocities. Figure 8.4 compares FM-CW Doppler winds with winds observed using a tethered balloon and a rawinsonde. The FM-CW radar is becoming a standard instrument for boundary-layer studies and has proved especially useful in the studies of wave and turbulence in the stable boundary layer (see, for example, Eaton, McLaughlin, and Hines, 1995; De Silva et al., 1996).

Figure 8.3. FM-CW radar images recorded on October 14, 1999. Record begins at 07:40:20 GMT. Kelvin–Helmholtz waves are between 1500 and 1800 m and between 500 and 600 m.

(Courtesy of Stephen Frasier, Univ. of Massachusetts, Amherst.)

Figure 8.4. FM-CW Doppler radar wind speed profile (dashed line) compared with tethered balloon wind profiles (solid lines) and rawinsonde profile (circles).

(From "A new radar for measuring winds," R.B. Chadwick et al., Bull. Am. Meteorol. Soc., 57: 1123, 1976.)

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An Introduction to Atmospheric Gravity Waves

Carmen J. Nappo , in International Geophysics, 2012

9.4.3 FM-CW Radar

Generally, Doppler radar returns are limited to temperature and humidity inhomogeneities on the scale of meters, and to ranges greater than several hundreds of meters above the ground surface. The first restriction is imposed by the radar frequency, and the latter by the fact that during the transmission of the radar pulse no signal can be received. However, to better understand the dynamics of the planetary boundary layer it is necessary to know the true thickness of thin radar backscatter layers and the processes generating these fine-scale refractive index inhomogeneities. The frequency-modulated continuous-wave (FM-CW radar) developed by Richter (1969) makes these observations possible. To eliminate the need for radar pulses which limits the range, a continuous microwave frequency is transmitted and simultaneously received by an identical antenna close bye. In itself, this mode of operation would provide high spatial resolution, but no range information. To get range information, the transmitted frequency is linearly modulated between two frequencies over a time $T_{\mathrm{M}}$ . The received signal will be Doppler shifted by moving scatters, and when the transmitted and received signals are combined in real time, a sinusoidal beat frequency, $f_{\mathrm{b}}$ is generated. The time delay, $\mathrm{\Delta }t$ , of the appearance of reflected signal is related to the distance of the scatter by

(9.42) $f_{\mathrm{b}}=\frac{F}{T_M}\mathrm{\Delta }t=\frac{2F}{{\mathit{cT}}_M}H\text{,}$

where $F$ is the frequency excursion, $c$ is the velocity of propagation, and $H$ is the height of the scatter (assuming the instrument is pointed upward). In the case of multiple returns, a spectrum analysis of the beat frequency allows the different targets to be resolved according to their range, and the amplitudes of the beat frequencies are measures of the reflection coefficients of the targets. Fig. 9.25 taken during the CASES-99 field program illustrates the fine wave-like structures that can be revealed by the FM-CW radar. The capability of the FM-CW radar was enhanced in 1976 when Doppler capability was added (Chadwick etal., 1976; Strauch etal., 1976). This was accomplished by using a digital Fourier transform that preserved the phase and amplitude of spectral density of the radar signal obtained during each sweep. Monitoring the change in phase from sweep to sweep provides the Doppler information needed to estimate radial velocities. Fig. 9.26 taken from Chadwick etal. (1976) compares FM-CW Doppler winds with winds observed using a tethered balloon and a rawinsonde. The FM-CW radar is becoming a standard instrument for boundary layer studies, and has proved especially useful in the studies of wave and turbulence in the stable boundary layer (see, for example, Eaton, McLaughlin, and Hines, 1995; De Silva etal., 1996).

Fig. 9.25. FM-CW radar images recorded on October 14, 1999. Record begins at 07:40:20 GMT. Kelvin–Helmholtz waves are between 1500 and 1800   m and between 500 and 600   m. Courtesy of Stephen Frasier, Univ. of Mass.

Fig. 9.26. FM-CW Doppler radar wind speed profile (dashed line) compared with tethered balloon wind profiles (solid lines) and rawinsonde profile (circles). (Taken from Chadwick etal. (1976).)

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Detection of Airborne Volcanic Ash Using Radar

M. Hort , L. Scharff , in Volcanic Ash, 2016

2.4 Pulsed and Continuous Wave: Measuring Distance or Velocity

Radar is an active measurement that has a controlled source and does not require any radiation emitted by the targets. Radars are used to detect location and velocity of targets simultaneously and irrespective of whether they are individual targets (aircraft, etc.) or volume filling distributed targets (eg, rain or volcanic ash).

In principle, there are two different types of radars: pulsed and continuous wave (CW) (see Fig. 2). Both have their advantages and disadvantages. The basic version of a pulsed radar is designed for range measurements without Doppler information, whereas the basic version of a CW radar is designed for Doppler measurements without range information. Measuring distance (also known as range evaluation) with a pulsed system is fairly easy: one sends out a pulse (wave train of carrier frequency with duration τ) and measures the round-trip time, δt, of the echo. Two or more targets return individual echoes if their spatial distance is larger than cτ/2 (c: speed of light, τ: pulse duration). By sending out a pulse train, the maximum unambiguous range depends on the pulse repetition period T _p, as echoes of objects farther away than cT _p/2 return after the following pulse has been sent and thus appear much nearer to the radar as they are. For typical weather radar applications, T _p  ∼   10⁻³  s, and thus the maximum unambiguous range is about 150   km. Some techniques exist in radar meteorology to discriminate between targets within and beyond the maximum range (eg, using multiple pulse repetition periods, see Doviak and Zrnić, 1984). These techniques are needed and automatically applied in weather radar processing, but they may not be needed when using mobile ground-based Doppler radars in volcanology, as the distance between radar and target can be kept small.

Figure 2. Schematic functional principle of various types of radars. The CW radar measures velocity by examining the Doppler frequency shift (top row). A pulsed radar measures range using the round-trip time of a pulse (second row). Pulsed Doppler radars (third row) measure round-trip times of consecutive pulses for the additional determination of the target's velocity. The FMCW radar (bottom row) measures the difference in frequency of sent and received signals, which contains velocity and range information. Detailed description is in the text.

Complications arise for distributed targets like rain and volcanic ash because owing to their close proximity to each other, individual targets cannot be resolved. Due to the superposition of individual echoes (see Eq. [3]), distributed targets lead to an elongated echo. This echo is then split into discrete time intervals and sampled. Each sample corresponds to the integrated amplitude within a distance interval, a so-called range gate. The range resolution is then δR  = cT _p/(2n _s) and depends on the pulse repetition period, T _p, and the number of samples taken between pulses n _s (commonly n _s  ∼ T _p/τ   –  1 and because T _p  ≫  τ the range resolution commonly reduces to δR  ∼ cτ/2).

Measuring velocity with a CW radar is also simple: one measures the change in frequency of the echoed signal, which is known as the Doppler effect. A single moving target experiences the incoming wave crests at a different rate, either faster when approaching the radar or slower when moving away from it. Scattering at the target happens with this new frequency, but because the target moves, the back-scattered wave undergoes a second shift when received back at the stationary radar. The total frequency shift (also called Doppler shift) is therefore f _d  = 2v _r f ₀/c (f ₀: radar carrier frequency). The measured velocity, v _r, is called the radial velocity because it is the relative velocity of the target with respect to the radar. The CW radar can handle targets at any range and with almost any velocity without any ambiguity.

The measurement of frequency shifts in a CW radar is technically realized by mixing the incoming signal M _r (t) with an amplitude reduced portion of the outgoing signal, M _t (t). If for simplicity, M _t (t)   = A ₀ sin(2πf ₀ t  + ϕ), the incoming signal is M _r(t)   = A ₁ sin(2πf ₀(t  – δt)   + ϕ), the same as the signal sent δt  = 2R(t)/c seconds earlier only having a smaller amplitude, A ₁. The distance varies because of the target's velocity by R(t)   = R ₀  ± v _r t (R ₀ is the distance at t  =   0). The sign ± indicates that there are particles moving towards as well as away from the radar, and those need to be distinguished. By mixing (multiplication of signals) and subsequent low-pass filtering (removing the summed frequency term), the remaining processed signal contains the difference frequency

[9] $\begin{array}{c}M\left(t\right)=A_2\cos \left(2\text{π}{f}_0\mathrm{\delta }t\right)\\ =A_2\cos (\pm \frac{4\text{π}{f}_0{\mathrm{\nu }}_{\text{r}}}{c}t+4\text{π}\frac{f_0{R}_0}{c})\\ =A_2\cos \left(\pm \underset{\text{frequency}}{\underbrace{2\text{π}{f}_{\text{d}}}}\times t+\underset{\text{phase}}{\underbrace{4\text{π}\frac{f_0{R}_0}{c}}}\right)\text{,}\end{array}$

which corresponds to the Doppler shift. A Fourier transform of this mixed and filtered signal (heterodyne signal in "radar-language") reveals the Doppler shift and thus the velocity of the target. It is obvious that using a pure CW radar, absolute range cannot be determined. However, in some applications (eg, police radars) the measurement of instantaneous velocity using minimum power (for minimum counter detectability) is advantageous. The respective other parameter—velocity for pulsed, range for CW radars—can be measured by extending the basic concepts, which is described next.

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The Science of Hydrology

S.S. Hubbard , N. Linde , in Treatise on Water Science, 2011

2.15.2.5 GPR Methods

GPR methods use EM energy at frequencies of ∼10   MHz to 1   GHz to probe the subsurface. At these frequencies, the separation (polarization) of opposite electric charges within a material that has been subjected to an external electric field dominates the electrical response. GPR systems consist of an impulse generator which repeatedly sends a particular voltage and frequency source to a transmitting antenna. When the source antenna is placed on or above the ground surface, waves are radiated downward into the soil. In general, GPR performs better in unsaturated coarse or moderately coarse textured soils; GPR signal strength is strongly attenuated in electrically conductive environments (such as systems dominated by the presence of clays or high ionic strength pore fluids). Together, the electrical properties of the host material and the frequency of the GPR signal primarily control the resolution and the depth of penetration of the signal. Increasing the frequency increases the resolution but decreases the depth of penetration.

GPR data sets can be collected in the time or in the frequency domain. Time-domain systems are most commonly used in near-surface investigations. Generally, one chooses a radar center frequency that yields both sufficient penetration and resolution; for field applications this is often between 50 and 250   MHz. However, significant advances have been made in the development of frequency domain systems. Lambot et al. (2004a) describe a stepped-frequency continuous-wave radar deployed using an off-ground horn antenna over the frequency range of 0.8–3.4   GHz. The wide bandwidth and off-ground configuration permits more accurate modeling of the radar signal, thus potentially leading to improved estimates of subsurface parameters (Lambot et al., 2004b, 2006).

The most common ground surface GPR acquisition mode is surface common-offset reflection, in which one (stacked) trace is collected from a transmitter–receiver antenna pair pulled along the ground surface. With this acquisition mode, GPR antennas can be pulled along or above the ground surface at walking speed. When the EM waves in the ground reach a contrast in dielectric constants, part of the energy is reflected and part is transmitted deeper into the ground. The reflected energy is displayed as 2D profiles that indicate the travel time and amplitude of the reflected arrivals; such profiles can be displayed in real time during data collection and can be stored digitally for subsequent data processing. An example of the use of GPR profiles for interpreting subsurface stratigraphy is provided in Section 2.15.5.1.

The velocity of the GPR signal can be obtained by measuring the travel time of the signal over a known distance between the transmitter and the receiver. The propagation phase velocity (V) and signal attenuation are controlled by the dielectric constant (κ) and the electrical conductivity of the subsurface material through which the wave travels. At the high-frequency range used in GPR, the velocity in a low electrical conductivity material can be related to the dielectric constant, also known as the dielectric permittivity, as (Davis and Annan, 1989)

(3) $\kappa \approx (\frac{c}{V}{)}^2$

where c is the propagation velocity of EM waves in free space (3×10⁸  m s⁻¹).

Approaches that facilitate EM velocity analysis include surface common-midpoint (CMP), crosshole tomography acquisition, as well as analysis of the groundwave arrival recorded using common-offset geometries. Full-waveform inversion approaches have recently been developed (e.g., Ernst et al., 2007; Sassen and Everett, 2009) that offer potential for improved subsurface property characterization over methods based on travel times alone. Discussion of petrophysical relationships that link dielectric permittivity with hydrological properties of interest is described in Section 2.15.3.2. A review of GPR methods applied to hydrogeological applications is given by Annan (2005).

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Small Scale Processes in Geophysical Fluid Flows

In International Geophysics, 2000

3.1 Salient Characteristics

The atmospheric boundary layer is quite important to many aspects of human life. It is in a very thin layer of the lower ABL that most people live and as such, many aspects of the ABL affect daily life. Dispersion of pollutants is one such example. The characteristics of turbulent mixing in the ABL determine the concentration levels of pollutants. Most importantly, the momentum, heat, and moisture exchanges between the atmosphere, Earth, and oceans takes place through the ABL, and it is for this reason that ABL has received intense attention.

The ABL over land can be grouped into two types—the daytime convective ABL (CABL) and the nighttime or nocturnal ABL (NABL). The mixing in the CABL and NABL is basically different. In the former, it is primarily due to solar heating at the lower boundary, and in the latter, it is primarily due to winds. The CABL is extensively studied, while the NABL has not received that much attention. The presence or absence of condensation of water vapor and clouds is another important distinction.

The CABL can be divided into three parts—the lower part close to the surface (composing perhaps 10% of its depth), the middle layer (constituting the bulk of the ABL), and the upper part near the capping inversion layer, which makes up another 10–20% of the ABL. Turbulence in the entire CABL is driven by the heat flux from the ground. However, the salient processes, characteristics of mixing that goes on, and scaling properties are all different in these regions. In the layers close to the surface, fluxes of various properties such as momentum, heat, water vapor, and trace gas concentrations are nearly constant. In this constant-flux surface layer, the important nondimensional variable is the distance z from the surface normalized by the Monin–Obukhoff length that characterizes the stability conditions. The surface layer is the part that is the most well-measured and well-understood part of the ABL.

In the bulk of the ABL, the scaling is determined by the depth of the inversion z_i. Nevertheless, it is also driven by the convective, destabilizing heat flux to the atmosphere near the ground. Mixing processes are so efficient that the gradients of properties in the bulk of the CABL are small, and the transport is mainly due to large eddies and thermals. Near the top, close to the capping inversion, the dynamics are different. The ambient stratification is such that stable, lighter air masses from above the ABL are entrained into the ABL by the large eddies. The intensity of this entrainment determines the properties in the upper parts of the CABL. It is, in fact, possible to divide the turbulent diffusion of a passive scalar such as a pollutant in the CABL into two parts, top–down and bottom–up. The top–down diffusion can be scaled using the entrainment characteristics at the top of the CABL. The bottom–up diffusion depends on the characteristics of the turbulence driven by heat flux near the ground. The timescale for mixing a scalar released at the ground throughout the CABL is typically on the order of an hour. Therefore, the vertical profile of the scalar through the CABL depends on the ratio of its lifetime (determined by chemical reaction rates) to this mixing time. If this ratio is not large, the profile will be different than that of a conserved scalar. Often fair weather cumulus clouds form at the top of CABL from condensation of moisture transferred upward from near the ground surface by convective eddies. If these are extensive, they affect the further evolution of the CABL by modifying the fluxes through it.

The NABL is of a fundamentally different character than the CABL. Here the source of mixing is the shear from winds aloft, and not the destabilizing heat flux to the atmosphere from the bottom. In fact, the heat flux is normally from the atmosphere to the ground, and turbulence has to work against gravity, and therefore the NABL is also often called a stable boundary layer (SBL). Since winds are the sole source of mixing, their variability affects the NABL. Consequently, mixing in the NABL can be weak and very intermittent, and accompanied by internal wave motions. Continuous turbulence is often confined to the lower parts of the NABL, with intermittent turbulence characterizing the upper part. Strong stable stratification and gradient Richardson numbers close to critical are salient features. Because of the relative inefficiency of shear-induced mixing vis-à-vis convective mixing, properties often show strong gradients in the NABL, whereas the CABL tends to be more uniformly mixed, except perhaps close to the inversion. NABL depths are also smaller, several tens of meters to a few hundred meters at the most, whereas the CABL is typically one to a few kilometers deep. Very stable NABLs occur under light winds and strong surface cooling under clear skies. Unlike CABL, where simple similarity laws suffice and numerical models can be easily constructed, here the prevailing processes are complex, and difficult to characterize by any simple theory and to model: layered structures, intermittent turbulence, internal waves, and low level jets above the surface inversion.

The normal sequence of events in the ABL in the midlatitudes is as follows. Over the previous night, a low level inversion has formed close to the ground, typically 100–200 m high, and the atmospheric column has also cooled by radiation into space during the night. The heat flux is to the ground and on the order of a few tens of W m⁻². When solar heating commences in the morning, the layers close to the ground get heated, convective instability ensues, and the resulting turbulence begins to erode the inversion above. Gradually, over the course of the day, the CABL deepens and by mid-afternoon begins to approach an asymptotic value of 1–2 km. Maximum temperatures are reached about mid-afternoon. All this time, vigorous entrainment takes place at the top of the ABL. Once the solar heating ceases, turbulence in the bulk of the CABL collapses in a matter of a few tens of minutes and it is then confined to the vicinity of the ground. The depth of this turbulent mixed layer depends on the strength of the winds aloft, since it is the wind-induced shear that is the principal source of mixing. Throughout the night, the NABL is fairly constant in depth, although in many cases, there are some changes; the NABL may grow slowly through the night. Nocturnal inversion strength normally increases during the night and the stage is set for the diurnal cycle to start all over again in the morning. There are many other factors that influence the course of these events, such as the presence of clouds, which tend to decrease the cooling during the night, and the presence or absence of phase conversion. Wyngaard (1992) presents an excellent review of processes that occur in the CABL and NABL.

A similar diurnal cycle occurs in the oceanic mixed layer (OML) as well, although its character is somewhat different. Strong solar heating during the day gives rise to a shallow, diurnal mixed layer a few meters deep, especially during summer and when the winds are low. The turbulence in the bulk of the seasonal OML is extinguished. A strong temperature gradient builds up at the bottom from the strong heating of this shallow, mixed layer. But cessation of solar heating and nocturnal cooling begins to erode the "inversion" built up during the day and if the winds are not light, mixing penetrates to the depth of the seasonal thermocline and mixes the heat gained during the day by the shallow upper layers into the rest of the OML.

Seasonal modulation due to changing solar insolation is normally not as important as the predominant diurnal variations, as far as mixing in the ABL in midlatitudes is concerned. In polar regions, however, the seasonal changes are quite strong. In the Arctic, during the long polar night, the principal source of turbulence in the ABL is the wind. Arctic winds can be strong and sustained. The heat flux from leads and polynyas is usually not a major factor, except locally. Consequently, generally speaking, the ABL is quite shallow, 50–300 m deep (Andreas, 1996). In contrast, the ABL during an Arctic summer can be deeper due to the steady and incessant insolation. The much longer timescales of principal variability are the most distinguishing feature of the polar ABL, relative to the diurnally modulated ABL at lower latitudes.

A very important aspect of the ABL that distinguishes itself from its counterpart in the oceans is the presence of water in both vapor and condensed liquid form, and the associated phase conversions. Condensation releases the latent heat of vaporization and this internal source of heating is quite important to the fate of the ABL. Conversely, evaporation acts as a heat sink. Low level convective clouds are typically found in the upper part of the ABL and their flat bottoms often characterize the lower boundary of the capping inversion. Cloud-top cooling is an important source of energy for mixing in the ABL. Clouds also affect the heat balance at the air–sea and air–ground interfaces and are therefore important to the dynamics of both the ABL and the OML. Cloud-topped ABL (CTBL) is therefore quite complex and difficult to understand and model. Our lack of familiarity with the subject prevents us from dealing with the subject of phase conversions of water in the ABL and cloud dynamics, and its impact on the ABL, except cursorily. An excellent reference for this important topic is Houze (1993).

The ABL can also be grouped into that over land and that over sea. The ABL over the sea is fundamentally different. Because of the large heat capacity of the oceans, which constitute a strong source of heat and moisture, the temperature at the bottom, the sea surface temperature (SST), changes by a much smaller amount, and the diurnal cycle in the marine ABL (MABL) is therefore much different. The abundance of moisture in the MABL leads most often to cloud formation there and this has a large effect on the MABL structure and dynamics. Also under clear conditions the MABL is directly heated by the sun, leading to less stable conditions than in a NABL over land that suffers from strong IR cooling (Dabberdt et al., 1993). In mid to high latitudes, the strong seasonal cycle of the OML affects the MABL. Warm air advection over cooler waters leads to strongly stable MABL, whereas cold air masses transiting over warm waters give rise to strong convection and an unstable convectively mixed MABL.

The ABL over sea ice is affected by the insulating properties of sea-ice cover. The heat flux is usually small or negligible so that most often the ABL over ice is close to neutral stratification with winds being the major source of turbulent mixing. Consequently, the ABL is shallow, a few hundred meters in most cases. Advection of air masses from relatively warmer water on to ice causes suppression of turbulence in the ABL and strong inversions can develop over ice under these conditions.

Extensive measurements from aircraft, towers, and tethered balloons over the past two decades (Kaimal et al., 1976; Caughey, 1982; Lenschow, 1979; Lenschow et al., 1988; Caughey and Wyngaard, 1979) have increased our knowledge of the CABL considerably. For those quantities that are hard to observe and measure accurately, LES's (Moeng and Wyngaard, 1986, 1989; Moeng and Sullivan, 1994) have filled the gap (see Chapter 1). As a result, a very accurate picture of mixing in the CABL has emerged. As a result, it is also possible to postulate simple models of mixing in the ABL (Moeng and Sullivan, 1994). In contrast, the picture for the NABL and CTBL is not that complete. Also, most of our knowledge comes from measurements in a relatively horizontally homogeneous ABL. Only recently has increasing attention been given to orographic effects and horizontal inhomogeneities such as those across the land–sea boundary.

In the seventies and eighties, the team of James Deardorff and Glen Willis performed laboratory simulations of convection in a laboratory convection tank (Deardorff et al., 1969; Willis and Deardorff, 1974; Deardorff, 1980; see also Kantha, 1980b) that shed some light on the structure of the CABL, and the nature of entrainment processes near the capping inversion. The entrainment rate was measured and used to establish simple models (Deardorff, 1980). These experiments have been very useful, even though the Reynolds numbers that could be achieved were less than the atmospheric values (R_t is several orders of magnitude less, typically less than 10⁴). The main problem has been the finite aspect ratio effects, brought on by practical limits on the size of the tank (Deardorff and Willis, 1985; Kantha, 1980b). Nevertheless, the knowledge gained from laboratory simulations has been invaluable. Turbulent entrainment across a buoyancy interface (Kantha et al., 1977; Kantha, 1980a,b) has long been a subject of laboratory studies (see Fernando, 1991, for a recent summary; see also Nokes, 1988; Gregg, 1987), and has added to our understanding of mixing processes in the ABL. Needless to say, the various careful field observations made over the past two decades (see, for example, Sorbjan, 1989; Kaimal and Finnigan, 1994) has helped further our understanding of the ABL.

3.1.1 Ground-Based Remote Sensing

While in situ measurements from towers, balloons, kites, sondes, and aircraft have yielded a wealth of information on the ABL structure and dynamics over the past few decades, their obvious limitations w.r.t. spatial and temporal coverage have spurred the development of satellite-orbited and ground-based remote sensors. There has been rapid development in the latter over the past 25 years, and ground-based radars, sodars (SOund Detection And Ranging), and lidars (Light Detection And Ranging) have matured enough to be routinely employed to probe the ABL structure (Lenschow, 1986; Atlas, 1990; Wilczak et al., 1996) and add significantly to our knowledge of ABL processes, such as drainage flows, nocturnal jets, internal waves, land–sea breezes, flow convergences, and pollutant transport. We draw upon a compact review of the progress to date in Wilczak et al., (1996).

The principal advantage of most ground-based sensors is that not only can they monitor continuously the vertical profiles of properties in the ABL but they can also scan a large volume of the ABL continuously in time to provide horizontal distributions as well. A classic example is the Doppler radar, an operational network (NEXRAD) of which is now routinely used in the United States for assisting regional weather forecasts around the country.

Frequency-modulated (FM) continuous wave (CW) radars (frequencies of a few hundred MHz to a GHz) depend on backscattering of microwave energy from point scatterers in the ABL such as raindrops, snow particles, and insects, as well as from refractive index inhomogeneities. The Radio Acoustic Sounding System (RASS) that uses both acoustic and microwave energies enables monitoring of both wind and temperature profiles in the ABL. Sodars, on the other hand, depend principally on backscattering of acoustic energy by refractive index changes in the ABL, although they are sensitive to point scatterers as well. Time–height images of backscattered acoustic intensity have provided a wealth of information on the ABL structure, such as convective plumes, temperature inversions, and thermal fronts. Doppler techniques have enabled mean wind profiles to be measured in the lower ABL. Lidars employ backscattering by aerosol particles and hydrometeors of energy in the visible range of the electromagnetic spectrum to probe the ABL structure. Once again Doppler techniques enable the velocity to be profiled. Lidar ceilometers have been used to measure the height of the cloud base, and lidars have been useful for monitoring the vertical aerosol structure in the ABL and tracking pollutant plumes. Use of Raman backscatter enables water vapor profile measurements to be made.

All three techniques have advantages and limitations; for example, only radars can probe through clouds. Because of the presence of large turbulent fluctuations in temperature and humidity and particulates in the entrainment zone at the top, all three can be used to monitor the depth and evolution of the daytime CABL readily, but the absence of strong discontinuities makes it hard to use them for the NABL. Appropriate use of temporal averaging provides a better estimate of the ABL depth than a single sonde profile can, in spite of the resolution limitations (a few tens of meters typically). Mean wind profiles can be measured to within 1 m s⁻¹ from both Doppler radars and sodars. Adding an acoustic source with a wavelength half that of the radar enables the radar to sense Bragg backscattering from the acoustic wave and measure its velocity, which is a function of the ambient temperature. A 915-MHz profiler system (RASS) appears to be able to profile the temperature to within 1 K to a height of 500 m to 1 km (Wilczak et al., 1996). Most importantly, radars and sodars appear to hold the promise of measuring turbulence-related properties in the ABL. The techniques are well-suited to neutral and convective ABL (not NABL). Figure 3.1.1 shows a vertical profile of momentum flux measured from a dual-Doppler radar. If the radar or sodar wavelength lies within the Kolmogoroff inertial subrange, it is possible to deduce the dissipation rate of TKE. Thus, it is in principle possible to use ground-based remote sensors, to profile both the mean properties such as velocity, temperature and humidity, and turbulence properties (Gal-Chen et al., 1992) such as the fluxes of momentum, heat, and water vapor, and the dissipation rate in the daytime ABL. The accuracies involved, the limitations in resolution and range, and the difficulties are discussed in detail by Wilczak et al., (1996). He also provides examples of applications to studies of processes in the ABL such as sea breezes, convergence boundaries, drainage flows, nonprecipitating cloud systems, and pollutant dispersion.

Figure 3.1.1. Vertical profiles of momentum flux from dual-Doppler radar (squares), aircraft (triangles), and towers (circles)

(from Wilczak et al., 1996 with kind permission from Kluwer Academic Publishers). Copyright © 1996

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Data Processing and Analysis Methodology

D Perissin , in Comprehensive Remote Sensing, 2018

2.04.2 Radar Positioning

A radar is a device that transmits electromagnetic waves through an antenna, listening then for echoes reflected back by targets. Primitive radar systems were based on the transmission of energy pulses. The time Δt taken by the pulse to travel from the antenna to the target and back is used to estimate the distance R ₀ between them (see Fig. 1 ). Assuming that the signal is traveling in vacuum (at the speed of light c), and considering the two-way path, the distance can be calculated as

Fig. 1. Simplified sketch of a radar system. The antenna transmits a pulse; the pulse hits the target and travels back to the antenna. The radar measures the time between transmission and return of the pulse, and in this way it can retrieve the target range R.

(1) $R_0=\frac{c\mathrm{\Delta }t}{2}$

The capacity to distinguish between two close targets is called range resolution and it can be considered as a first approximation of the precision with which the distance radar-target is estimated. The range resolution of primitive radars was given by the length τ of the transmitted pulse. This was a clear limitation, considering that, for reaching the energy needed to detect a target in the presence of noise, a short pulse (good range resolution) requires high power.

The solution to this problem came with the discovery of continuous-wave (CW) radars and with the adoption of modulated signals like chirps. A chirp is a waveform whose frequency changes as a function of time, sweeping a given bandwidth B around the carrier frequency f _c . The frequency content of such \wave is used to increase the resolution of the system by filtering accordingly the received signal (using a matched filter, conceptually similar to a cross-correlation between the transmitted signal and the received one). We can simplify the discussion by assuming that the final waveform y(t) recorded by the radar after filtering the received signal can be written as follows

(2) $y\left(t\right)=e^{j2\pi f_c\mathrm{\Delta }t}\mathrm{sinc}\left[B\left(t-\mathrm{\Delta }t\right)\right]$

Or expressing it as a function of the range coordinate r and using the wavelength λ and speed of light c

(3) $y\left(r\right)=e^{j\frac{4\pi }{\lambda }{R}_0}\mathrm{sinc}\left[\frac{2B}{c}\left(r-R_0\right)\right]$

The above equations say that the recorded signal is made of two terms. The term that usually captures most of the attention is a cardinal sine (A cardinal sine is defined as $\mathrm{sinc}\left(x\right)=\frac{sin\left(\pi x\right)}{\pi x}$ ) (see Fig. 2 ), and it represents the real component of the signal. The cardinal sine is centered around the range R ₀ of the target of interest, and the width of its main lobe leads to the range resolution ρ _rg of the system

Fig. 2. The radar end-to-end system impulse response: the cardinal sine. The size of the main lobe of the cardinal sine corresponds to the resolution of the system and it is inversely proportional to the bandwidth B.

(4) ${\rho }_{rg}=\frac{c}{2B}$

The above equation shows that the resolution of the system is inversely proportional to the bandwidth B of the chirp (the higher the bandwidth, the better the resolution) and not directly related to its time duration. For systems, e.g., with 20   MHz bandwidth, the range resolution is about 7.5   m. This is the first element in our discussion that gives us (in first approximation) a quantification of the precision with which we can locate a target in range.

The left term in Eq. (3) is a complex exponential. For the sake of simplicity, we are neglecting other factors that are not useful for this discussion and we assume that its amplitude is equal to 1. The argument of the complex exponential is called phase ϕ, it corresponds to an angle and it is measured in radians

(5) $\varphi =\frac{4\pi }{\lambda }{R}_0$

The left term in Eq. (3) it is often neglected. In fact the phase ϕ is still a function of the range R ₀, but with a sensitivity equal to the wavelength λ, about three orders of magnitude smaller than the range resolution for common systems. The accuracy with which we can estimate the range R ₀ from the peak of the cardinal sine (a fraction of the resolution cell in the best case) is not enough to read the phase of the complex exponential: the phase changes too fast as a function of R ₀. Conversely, we cannot estimate R ₀ from the phase of the complex exponential, because the phase is wrapped and ambiguous. We could thus conclude that the left term of Eq. (3) is not useful to better locate the target in space. Instead, we will see in the rest of this article that it is exactly that this term is the key to improve the localization ability of radar systems.

Simple radar systems cannot tell much about the position of a target in the direction orthogonal to the range. Since the antenna is directional and characterized by an angular aperture θ _ant (the signal propagates within the main lobe of the antenna scattering pattern), if a target is detected, we can simply conclude that its azimuth location falls within the antenna cone (see Fig. 3 ). The angular aperture θ _ant is a function of wavelength λ and antenna's length L

Fig. 3. Azimuth resolution of a radar system. The radar can detect only targets falling within the antenna beam. The aperture of the beam is equal to the wavelength divided by the antenna length.

(6) ${\theta }_{\mathit{ant}}=\frac{\lambda }{L}$

And, as a consequence, we can quantify the range-dependent radar azimuth resolution

(7) ${\rho }_{az}=\frac{\lambda }{L}{R}_0$

It is evident to realize that, with such a system, it would be particularly difficult to generate radar images: the azimuth resolution degrades linearly with the range distance. A radar mounted on a satellite at 800   km distance from the ground, with 10   m antenna and 5   cm wavelength, would have 4   km azimuth resolution.

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50 years of lake ice research from active microwave remote sensing: Progress and prospects

Justin Murfitt , Claude R. Duguay , in Remote Sensing of Environment, 2021

3.4 Other applications of radar data

Active microwave data can also be used to monitor other characteristics of ice cover, including thickness and the presence of grounded ice. Section 3.4.1 will highlight the use of radar data for estimating ice thickness of floating and grounded ice regimes and Section 3.4.2 will highlight the use of radar data for classifying and monitoring grounded ice cover.

3.4.1 Retrieval of ice thickness

Ice thickness is a difficult parameter to extract using SAR data. In Section 3.2 it was discussed that increasing backscatter observed from lakes is most likely caused by changes in roughness at the ice-water interface. Recent research evaluated the relation between ice thickness and backscatter for a small lake located in Central Ontario, but found that when using a linear model, predictions were inaccurate above 40 cm (Murfitt et al., 2018a). This could be due to a steeper increase in roughness associated with early ice growth as demonstrated in other analysis of polarimetric decomposition experiments for Churchill, Manitoba (Gunn et al., 2018).

SAR data has been used to determine the thickness of ice cover in areas with grounded ice regimes. Jeffries et al. (1996) combined ERS-1 SAR data and numerical ice modelling to identify the relative depths of lakes near Barrow Alaska. Areas of these lakes that did not experience the decrease in backscatter were determined to be deeper than the maximum ice thickness obtained from a numerical model (Jeffries et al., 1996). This was further explored in both Subarctic (Churchill, Manitoba (Duguay and Lafleur, 2003)) and Arctic (Northwest Territories (Hirose et al., 2008)) Canada. Areas of bedfast ice were determined using SAR data and connected to a source of ground truth data to estimate ice thickness. Examples of ground truth data include lake depths determined from optical imagery (Duguay and Lafleur, 2003) and bathymetric sounding data (Hirose et al., 2008). However, there are limitations associated with these data. Lake depths determined from optical images are influenced by the limnology of the lakes (i.e. dissolved organic carbon and water colour) (Duguay and Lafleur, 2003) and the accuracy of bathymetric data can be impacted by the water level at the time of measurement (Hirose et al., 2008).

Other active microwave data has shown success in estimating ice thickness. The most promising method on local scales is the application of Frequency Modulated Continuous Wave (FMCW) radars. Originally applied using airborne platforms for monitoring river ice (Venier and Cross, 1975; Yankielun et al., 1993), FMCW was tested on laboratory freshwater ice with a maximum thickness of 24 cm at C-band wavelengths (Leconte et al., 2009). The experiment found a strong linear relationship using the difference between the frequencies of interface reflections (ice-water and ice-air) and ice thickness (R² = 0.99) (Leconte et al., 2009). This method was further explored using an X and Ku-band FMCW radar under field conditions for Malcolm Ramsey Lake near Churchill, Manitoba (Gunn et al., 2015b). This research showed that the transmission angle of the signal through ice and the slant range distance from the ice-surface to ice-bottom interface for X and Ku-band frequencies can be used to estimate thickness with R² values of 0.95 and 0.96, respectively (Gunn et al., 2015b). Alternatively, the use of satellite radar altimetry has proven useful in estimating Arctic sea ice thickness (Laxon et al., 2003; Tilling et al., 2018), however, it has seen limited application for lake ice thickness retrieval. Recently, drawing from the work of Gunn et al. (2015b) on the exploitation of waveforms obtained with ground-based FMCW radar, CryoSat-2 (Ku-band) waveforms were used to estimate ice thickness on Great Bear and Great Slave Lake in northern Canada between 2010 and 2014 (Beckers et al., 2017). Correlation coefficients for ice thickness were > 0.65 with root mean square error (RMSE) values of 0.12–0.41 m (Beckers et al., 2017). These errors are also influenced by Great Slave Lake in-situ data being interpolated for validation of Great Bear Lake estimations. These methods require further improvement for accurate and consistent monitoring of lake ice thickness to meet the goals put forth by GCOS (1–2 cm).

3.4.2 Bedfast ice identification

Section 3.1 discussed the special case of grounded ice covers regarding the decrease in backscatter noted for these lakes when maximum ice thickness is reached. Methods to determine the timing of these events/the amount of grounded ice cover has been an area of ongoing research in lake ice SAR remote sensing. Development of methods using SAR to actively determine bedfast ice regimes is critical for understanding water availability in northern communities during winter months (Jeffries et al., 1996; White et al., 2008). It can also help reduce the impact of water extraction from shallow lakes on northern fish ecology and has helped to identify important overwinter habitat for fish in Alaskan river systems (Brown et al., 2010; Hirose et al., 2008). Furthermore, the continued development and improvement of algorithms for identifying grounded ice cover is important as long term time series have shown that there is a decrease occurring in the fraction of grounded ice on the North Slope of Alaska with warming climates (Arp et al., 2012; Surdu et al., 2014). This decrease in grounded ice cover has important implications for permafrost thaw and the formation of taliks beneath these lakes (Ling and Zhang, 2003).

Methods for the classification and identification of lakes with grounded ice cover typically fall into two groups, The first, thresholding methods, has provided consistent classification results between grounded and floating ice covers. Kozlenko and Jeffries (2000) used the difference in backscatter between floating ice, grounded ice, and frozen tundra to identify a threshold capable of differentiating between the two types of ice cover. French et al. (2004) used a binary threshold classification and uncalibrated pixel values to determine if lakes were frozen to bed (all pixel values for the lake ≤ 78) or not (at least one pixel value for the lake >78). These methods were further developed in a study that analyzed changes in the area of floating and bedfast ice in Alaska over 25-years (Engram et al., 2018). Rather than use a single threshold, a variable threshold for each SAR scene in the time series was used, reporting a 93% accuracy in identifying grounded ice. This method avoided problems caused by differences in ice structure, issues with sensor degradation, and allowed for comparison between SAR products (Engram et al., 2018). Recently, Tsui et al. (2019) developed a threshold method using dynamic time warping (DTW), a measure of similarity between time series, to compare time series of backscatter from lake ice pixels to reference time series for grounded lake ice pixels. Pixels were classified as being grounded ice if the normalized similarity was under 0.69; overall classification results for floating and grounded pixels was 89% (Tsui et al., 2019).

Regression-based thresholds have also been developed taking the dependence of backscatter on incidence angle into account for identification of grounded ice regimes. Bartsch et al. (2017) used this relation to develop a threshold function that was applied to lakes within the Arctic Circle and identified the total area of grounded ice cover during April 2008 (assumed maximum ice thickness). Pointner et al. (2019) proposed a flood-fill step when using the incidence angle thresholding method. This step 'fills' all connected background (non-grounded ice) and grounded ice pixels allowing for unconnected lake pixels to be reclassed as floating ice and a less patchy classification result (Pointner et al., 2019). Additionally, automated techniques (i.e. the previously mentioned IRGS method and watershed segmentation) have also been used to classify bedfast and floating ice cover (Pointner et al., 2019; Surdu et al., 2014). However, a recent study demonstrated that a threshold method, obtaining an accuracy of 92.6%, can provide slight improvement over IRGS and further improvement over an unsupervised k-means method for identifying grounded versus floating ice regimes when applied to lakes in Alaska, Canada, and Russia (Duguay and Wang, 2019).

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